Input: Spatial domain $\mathbf{\Omega }$, field parameters $\mathit{\theta }$, inclusion regions ${\mathbf{\Omega }}_{\mathit{i}\mathit{n}\mathit{c}\mathit{l}}$, noise level $\mathit{\sigma }$ Output: Reconstructed field $\hat{\mathit{u}}\left(\mathit{x}\right)$, evaluation metrics (RMSE, PSNR, SSIM) Procedure:       1.  Initialize domain and field:  Define $\mathbf{\Omega }\subset \mathbb{R}\mathbf{ᵈ}$ ($\mathit{d}$ = 2,3): generate field $\mathit{u}\left(\mathit{x}\right)=\mathit{f}(\mathit{x};\mathit{\theta })$       2.  Apply geometric modeling:  Define ${\mathbf{\Omega }}_{\mathit{i}\mathit{n}\mathit{c}\mathit{l}}\subset \mathbf{\Omega }$: introduce heterogeneous inclusions       3.  Generate multimodal fields:  Simulate Gaussian, wave-based, and stepwise patterns       4.  (Optional) Construct 3D volume:  Define ${\mathbf{\Omega }}_{\mathit{B}}$: generate activations using Gaussian model       5.  Add noise:  $\mathit{\eta }\left(\mathit{x}\right)~\mathit{N}\left(0,{\mathit{\sigma }}^2\right)$: compute $\mathrm{ũ}\left(\mathit{x}\right)=\mathit{u}\left(\mathit{x}\right)+\mathit{\eta }\left(\mathit{x}\right)$       6.  Initialize network:  Define CNN ${\mathit{N}}_{\mathit{\theta }}$ mapping $\mathrm{ũ}\left(\mathit{x}\right)\to \hat{\mathit{u}}\left(\mathit{x}\right)$       7.  Define loss function:  $\mathit{L}\left(\mathit{\theta }\right)={\mathit{\lambda }}_{\mathit{d}}\Vert {\mathit{N}}_{\mathit{\theta }}\left(\mathit{x}\right)-\mathit{u}\left(\mathit{x}\right){\Vert }^2+{\mathit{\lambda }}_{\mathit{p}}\Vert \mathit{R}\left({\mathit{N}}_{\mathit{\theta }}\right(\mathit{x}\left)\right){\Vert }^2+{\mathit{\lambda }}_{\mathit{b}}\Vert \mathit{B}\left({\mathit{N}}_{\mathit{\theta }}\right(\mathit{x}\left)\right)-\mathit{g}\left(\mathit{x}\right){\Vert }^2$       8.  Train model:  For each epoch: forward pass → compute $\mathit{L}$ → backpropagate → update $\mathit{\theta }$ (Adam)  Repeat until convergence       9.  Reconstruction and analysis:  Obtain $\hat{\mathit{u}}\left(\mathit{x}\right)$: extract structural/functional patterns       10.  Evaluate performance:  Compute RMSE, PSNR, SSIM across all scenarios End Algorithm