Correction: Deployment and validation of predictive 6-dimensional beam diagnostics through generative reconstruction with standard accelerator elements

Correction to: Scientific Reports 10.1038/s41598-025-26954-6, published online 03 December 2025

The original version of this Article contained errors, where inconsistencies were found in the simulation lattice during follow-up studies while using the same experimental setup. These inconsistencies mainly arose from errors during the conversion of lattice information data into the simulation format. The simulation lattice was corrected, and the phase-space reconstruction and data analysis were re-performed. Consequently, the following changes were made to reflect the corrected data.

The beamline length from (i) the Q1 and screen 1 is approximately 0.1 m shorter than before adjustment, and (ii) that from bunch compressor to screen 2 is approximately 1.3 m shorter than before adjustment. As a result, instances of the beamline length in the main text have been corrected from 27 to 25 m. Specifically, the changes occurred in the Introduction, in the Results section, under the subheadings ‘Experimental setup’ and ‘Validation of the methodology via independent downstream measurements’.

Furthermore, Figures 2, 3 and 4 were corrected to reflect the updated experimental data. The original Figures 2, 3 and 4 and accompanying legend appear below.

Fig. 2.

Comparison between measured beam distributions and predictions at the screen 1. Training dataset is highlighted with orange box. k indicates the quadrupole magnetic field strength in T/m. Contour lines indicate 90 and 50th percentiles, where solid(dashed) lines represent the measurement(prediction). Colormap image shows the measurement for a, while it illustrates the prediction for b.

Fig. 3.

For the Comparison of LPSs and (y,δ) correlations at the screen 2. In case of the LPS, the beam head is placed at positive z while the tail is at negative z. Colormap image indicates the measured distribution. The average kinetic energy is indicated in each sub-figure, as the is distributed with respect to zero. White dashed(yellow solid), projected histogram indicates predicted(measured) density distribution. White contour lines indicate 90 and 50th percentiles. Top row a–e LPS where BC ON. Middle row f–j LPS where BC OFF. Bottom row k–o (y,δ)correlations with BC OFF.

Fig. 4.

a Reconstructed 6-dimensional phase space. Contour lines indicate 90 and 50th percentile, while different line styles represent three cases in the error study. “Reference” indicates the nominal case. Note that only 90th percentile is shown for (z − δ) distribution. Blue histogram indicates the 1-dimensional histogram in each coordinate. b 3-dimensional scatter/density plot of the reconstructed beam phase space.

Additionally, in the Results, under the subheading ‘Reconstructed 6-dimensional beam phase space’

“In the third case, correlations regarding x are somewhat deviated compared to the other cases, implying that the chosen cavity phases may not have been optimal to get beam correlations during the training.”

now reads:

“For the (x, y′) projection and correlations associated with x′, slight variations in the density levels are observed, indicating the uncertainty of the reconstruction.”

Table 1 was corrected to reflect the updated experimental data. The original Table 1 appears below.

Table 1.

Comparison of the Twiss parameters, emittances, and RMS quantities. Values in parenthesis show the averaged values with standard deviation 1σ for several different GPSR setup. See Sec. 1.5 for more details on the setup.

Case	4D reconstruction	6D reconstruction	unit
	0.42	0.40 (0.42±0.01)	mm mrad
	0.39	0.40 (0.39±0.01)	mm mrad
	4.53	4.67 (4.59±0.15)	m
	7.78	8.12 (7.87±0.29)	m
		(0.04)	rad
	1.25	1.17 (1.16±0.09)	rad
Case	Measurement	Reconstruction	unit
	137.34±17.24	140.05 (141.29±6.27)	mm mrad
		0.49 (0.47±0.01)	mm
		0.22 (0.22±0.00)	%

Furthermore, in the Methods section the following sentences were modified. In the ‘Setup for data acquisition and GPSR training’ subsection the sentence:

“The distance between Q1 magnet and screen 1 is about 12.6 m.”

now reads:

“The distance between Q1 magnet and screen 1 is about 12.5 m.”

In the subsection ‘Image processing and downstream measurements’ the sentence:

“Likewise, the estimated TCAV calibration factors were roughly 4.8 μm/pixel for BC OFF and 4.4 μm/pixel for BC ON according to the TCAV voltage set to 1.7(1.1)”

Now reads:

“Likewise, the estimated TCAV calibration factors were roughly 4.8 μm/pixel for BC OFF and 4.4 μm/pixel for BC ON according to the TCAV voltage set to 1.87(1.2)”

Finally, the Supplementary Information File contained errors in which Figures 1, 2 and 3 did not correspond to the new data. The original Supplementary Information file is provided below.

The original Article and accompanying Supplementary Information files have been corrected.