Tensor-Train Compressed Separable PINNs: A Curvature-Aware Optimization Framework for Parametric PDEs in High Dimensions

תקציר מקורי באנגליתarXiv:2609.36165v1 Announce Type: cross Abstract: In this work, we develop a second-order optimization framework for physics-informed neural networks (PINNs) applied to high-dimensional parametric partial differential equations (PDEs). The framework is built on the Gauss--Newton pullback metric, which provides an operator-informed notion of curvature in parameter space and connects the method to the broader family of natural gradient schemes. We show that, for coordinate-separable neural architectures and linear differential operators (or linearized operators in the nonlinear case) admitting a finite separable representation, the residual Jacobian inherits a structured separable factorization. This yields an exact compressed formulation of the Gauss--Newton step in a reduced space, without