What architecture of CNN to solving a image regression problem (case study: solving Poisson equation)?

Question

I've been working on solving Poisson problem using CNN model (you can ignore Poisson problem part if you not familiar and jump to image processing/CNN part). More specific, I am solving electric potential problem ($\phi$) by CNN algorithm with particle distribution ($\rho$) as the input in cartesian coordinate, similar to Study on a Fast Solver for Poisson’s Equation Based On Deep Learning Technique (PDF), but with no permitivity.

The training input ($\rho$) is 20x20 pixels matrix and the data label ($\phi$) is also 20x20 matrix. Either input and label is contain of 5000 matrix (5000, 20, 20, 1). The input-label data set was obtained from Gauss-Seidel method.

The goal is to obtain electric potential ($\phi$) from input data particle distribution (\rho) with CNN model.

With this regression case, how the best CNN architecture to use?

Answer 1

Currently, the classic architecture for pixel level regression over 2D / 3D / 4D data is U-Net and its extensions.

They are simple to implement. See Image Segmentation Using Deep Learning for a reference MATLAB code.

Since you solve basically a differential equation I'd actually go another path.
Look at the work ML-Assisted Tooling for Model Acceleration in Julia's SciML.