ReflectoRNN: AI-Enabled In-Operando Optical Reflectometry for Evolving Materials Using a Recurrent Neural Network

Abstract

Complex refractive indices of materials encode fundamental information on light-matter interactions and are critical for the design of advanced photonic and optoelectronic devices. In many emerging materials, refractive indices change under external stimuli such as temperature, electric fields, or strain. Tracking these changes in-operando is critical for active photonic and optoelectronic device design, but remains challenging. Conventional methods such as ellipsometry rely on labor-intensive model fitting and are often impractical for multilayer stacks or in-operando measurements. Optical reflectometry offers a simpler alternative but suffers from ambiguous extraction of refractive index from reflectance spectra and limited applicability under dynamic modulation. Here, we present ReflectoRNN, an artificial intelligence (AI)-powered reflectometry framework based on recurrent neural networks (RNN), for real-time extraction of complex refractive indices in evolving materials. ReflectoRNN extracts refractive indices from reflectance spectra under thermal, electrical, magnetic, or mechanical stimuli. It achieves a median Pearson’s correlation coefficient (PCC) of 0.998 and a relative accuracy score (RAS) of 0.968 on generated datasets. Validation experiments on MoS₂ and WS₂ across diverse substrates, including single-layer and multilayer dielectric stacks, and distributed Bragg reflectors (DBRs), demonstrate high accuracy and physical consistency, with temperature-dependent exciton resonance energy matching Bose–Einstein predictions. ReflectoRNN enables in-operando optical characterization of materials across complex photonic structures and offers a pathway toward automated, real-time monitoring and accelerated materials discovery.

Introduction

The complex refractive index (n + ik) is a fundamental property of materials, serving as an optical fingerprint of light-materials interactions. It carries essential information on interband and intraband transitions, excitonic effects, quantum confinement, and polaritonic resonances. Emerging materials such as semiconductors, two-dimensional (2D) crystals, and phase-change compounds exhibit evolving optical responses under thermal, electrical, magnetic, or mechanical modulation. − Capturing these modulation-dependent refractive indices in-operando is critical for enabling the design of next-generation photonic and optoelectronic technologies. −

Ellipsometry is widely used to extract refractive indices and is effective for simple structures with known substrates. However, it is often impractical for in-operando modulation experiments due to the sophistication in experimental setup and the extralong data acquisition time. , In addition, ellipsometry requires labor-intensive model fitting, becomes unreliable in multilayer stacks, and is incompatible with many device-relevant conditions. For instance, thermal modulation can introduce misalignment due to thermal expansion of the stage and optical components, while electrical modulation typically requires liquid or solid electrolytes that are difficult to integrate with angled-incidence ellipsometry setups. Optical reflectometry provides a simpler alternative. However, refractive index extraction is often ambiguous, as multiple material and structural configurations can yield similar reflectance spectra. , These challenges are further amplified in evolving materials with continuously varying refractive indices and in complex photonic substrates, such as multilayer dielectric stacks and distributed Bragg reflectors (DBRs), where strong interference effects make refractive index extraction particularly difficult. Together, these challenges underscore the urgent need for approaches capable of retrieving refractive indices of evolving materials directly from reflectance spectra in real time, without extensive human intervention, while preserving physical reliability.

Artificial intelligence (AI), especially deep learning, has recently emerged as a powerful tool for solving inverse optical problems. − By learning high-dimensional mappings from large datasets, neural networks can bypass explicit fitting and capture nonlinear relationships between optical spectra and material properties. − Previous studies have applied AI to ellipsometry and reflectometry, but these efforts remain limited to static conditions and cannot resolve gradual, modulation-dependent changes in optical properties. − No existing framework enables real-time retrieval of dynamic refractive indices under operando stimuli.

In this work, we present ReflectoRNN, an AI-powered, in-operando optical reflectometry framework for real-time, modulation-dependent extraction of complex refractive indices in evolving materials (Figure ). The framework consists of three main components. First, reflectance spectra with (R) and without (R ₀) the target material are collected using a microscope-based setup (Figure a). Second, the target material is modulated by thermal, electrical, magnetic, or mechanical stimuli, which dynamically alter its optical properties (Figure b). The resulting modulated reflectance spectra are then measured. Third, these reflectance spectra are input into ReflectoRNN, which outputs the complex refractive index of the target material at each modulation state (Figure c). To establish material-specific optical behavior, the model is initialized with baseline data comprising the target layer’s refractive index and the corresponding reflectance spectra of the entire material stack under a single modulation state. Our method achieves high performance on independent test sets, with a median Pearson’s correlation coefficient (PCC) of 0.998 and a relative accuracy score (RAS) of 0.968. We further validated ReflectoRNN using experimentally measured reflectance data from materials modulated by thermal stimuli, with complex multilayer and DBR substrates. The temperature-dependent exciton resonance energy predicted by our model closely matches the Bose–Einstein model, demonstrating the physical reliability of our predictions. ReflectoRNN offers a powerful tool for in-operando optical characterization of evolving materials within complex photonic structures, including DBRs, and has the potential to advance real-time device monitoring and automated materials discovery.

1.

Overview of the ReflectoRNN framework for in-operando optical characterization of evolving materials. (a) Schematic of the AI-enabled reflectometry setup. (b) Evolving material modulated by external stimuli, exhibiting dynamic optical properties. (c) Architecture of the ReflectoRNN model. R: reflectance spectra with the target material. R ₀: reflectance spectra without the target material. n: real part of refractive index. k: imaginary part of refractive index. RI encoder: refractive index encoder. RL encoder: reflectance encoder.

Results

Model Performance on Simulated Materials

The structure of the material stack used for simulation consists of three components: (1) a target evolving material modulated by external stimuli, (2) 0–3 bottom dielectric layers, or a 10-layer DBR, and (3) a thick substrate (Figure b). The prediction task is set up as follows. As input, the model first receives a baseline pair of complex refractive index spectra (n and k) and reflectance spectra under a single defined modulation state of the target material, which guides the learning of material-specific optical behavior. Both reflectance spectra with (R) and without (R ₀) the target material are provided. When external stimuli are applied, the optical properties of the target material evolve. The resulting modulated reflectance spectra of the material stack are sequentially input to the model, which predicts the corresponding complex refractive index comprising the real part (n) and imaginary part (k) of the target material at each modulation state (Figure c).

Reflectometry inversion is inherently nonunique, as different material configurations can produce similar reflectance spectra. In our model, this ambiguity is mitigated by incorporating additional constraints, including baseline conditioning, paired reflectance spectra with and without the target material, and sequential modulation information. These constraints reduce the solution space and guide the model toward stable and physically meaningful retrieval of refractive indices. As a result, the identity and layer thickness of the bottom materials can remain unknown to the model, highlighting its generalization capability.

The model architecture is based on a sequence-to-sequence recurrent neural network (RNN), named ReflectoRNN, as illustrated in Figure c. Pretrained convolutional neural network (CNN) autoencoders are used to extract latent representations of refractive index and reflectance spectra (Materials and Methods) with greatly reduced dimensionality. The RNN part in ReflectoRNN first uses a gated recurrent unit (GRU) encoder to capture material-specific optical behavior from the baseline input, using the refractive index as the hidden state and the reflectance spectra as input. A GRU decoder then models the gradual and sequential spectral changes caused by modulation and outputs the corresponding refractive index at each step. Further details on the implementation of ReflectoRNN can be found in the Materials and Methods section and Table S1.

AI models require large datasets for training. To create a scalable and generalizable dataset without relying on extensive experimental measurements, we developed a simulation pipeline informed by literature-reported modulations of evolving materials. ,,, In this approach, modulation-dependent target materials were simulated using oscillator models combined with nonlinear transformations, while the dielectric layers were modeled using the Sellmeier formula (Materials and Methods). We generated multilayer material stacks and, for each stack, computed modulation-dependent reflectance spectra using the transfer matrix method (Figure S1 and Materials and Methods). While this study focuses on the visible spectral range (400–800 nm), the approach is readily extendable to other wavelength regions. To ensure structural diversity and model generalizability, we generated 800,000 unique material stacks covering a broad range of optical scenarios. Each stack was paired with a target evolving material representing semiconductor- and dielectric-like stack configurations and exhibiting five modulation-dependent complex refractive index spectra, which are computed from perturbed oscillator parameters at each modulation state (Materials and Methods). The stacks included single-layer and multilayer dielectric configurations with 0–3 bottom layers of varying thicknesses (10–500 nm) and 10-layer DBRs, all placed on thick substrates (Materials and Methods). For each stack, one pair of refractive index and reflectance spectra was designated as the baseline, while the modulation-dependent reflectance spectra were used as inputs to ReflectoRNN. During training, the corresponding modulation-dependent refractive indices of the target material were used as the ground truth. In addition, independent validation and test sets, each containing 50,000 samples, were generated to evaluate model performance. Details of the training procedure are provided in the Materials and Methods section.

To measure the performance of ReflectoRNN, we used two metrics: Pearson’s correlation coefficient (PCC) and relative accuracy score (RAS), defined as

$$PCC=\frac{{\mathrm{\Sigma }}_i({ŷ}_i-\overline{\widehat{y}})(y_i-\mathrm{y̅})}{\sqrt{{\mathrm{\Sigma }}_i{({ŷ}_i-\overline{\widehat{y}})}^2}\sqrt{{\mathrm{\Sigma }}_i{(y_i-\mathrm{y̅})}^2}}$$ 1

$$RAS=1-\frac{\sqrt{\mathrm{MSE}(ŷ,y)}}{\mathrm{y̅}}$$ 2

where ${\hat{y}}_i$ and y _i denote the predicted and ground truth spectral values at wavelength index i, respectively; $\stackrel{-}{\hat{y}}$ and y̅ are the means of the predicted spectrum and ground truth spectra across all wavelengths. MSE­(ŷ,y) is the mean squared error between the predicted and ground truth spectra. PCC quantifies the similarity in spectral shape between the predicted and ground truth spectra, with a value of 1 indicating perfect agreement in overall trend and shape. RAS measures the relative difference in the absolute values of the predicted spectra compared to the ground truth, providing a normalized measure of magnitude accuracy. An RAS value close to 1 indicates that the predicted spectra closely match the absolute values of the ground truth (Materials and Methods).

Figure a shows the PCC and RAS for the train, validation, and test sets. All three sets achieve high median PCC values above 0.998, indicating excellent agreement in spectral shape between predictions and ground truth. The RAS values for the training, validation, and test sets are 0.976, 0.968, and 0.968, respectively. Representative examples in Figure S2 further illustrate that the predicted n and k closely match the ground truth across all sets. These results demonstrate the high accuracy and robustness of ReflectoRNN’s predictions.

2.

Performance of ReflectoRNN on simulated datasets. (a) Violin plots of PCC and RAS for the train, validation, and test sets, with inset box plots showing the 25th, 50th, and 75th percentiles. (b) Violin plots of PCC and RAS for different substrate complexities: single, multiple dielectric layers, and DBR substrates, with inset box plots showing the 25th, 50th, and 75th percentiles. (c) Illustration of the three material stack configurations, with increasing optical complexity from left to right. (d) Representative input reflectance spectra and predicted refractive index for simulated material stacks with different substrates. The top panel shows reflectance spectra with (R, purple) and without (R ₀, brown) the target material. The bottom panel shows predicted (dashed lines) and ground truth (solid lines) refractive index spectra, including both real (n, red) and imaginary (k, cyan) parts, for different modulation states. Baseline refractive indices are shown as the darkest solid lines.

Since ReflectoRNN is designed for generalizability, the identity and layer thicknesses of the underlying materials are unknown to the model. We next evaluated how the complexity of the dielectric layer structure affects its performance by examining predictions across different substrate complexities in the test set. Three material stack configurations with increasing optical complexity are considered (Figure b): (1) Single dielectric layer, a target evolving material on one dielectric layer over a thick substrate; (2) Multiple dielectric layers, a target evolving material on three dielectric layers over a thick substrate; (3) DBR substrate, 10-layer DBRs designed for near perfect reflection at 600 nm (Materials and Methods). Figure b shows violin plots of PCC and RAS for the three configurations. All achieve median PCC values above 0.998, indicating excellent agreement in spectral shape. The PCC distribution becomes progressively narrower from the single to the multiple to the DBR configuration. The median RAS values are 0.964, 0.967, and 0.975 for the single, multiple, and DBR configurations, respectively, with distributions showing the same trend. Interestingly, the DBR configuration yields the highest accuracy. This may be because DBRs enhance reflectance features, providing richer spectral variations for ReflectoRNN to capture modulation-induced changes in the target layer. Representative input reflectance spectra and corresponding predictions are shown in Figure d, and additional examples are provided in Figure S3. For the single dielectric configuration, small deviations in both n and k are observed at certain modulation states. Predictions improve for the multiple dielectric configuration, while the DBR configuration achieves the closest match to the ground truth across all modulation states.

Model Performance on Experiment Materials

Having established that ReflectoRNN performs well on simulated materials, we next validated its performance on experimentally measured materials under real-time thermal modulation. These experimental materials were not included in the training data and therefore provide an independent test of model generalization. Temperature modulation was chosen because it commonly arises during practical device operation and thermal tuning, is experimentally accessible, and induces continuous and well-understood refractive index changes through temperature-dependent bandgap shifts and phonon–exciton coupling. The resulting refractive index evolution can be independently verified by ellipsometry, enabling quantitative benchmarking of ReflectoRNN’s predictions (Materials and Methods).

We prepared five representative material stacks based on MoS₂ and WS₂, varying layer thickness and substrate complexity (single, multiple, and DBR substrates, Figure ). MoS₂ and WS₂ were selected as representative 2D semiconductors with strong excitonic features and well-established use in photonic and optoelectronic devices. The chosen thicknesses range from few-layers to tens-of-nanometers, reflecting practical device geometries. The substrates include commonly used dielectric platforms (SiO₂/Si and Al₂O₃/SiO₂/Si) and a 10-layer DBR, which serves as a representative high-interference photonic environment relevant to optical cavities and resonant sensors. We chose the temperature range of 20–140 °C, which corresponds to practical operating and thermal-stress conditions in photonic and optoelectronic systems.

3.

Performance of ReflectoRNN on experimentally measured datasets. Left panels: Reflectance spectra with (R) and without (R ₀) the target material. Right panels: Predicted (dashed lines) and ground truth (solid lines) refractive index spectra, showing n and k. (a) 9 nm MoS₂ on 76 nm SiO₂/Si, (b) 25 nm MoS₂ on 287 nm SiO₂/Si, (c) 62 nm WS₂ on 22 nm Al₂O₃/76 nm SiO₂/Si, (d) 51 nm MoS₂ on 22 nm Al₂O₃/76 nm SiO₂/Si, (e) 47 nm WS₂ on a 10-layer DBR (62 nm TiO₂/ 96 nm SiO₂) on Si. Insets: optical images of the materials, scale bar, 30 μm. (f) Violin plots of RAS (left) and PCC (right) for simulated test data, with experimental results overlaid as stars.

Figure a–e show measured temperature-dependent reflectance spectra (left) and the predicted complex refractive index spectra (right) for various samples. They are Figure a is 9 nm MoS₂ on 76 nm SiO₂/Si; Figure b is 25 nm MoS₂ on 287 nm SiO₂/Si; Figure c is 62 nm WS₂ on 22 nm Al₂O₃/76 nm SiO₂/Si; Figure d is 51 nm MoS₂ on 22 nm Al₂O₃/76 nm SiO₂/Si; Figure e is 47 nm WS₂ on a 10-layer DBR (62 nm TiO₂/96 nm SiO₂) on Si. Optical microscopy images of each target material are shown as insets. Temperature-dependent reflectance spectra were acquired using a custom-built heating stage integrated with microscope-based reflectometry, while temperature-dependent refractive indices were measured by ellipsometry (Figure S4, Materials and Methods). The reflectance spectra (R) and refractive indices at room temperature (20 °C) served as the baseline. In the left panels of Figure a–e, the baseline R is shown as the darkest purple solid line, and the substrate reflectance R ₀ as the brown line. In the right panels, the baseline refractive index spectra are shown as the darkest solid lines for n (red) and k (cyan). The sample temperature was subsequently increased stepwise to 50 °C, 80 °C, 110 °C, and 140 °C, and R and R ₀ were measured at each step. ReflectoRNN predictions (dashed lines) are compared with ellipsometry-derived ground truth refractive indices (solid lines) in the right panels of Figure a–e. As the temperature increased, distinct spectral shifts and intensity variations were observed, consistent with thermally induced bandgap narrowing and excitonic redshift.

ReflectoRNN was then applied to these temperature-dependent reflectance spectra to retrieve the refractive indices of the target layers at each modulation state. The predicted spectra (dashed lines) are compared with ground truth values obtained from ellipsometry (solid lines) in the right panels of Figure a–e. Across all material configurations, ranging from single-layer to multilayer and DBR substrates, ReflectoRNN successfully reproduced both the overall spectral trends and fine features of the refractive index evolution. Quantitatively, the model achieved high RAS and PCC: 9 nm MoS₂ on 76 nm SiO₂/Si (RAS = 0.976, PCC = 0.998), 25 nm MoS₂ on 287 nm SiO2/Si (RAS = 0.957, PCC = 0.996), 62 nm WS₂ on 22 nm Al₂O₃/76 nm SiO₂/Si (RAS = 0.945, PCC = 0.990), 51 nm MoS₂ on 22 nm Al₂O₃/76 nm SiO2/Si (RAS = 0.968, PCC = 0.996), and 47 nm WS₂ on a 10-layer DBR (RAS = 0.931, PCC = 0.986).

To compare ReflectoRNN’s performance on experimental materials with that on the simulated test dataset, we plotted the RAS and PCC distributions for all test data, with experimental results overlaid as individual points (Figure f). Each dot represents an experimentally measured material stack. The experimental data points fall mainly within the high-density regions of the violin plots, indicating that ReflectoRNN achieves accuracy on real materials comparable to that obtained in simulation. The few experimental points with slightly lower PCC and RAS correspond to samples with the highest optical complexity, particularly DBR and multilayer dielectric substrates, where strong interference effects make refractive index extraction more challenging. Notably, even in these cases, the predictions remain within the overall test distribution, demonstrating robust generalization under realistic experimental conditions and validating the physical reliability of ReflectoRNN. We also compared ReflectoRNN with an artificial neural network (ANN) and conventional transfer matrix fitting (Figure S5, Materials and Methods). ReflectoRNN consistently outperforms the ANN (median test RAS of 0.968 for ReflectoRNN, Figure S5a, compared to 0.814 for the ANN, Figure S5b) and achieves closer agreement with experimental refractive index spectra than conventional fitting (Figure S5c and Figure S 5d), highlighting the advantage of incorporating sequential modulation within a learning-based framework.

Overall, the predictions show excellent agreement with ground truth across all temperature states and structural configurations. The results confirm that ReflectoRNN generalizes effectively to real materials and can accurately extract dynamic refractive indices even in complex multilayer and DBR photonic environments. The consistent spectral agreement across MoS₂ and WS₂ stacks demonstrates the model’s robustness and physical reliability. Validation on representative substrate and cavity structures used in optical cavities, resonant sensors, and integrated photonics further demonstrates the practical utility of ReflectoRNN for in-operando optical characterization of evolving materials.

Optimization Strategies for ReflectoRNN

We achieved the high performance and robustness of ReflectoRNN on both simulated and experimental datasets through careful architectural design and systematic configuration testing. One key AI model innovation was the design and pretraining of autoencoders for refractive index and reflectance spectra (Figure a) to reduce dimensionality and extract high-level spectral features. Each autoencoder comprises an encoder that compresses the input spectra into a latent vector and a decoder that reconstructs the original spectra from this representation. We developed CNN autoencoders for both refractive index and reflectance spectra, and integrated their encoder modules as front-end feature extractors in ReflectoRNN (Materials and Methods). The reconstruction RAS values for both refractive index and reflectance spectra reached medians of 0.999 across train, validation, and test sets with small deviation (Figure b), indicating near-complete information preservation in the latent space. Consistently, the PCC values also exceeded 0.999 (Figure S6), confirming the reconstruction accuracy. Representative examples of reconstructed refractive index and reflectance spectra are shown in Figure S7, all exhibiting excellent agreement with the original spectra.

4.

Model improvement strategies for ReflectoRNN. (a) Autoencoder architecture for refractive index (n, k) and reflectance (R, R ₀) spectra, inputting original spectra (left) and outputting reconstructed spectra (right). (b) Reconstruction RAS for refractive index and reflectance autoencoders across train, validation, and test sets. (c) Top: RAS of refractive index predicted by RNN without an autoencoder and with two different autoencoder types. Bottom: RAS using a CNN autoencoder with varying latent space dimensions (64–448). AE: autoencoder. (d) RAS and PCC of refractive index predictions under different RNN configurations, including architecture type (Transformer, LSTM, GRU, decoder only), number of layers, and dropout rate. (e) Training and validation loss (left axis) and RAS (right axis) versus training epochs in training of ReflectoRNN.

We then evaluated the downstream RNN prediction performance (Figure c, top). Without an autoencoder (w/o AE), the validation median RAS is 0.934. Incorporating a fully connected autoencoder (AE 1) improved the median RAS to 0.957, while our CNN autoencoder (AE 2) further increased it to 0.968, with PCC values showing the same trend (Figure S8). Details of the model structures are in Table S2. We also examined the effect of latent space dimensionality (Figure c, bottom). RAS values improved from 0.810 (64 dimensions) to 0.940 (128 dimensions), 0.960 (256 dimensions), and 0.968 (448 dimensions). While increasing the latent space generally improved prediction accuracy, excessively large latent spaces (800 dimensions) without proper feature compression (w/o AE) led to reduced performance (RAS 0.934), likely due to the inclusion of redundant or noisy features.

Then, we systematically compared different RNN configurations (GRU, LSTM, and Transformer) to identify the optimal architecture (Figure d, Table S3). Among the sequence structures tested, the GRU achieved the best performance (validation RAS 0.955, PCC 0.995), outperforming LSTM and transformer variants. This advantage arises from the GRU’s simpler structure, which allows it to effectively capture the essential temporal dependencies in modulation-dependent spectral data while reducing the risk of overfitting. As a result, GRUs are particularly well-suited for relatively short and structured sequences such as reflectance spectra at several modulation conditions, where long-range dependencies are limited and added model complexity often introduces noise rather than improving accuracy.

To further assess architectural components, we examined the importance of the GRU encoder, network depth, and dropout regularization. Removing the GRU encoder and leaving only a GRU decoder without guidance from baseline material-specific optical behavior led to a significant performance drop (validation RAS 0.820, PCC 0.935), confirming the importance of encoding baseline information. Increasing the number of recurrent layers from 3 to 5 improved accuracy, with 5 layers achieving the highest validation RAS (0.958) and PCC (0.996). Increasing to 7 layers improved training metrics but did not further enhance validation performance, because the added model capacity increased optimization complexity and overfitting without providing additional information for the relatively short and smoothly varying modulation sequences. Dropout tuning revealed that a moderate value (0.1) provided the best balance between regularization and information retention, yielding the highest overall validation PCC (0.998) and RAS (0.968). The 0 dropout setting gave a slightly higher training RAS (0.978) but reduced validation RAS to 0.958, indicating overfitting. With the chosen configuration, ReflectoRNN achieved its best overall performance.

We also analyzed the training dynamics of ReflectoRNN (Figure e and Figure S9). The training and validation loss decreased rapidly within the first 50 epochs and stabilized. Training was continued to 200 epochs to ensure full convergence. The validation RAS remained consistently high throughout, indicating strong convergence and minimal overfitting.

These systematic design choices, including integrating CNN autoencoders, optimizing latent space size, selecting GRU-based architectures, and fine-tuning layer depth and dropout, collectively contributed to the high robustness and accuracy of ReflectoRNN across diverse materials and modulation conditions.

Further Evaluation of ReflectoRNN’s Capability

Having established ReflectoRNN’s optimized accuracy and robustness under both simulated and experimental conditions, we next investigated its ability to generalize across different scenarios and its effectiveness in preserving physical information (Figure ). We evaluated three aspects of model performance: predictive stability under increasing modulation, resilience to incomplete datasets, and accuracy in capturing excitonic features.

5.

Further evaluation of ReflectoRNN capability. (a) Predicted (dashed) and ground truth (solid) refractive indices (n, k) across ten sequential modulation states (1–9 are modulation states, lighter to darker shading), with baseline shown as the darkest curve (no number). (b) Testing RAS across modulation states. Red line: 4 modulation states used in training. Light gray shading indicates a slight decrease in RAS beyond the training range. Dark gray shading highlights larger decreases at higher modulation states. (c–f) Testing RAS for predictions of real and imaginary parts (n in red, k in cyan) with incomplete datasets when intermediate modulation states are skipped. (g–h) Predicted (red) and experimental (blue) exciton peak energies as a function of temperature for the A exciton (g) and B exciton of MoS₂ (h). Solid Line: Bose–Einstein model fit with model predicted exciton peak energies.

ReflectoRNN was trained on n and k across five sequential modulations, including one baseline state. To test its generalizability, we evaluated the model with ten sequential modulation states (Figure a). The nine modulation states were numbered 1–9, with the baseline shown as the darkest curve without a number. The corresponding RAS values across modulation states are plotted in Figure b. For the first four states (matching the training setup), the testing RAS remained consistently above 0.957, showing a slight decline as modulation progressed, due to increasing distance from the baseline and gradual memory loss. At the fifth and sixth states, beyond the training distribution, the RAS decreased slightly to 0.92, indicating good generalization to unseen modulation levels (light gray). For states 7–9, the RAS dropped further, reflecting the increasing deviation from the training distribution (dark gray). Overall, ReflectoRNN generalizes well beyond its trained four modulation states, maintaining high accuracy up to six states, with performance only declining at more distant modulation levels.

In practical experimental settings, intermediate modulation states may be uneven and missing due to measurement limitations. To simulate this scenario, we removed intermediate modulation steps and evaluated ReflectoRNN’s ability to recover the refractive index spectra (Figure c–f). RAS values for the real (n, red) and imaginary (k, cyan) between prediction and ground truth are shown under four conditions (Materials and Methods): no skipped modulations (complete input), skipping the first and third states, skipping the first and second states, and skipping the first three states. Overall, k is consistently predicted with slightly lower accuracy than n, which may be due to the weaker sensitivity of reflectance spectra to absorption-related features. In the complete case (Figure c), the median RAS of n and k gradually decreased from 0.991 to 0.981 and 0.980 to 0.957, respectively, as modulation increased, with distributions becoming slightly broader. When the first and third states were skipped (Figure d), the model maintained high accuracy, with RAS above 0.983 for n and 0.960 for k, demonstrating its ability to interpolate optical responses across missing states. Skipping the first and second states (Figure e) led to larger performance drops (median RAS 0.978 for n and 0.950 for k at fourth modulation), likely due to loss of critical early modulation information. When the first three states were skipped (Figure f), accuracy decreased further (median RAS 0.964 for n and 0.919 for k), indicating significant information loss. PCC shows the same trends as RAS across all skip conditions (Figure S10). This robustness to incomplete datasets highlights ReflectoRNN’s capability to reconstruct refractive indices under realistic experimental conditions where measurements may be constrained by time, equipment stability, or sample degradation.

In addition to incomplete intermediate modulation states, the accuracy of ReflectoRNN may also depend on the quality of the baseline input, which establishes material-specific optical behavior. In practical settings, this baseline refractive index and reflectance may be subject to measurement uncertainty. The model is expected to be relatively insensitive to small baseline deviations, as it primarily relies on the relative evolution of spectra across modulation states. However, larger baseline inaccuracies may degrade prediction performance. In many experimental scenarios, the baseline can be obtained or reasonably approximated. For example, when the target material is not embedded in complex device structures, the baseline refractive index can be directly measured using ellipsometry. When the material is integrated into complex device architectures where ellipsometry is not readily applicable, the baseline refractive index can instead be estimated from reflectance data using data-driven approaches such as our previously established method. Building on such approaches, downstream integration with ReflectoRNN may enable self-calibrating frameworks in which the baseline is jointly inferred from reflectance data, further improving the applicability of the method.

While the training data are generated with oscillator-based (Tauc-Lorentz) representations and transfer matrix simulations, simulation data may not fully capture the complexities of real materials, such as defects, surface contamination, and measurement noise. To address this, we introduced randomized multiplicative perturbations and structural diversity during training to improve robustness to experimental variability (Figure S11, Materials and Methods). The strong performance of the model on experimental datasets suggests that the model trained with simulation data captures the dominant physical relationships governing optical reflectance.

To further evaluate robustness under realistic experimental noise, we introduced structural variations, including surface roughness and defect layers, into the simulated test set (Figure S12). As shown in Figure S12a, ReflectoRNN maintains consistently high PCC and RAS values across ideal, roughness, and defect conditions, with median RAS values of 0.968, 0.966, and 0.967, respectively. This indicates that the model is robust to interface imperfections and structural nonidealities commonly encountered in experimental measurements. In addition, we evaluated performance across a range of target layer thicknesses (Figure S12b) and observed stable PCC and RAS distributions, demonstrating that the performance of ReflectoRNN is not affected by thickness variations.

Although this study focuses on transition-metal dichalcogenides (TMDs), the framework is not limited to these materials. The training data are generated using Tauc-Lorentz oscillator models, which describe a broad class of materials, including amorphous semiconductors and dielectric materials with interband transitions. The successful application to TMDs suggests that ReflectoRNN can generalize to materials with similar optical characteristics. More broadly, the framework can be extended to other material families by incorporating appropriate physical models into the simulation pipeline. Retraining or fine-tuning may be required when applying the model to materials with fundamentally different optical responses, such as metals or heavily doped semiconductors, which are better described by Drude-type oscillator models. By augmenting the training dataset with additional oscillator models and parameter ranges, ReflectoRNN can be adapted to new material systems. This highlights that the model does not rely on empirical fitting alone, but can be systematically generalized through physics-informed data generation.

These analyses demonstrate that ReflectoRNN can generalize robustly under extended modulation conditions, maintain reliable accuracy with incomplete datasets, and remain stable under structural variations. The framework is further extendable to a broad range of material systems, supporting its applicability in realistic experimental environments.

Physical Consistency and Validation of ReflectoRNN

Beyond spectral fitting, predicting physical signatures is essential for material characterization. One such physical signature is excitonic resonances, which can be obtained from refractive index spectra. We extracted exciton peak positions from predicted and experimental spectra and compared their temperature evolution. Figures g and h show the temperature dependence of the A and B excitons in MoS₂, respectively, with the A excitons of WS₂ presented in Figure S13. The exciton energies extracted from the predicted excitonic resonances align closely with experimental measurements, particularly for the A exciton (Materials and Methods). The A exciton was fitted using the Bose–Einstein model (solid line), which describes the temperature-dependent redshift of exciton resonance energies arising from electron–phonon interactions. The model is parametrized by the exciton resonance energy at 0 K, electron–phonon coupling strength, and a characteristic temperature. The temperature dependence of the exciton resonance energy is given by

$$E_g(T)=E_g(0)-\frac{2a_B}{e^{{\mathrm{\Theta }}_B/T}-1}$$ 6

where E _g (T) is the exciton resonance energy at temperature T, E _g (0) is the exciton resonance energy at 0 K, a _B is the electron–phonon coupling strength in meV, and Θ _B is the Bose–Einstein characteristic temperature in K. Fitting was performed using nonlinear least-squares optimization.

The fit yields an electron–phonon coupling strength of 30 meV, a characteristic temperature of 250 K, and an exciton resonance energy at 0 K of 1.89 eV, consistent with literature values. Similarly, the B exciton (Figure h) shows strong agreement between predictions and experiments. These results confirm that ReflectoRNN not only reproduces spectra with high numerical accuracy but also preserves the underlying physics of excitonic transitions.

Kramers–Kronig (KK) relations impose causality constraints linking the real (n) and imaginary (k) parts of the refractive index. To further assess physical validity, we performed a post hoc KK consistency analysis (Figure S14). Specifically, we reconstructed k from the predicted n using KK relations and evaluated the agreement between predicted and KK-reconstructed spectra. As shown in Figure S14a, high median PCC (0.99) and low reconstruction error are observed consistently across the train, validation, and test sets. Representative simulated and experimental examples (Figure S14b and c) further demonstrate close agreement between predicted and KK-reconstructed spectra. Notably, KK consistency is not explicitly enforced in the current implementation of ReflectoRNN. Despite this, the model produces KK-consistent results. This behavior arises from both the training data and model design. The refractive index decoder is trained using oscillator-based data, which are inherently KK-consistent, and ReflectoRNN is trained on reflectance spectra generated via the transfer matrix method, ensuring physically consistent input-output relationships. In addition, n and k are not predicted independently but are jointly encoded and reconstructed through a shared latent representation, preserving their intrinsic coupling.

To further understand how ReflectoRNN captures physically meaningful information, we performed an interpretability analysis with global correlation and perturbation-based feature importance methods (Materials and Methods, Figure S15). The global correlation matrix (Figure S15a) shows strong diagonal components, indicating that reflectance at a given wavelength is strongly associated with the refractive index at the same wavelength. In addition, off-diagonal correlations are observed, reflecting the influence of neighboring wavelengths due to interference effects. Figure S15b shows a representative local feature importance map, with the corresponding reflectance spectra and predicted refractive index shown in Figure S15c and d. Larger values indicate that perturbations at those wavelength regions of the reflectance spectra lead to greater changes in the predicted refractive index. A dominant sensitivity region is observed near ∼ 460 nm, together with a broader secondary sensitivity region spanning approximately 580–650 nm. These high-sensitivity wavelength bands, selected from the perturbation-based feature importance map (top 10% sensitivity), are highlighted in Figure S15c and d. Notably, sensitivity arises from prominent spectral features, indicating that the model captures physically meaningful information for prediction. This behavior indicates that ReflectoRNN extracts physically relevant information from the spectra and leverages meaningful spectral features for prediction, rather than relying on arbitrary correlations. These results provide additional evidence that the model’s predictions are grounded in the underlying physics.

These analyses demonstrate that ReflectoRNN can capture physical parameters such as excitonic transitions while preserving KK and physical consistency, underscoring its utility for material science applications.

Conclusion

In summary, we developed ReflectoRNN, an AI-powered reflectometry framework for in-operando extraction of complex refractive indices in evolving materials under external modulation. By combining CNN autoencoders with a GRU-based sequence-to-sequence architecture, ReflectoRNN learns material-specific optical behavior and predicts modulation-dependent refractive indices from reflectance spectra. Through large-scale simulations, we established ReflectoRNN’s robustness and accuracy on single-layer, multilayer, and DBR substrates, achieving median PCC and RAS values of 0.998 and 0.968, respectively, across independent test sets.

We further validated ReflectoRNN on experimentally measured data from thermally modulated materials on single-layer, multilayer, and DBR substrates. The model demonstrated reliable accuracy under diverse experimental conditions, including extended modulation sequences and incomplete datasets. Importantly, ReflectoRNN not only reproduced refractive index spectra with high accuracy but also preserved key physical signatures, such as excitonic energies consistent with the Bose–Einstein model.

ReflectoRNN provides a powerful tool for real-time optical characterization of evolving materials within complex photonic environments. Its ability to generalize beyond training conditions and maintain physical interpretability broadly applies to materials discovery, device monitoring, and AI-driven experimental automation.

Materials and Methods

Dataset Preparation

To develop a scalable and generalizable training dataset for ReflectoRNN without requiring extensive experimental measurements, we designed a simulation pipeline based on literature-reported refractive index modulations of commonly studied evolving materials. ,,, The complex refractive index of each material was modeled using Tauc-Lorentz oscillators, defined as follows:

$${\epsilon }_2(E)=\{\begin{array}{rr}\frac{A{E}_{0}C{(E-E_g)}^2}{E[{(E^2-E_0^2)}^2+C^2{E}^2},& E>E_g\\ 0,& E\le E_g\end{array}$$ 3

Depending on the material complexity, we employed 2 to 6 oscillators, each defined by amplitude (A), broadening (C), bandgap (E _g ), and resonant frequency constant (E ₀). To simulate modulations of materials, we introduced a controlled variation in the oscillator parameters across multiple modulation states. For each randomly generated material, we applied parametric perturbations using quadratic scaling across modulation states, enabling smooth and continuous spectral changes that emulate realistic modulation responses.

To simulate the complex structure of the material stacks, we generated multilayer optical stacks with evolving materials and dielectric layers. Each stack consists of: target evolving material, 0 to 3 optional bottom dielectric layers or 10 layers of DBR layers, and a thick substrate. The refractive indices of dielectric layers are generated using the Sellmeier formula, described in our previous work. Dielectric layer thicknesses were uniformly sampled between 10 and 500 nm to align with practical constraints.

To ensure structural diversity and generalizability, we generated 800,000 unique stack configurations, each paired with a target evolving material with modulation-dependent refractive index. We also introduced randomized multiplicative perturbations to the reflectance spectra by applying a uniform scaling factor in the range of 0.95–1.05, simulating measurement variability such as intensity fluctuations and calibration uncertainty.

Reflection Simulations

We simulated the normal-incidence reflectance spectra using the transfer matrix method for each evolving material and corresponding multilayer stack. The transfer matrix accounts for multiple reflections, interference effects, and the wavelength-dependent complex refractive indices of each layer in the stack. The reflectance spectrum was computed over the wavelength range of 400–800 nm with 1 nm resolution. For each multilayer stack, the reflectance is calculated with and without the evolving material. For each modulation state, the reflectance is calculated with the corresponding modulation-dependent refractive index of the evolving material. This process was repeated across all modulation states and all generated stacks.

Autoencoder Structure and Training Procedure

To reduce the dimensionality of the reflectance and refractive index spectra and extract high-level representations, we employed two CNN autoencoders (refractive index autoencoder and reflectance autoencoder). Each autoencoder consists of two main components: an encoder that compresses the input spectra into a latent vector, and a decoder that reconstructs the original input from this representation. The encoder modules were used as front-end feature extractors in the ReflectoRNN framework.

For the refractive index spectra, a 1D CNN refractive index encoder was implemented. The input tensor has the shape (N, 2, 400), where N is the number of samples, 2 channels correspond to the real (n) and imaginary (k), and 400 represents the wavelengths. The encoder consists of six convolutional layers with progressively decreasing dimension using strides and padding (Table S4), followed by a fully connected layer that projects the extracted features into a latent vector of dimension 448. Batch normalization layers are applied after the early convolutional layers to improve training stability.

For the reflectance spectra, a reflectance encoder was designed with dual input pathways: one for the reflectance spectrum of the material structure with the evolving material, and the other for the reflectance spectrum of reference structure without the evolving material. These two pathways are encoded separately using 1D convolutional layers and then concatenated to form a unified latent representation.

The decoders mirror the encoder in structure, consisting of a fully connected layer followed by transposed 1D convolutional layers that upsample the latent vector back to the original spectral dimension. The output tensor is reshaped to (N, 2, 400) to reconstruct the original n and k spectra.

Both the refractive index autoencoder and reflectance autoencoder were trained using mean squared error (MSE) as the reconstruction loss. Optimization was performed using the Adam optimizer. To assess reconstruction quality, we computed the PCC and RAS between the input and reconstructed spectra. The trained models achieved PCC and RAS scores exceeding 0.99, confirming the compression and reconstruction performance. The trained encoders were then used as feature extractors in the ReflectoRNN.

ReflectoRNN Structure and Training Procedure

To predict the modulation-dependent refractive index from reflectance, we implemented an RNN based on a sequence-to-sequence (Seq2Seq) approach. The ReflectoRNN consists of five parts: an RNN encoder, an RNN decoder, a pretrained refractive index encoder, a reflectance encoder, and a refractive index decoder, as described above (Figure c). The RNN encoder and decoder are implemented using five-layer gated recurrent units (GRUs) with a hidden size of 448 and dropout regularization. The input of the RNN encoder is the latent representations of the baseline refractive index and reflectance spectra, extracted via the pretrained CNN autoencoders. The RNN encoder processes the baseline reflectance and encodes the material-specific optical response into its hidden state. The RNN decoder then uses the modulated reflectance as input to generate the predicted evolution of the complex refractive index under external modulation.

The model was trained using the MSE loss, optimized with the Adam optimizer (learning rate 10^–3). A learning rate scheduler with exponential decay (γ = 0.98) was used to improve convergence. Pretrained autoencoder components were frozen during initial training. The total number of trainable parameters in the final model exceeds 10 million. Training was performed for 200 epochs, with a batch size of 512.

Baseline and Conventional Methods

To benchmark ReflectoRNN against representative conventional approaches, we implemented two comparison methods: a feedforward ANN baseline and a conventional transfer matrix fitting approach.

For the ANN baseline, we constructed a multilayer feedforward neural network with fully connected layers, ReLU activations, and dropout regularization. To enable a fair comparison, the ANN used the same input information as ReflectoRNN, including the baseline refractive index, baseline reflectance, and modulated reflectance spectra as input, and directly predicted the modulation-dependent refractive index spectra (n and k) as output. Unlike ReflectoRNN, however, the ANN treats each modulation state independently and does not incorporate recurrent sequential modeling. The model was trained and evaluated using the same simulated training, validation, and test datasets as ReflectoRNN.

For comparison with conventional physics-based inversion, we implemented transfer matrix fitting based on a multioscillator Tauc–Lorentz dielectric model coupled with least-squares optimization. Specifically, the complex dielectric function of the target material was parametrized using five Tauc-Lorentz oscillators and fit by minimizing the difference between calculated and measured reflectance spectra through transfer matrix calculations. For the initial modulation state, fitting was initialized using the known baseline refractive index. For subsequent modulation states, the fitted parameters from the baseline state were used as initialization to fit the modulated reflectance spectra. This implementation follows standard ellipsometric optical-constant fitting methodology.

Performance Metrics

To evaluate the predictive performance of the model, we employed two metrics, PCC and RAS. PCC is commonly used to measure the correlation between two variables. It assesses the similarity in spectral shape between the predicted and ground truth spectra. A PCC value close to 1 indicates strong agreement in the overall trend and shape of the spectra.

RAS measures the relative difference in the absolute values of the predicted spectra compared to the ground truth, providing a normalized root-mean-square percentage error score. RAS approaches 1 as the prediction error becomes negligible relative to the signal magnitude.

PCC and RAS are defined as

$$PCC=\frac{{\mathrm{\Sigma }}_i({ŷ}_i-\overline{\widehat{y}})(y_i-\mathrm{y̅})}{\sqrt{{\mathrm{\Sigma }}_i{({ŷ}_i-\overline{\widehat{y}})}^2}\sqrt{{\mathrm{\Sigma }}_i{(y_i-\mathrm{y̅})}^2}}$$ 4

$$RAS=1-\frac{\sqrt{\mathrm{MSE}(ŷ,y)}}{\mathrm{y̅}}$$ 5

where ${\hat{y}}_i$ and y _i denote the predicted and ground truth spectral values at wavelength index i, respectively; $\stackrel{-}{\hat{y}}$ and y̅ are the mean of the predicted spectrum and ground truth spectra across all wavelengths, and MSE­(ŷ,y) is the mean squared error between the predicted and ground truth spectra.

MoS₂ and WS₂ Sample Preparation

Substrates were prepared for supporting exfoliated 2D MoS₂ and WS₂ flakes used in optical reflectance and ellipsometry measurements. A multistep cleaning process was used to ensure an atomically clean surface. First, the substrates were sonicated sequentially in deionized (DI) water, acetone, and isopropanol (IPA) to remove gross contaminants. Following this, they were dried with a stream of nitrogen gas. For the final cleaning step, the substrates were immersed in a Piranha solution, composed of a 3:1 volumetric ratio of sulfuric acid to hydrogen peroxide, to eliminate any remaining organic residues. The substrates were then thoroughly rinsed with DI water and blown dry with nitrogen gas.

2D flakes of MoS2 and WS2 were isolated from commercially available bulk crystals (HQ Graphene) using the mechanical exfoliation method. The standard Scotch tape technique was employed to cleave thin, few-layer flakes from the bulk material. These exfoliated flakes were subsequently transferred directly from the tape onto the surface of the cleaned substrates for subsequent analysis and fabrication.

Substrate Preparation for Temperature-Modulated Samples

P-type (100) 4-in. Si (University Wafer, Inc.) substrates were used to fabricate SiO₂/Si, SiO₂/Al₂O₃/Si, and SiO₂/TiO₂ DBR structures. The substrates were cleaned by sequential ultrasonic baths in acetone and isopropanol for 10 min each, followed by rinsing with deionized water, drying with N₂ gas, and oxygen plasma treatment. SiO₂ and Al2O₃ films were deposited by RF magnetron sputtering system (Lesker PVD 75 RF sputtering) using 3-in. diameter SiO₂ (99.995% pure) and Al₂O₃ (99.5% pure) targets at a target-to-substrate distance of approximately 4 in.. The base pressure of the chamber was 5 × 10⁶ Torr. For SiO₂ deposition, a 96% Ar and 4% O₂ gas mixture was used at 20 mTorr for plasma ignition and 3 mTorr during sputtering, with an RF power of 250 W. For Al₂O₃ deposition, pure Ar was used under the same pressures with an RF power of 200 W. Both targets were presputtered for 10 min to remove surface contaminants, and the substrates were maintained at room temperature and rotated at 20 rpm to ensure uniformity. The films were characterized by spectroscopic ellipsometry (J.A. Woollam Alpha-SE) over 300–1000 nm at an incidence angle of 70°, and the Ψ and Δ data were analyzed using CompleteEASE software with a Cauchy model. The SiO₂ layer in the SiO₂/Si stack had a thickness of 76 nm with a refractive index of 1.45 at 632.8 nm (MSE = 4.2). In the SiO₂/Al₂O₃/Si stack, the Al₂O₃ layer measured prior to SiO₂ deposition was 22 nm thick with a refractive index of 1.35 (MSE = 3.8). To evaluate the SiO₂ thickness on top of Al₂O₃, a reference Si substrate was placed adjacent to the wafer during sputtering. The thickness varied by approximately 10% between the wafer center and the reference, which measured 77 nm with a refractive index of 1.45 (MSE = 3.8). The DBR structure, consisting of five alternating SiO₂ and TiO₂ layers with thicknesses of 96.6 and 62.5 nm, respectively, was deposited using an electron-beam evaporation system (Lesker PVD 75). The deposition rate for both materials was maintained at 0.5 Å/s. The film thickness was monitored in situ using a quartz crystal microbalance integrated into the system, and the deposition rates were precalibrated (Bruker DektakXT Surface Profiler) to ensure thickness accuracy.

Ellipsometry and Reflectance Measurements

The ellipsometry is measured by J.A. Woollam M-2000DI spectroscopic ellipsometer. Focusing probes are added to reduce the beam diameter. The wavelength range is from 193 to 1690 nm with simultaneous data collection at 690 wavelengths. The measure angle varies from 45° to 65°. Tip-tilt and sample height are manually aligned to focus at the sample before each data acquisition. Ellipsometry measures the change in polarization of light due to reflection on a sample. The amplitude ratio Ψ and the phase difference Δ are measured and fitted using Tauc-Lorentz models. CompleteEASE software was used to perform the fitting and obtain the dielectric constant.

The reflectance is measured by a customized spectroscopy system. The broadband white light from EnergetiQ Laser-Driven Light Source is coupled to an Olympus microscope and normally incident on the samples from a 50× objective with a beam size of about 20 μm. The reflected light entered the slit of the Horiba 320 spectrometer, which is coupled with a 600 mm^–1 grating, and was measured by a Horiba Syncerity CCD detector in the visible wavelength. A Silver mirror is used as a reference to calculate the reflectivity of the samples.

Temperature-Dependent Reflectance Measurement

Temperature-dependent reflectance measurements were performed using a custom-built heating stage integrated with a microscope-based optical system. Samples were placed on an electrically heated plate mounted on a heat-resistant base to ensure uniform and stable thermal conduction. The temperature was controlled by a resistive heater connected to a power supply, allowing gradual and uniform modulation from room temperature to 140 °C. A thermal meter positioned near the sample surface provided real-time temperature feedback.

Evaluation under Incomplete Modulation Conditions

In practical experimental settings, intermediate thermal or optical modulation states may be uneven or missing due to instrument drift, unstable heating, or data loss during acquisition. To simulate these realistic measurement limitations, we systematically removed intermediate modulation steps from the sequential input data and evaluated ReflectoRNN’s ability to reconstruct the corresponding refractive index spectra. Specifically, four conditions were considered: (1) no skipped modulations (complete sequence input); (2) skipping the first and third modulation states; (3) skipping the first and second modulation states; and (4) skipping the first three modulation states. For each case, the model received incomplete modulation sequences as input while being tasked to predict the corresponding series of refractive index spectra.

Interpretability Analysis of ReflectoRNN

To interpret the predictions of ReflectoRNN, we performed global correlation and local perturbation-based sensitivity analyses. Pearson correlation matrices were computed between input modulated reflectance and predicted refractive index n across wavelengths using the test set to characterize global spectral dependencies.

For local sensitivity analysis, the input reflectance at each wavelength was independently perturbed by a small multiplicative change (2%), and the resulting variation in predicted n was used to quantify feature importance as wavelength-dependent prediction sensitivity. Specifically, for each perturbed wavelength, feature importance was calculated from the mean absolute change in predicted n induced by the perturbation. Repeating this across all wavelengths generated a local feature importance map describing how perturbations at each input wavelength influence refractive index predictions across the spectrum. High-sensitivity regions were identified as wavelengths within the top 10% of feature importance values (90th percentile threshold).

The data that support the findings of this study are available upon reasonable request from the authors.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsnano.6c04315.

• Figures S1–S15: Simulation workflow, representative predictions, experimental setup, benchmarking against conventional methods, autoencoder evaluation, robustness analysis, exciton energy analysis, Kramers–Kronig consistency validation, and interpretability analysis of ReflectoRNN. Table S1–S4: ReflectoRNN framework components, autoencoder and recurrent neural network configurations, and detailed neural network architecture parameters. (PDF)

The authors declare no competing financial interest.