Physics-Informed Neural Network Shape Optimization

Vanilla MLP PINNs suffer from spectral bias and slow convergence, which directly limits the quality of shapes produced by PINN-based shape optimizers. This project integrates Physics-Informed Gaussians (PIG) into the coordinate projection shape optimization framework of Zhang et al. (2024), replacing the MLP physics solver with learnable Gaussian basis functions that adaptively concentrate resolution in high-residual regions. I will build a PyTorch framework with swappable MLP, PIXEL, and PIG physics backends, validate all three on the published iron core torque optimization benchmark, and finally, apply the best-performing backend to a novel use case: optimizing Paul trap electrode geometries to maximize the geometric efficiency factor governing ion confinement. I will explore the open-source framework with backend comparison results and a working Paul trap shape optimizer with fabrication constraints.