Latent PDE mapping for efficient physics-informed learning across geometries with limited data
arXiv cs.LG5d4 min read
arXiv:2607.22215v1 Announce Type: new Abstract: In this study, we introduce latent PDE mapping, a broadly applicable physics-informed learning technique designed to enable efficient geometric generalization with sparse training data. Latent PDE mapping pulls back geometry-specific PDE residuals and boundary conditions to a predefined latent geometry via the deformation gradient, thereby enabling the automated calculation of geometry-consistent shape gradients that are missing in conventional physics-informed machine learning formulations. We demonstrate the utility of latent PDE mapping in sol
