FlashPDE: A Drop-In Fused Triton Operator Library for Neural PDE Solvers

תקציר מקורי באנגליתarXiv:2607.18020v2 Announce Type: replace Abstract: Physics-Informed Neural Networks (PINNs) solve PDEs by incorporating physical constraints into neural-network training, but large-scale problems are limited by automatic-differentiation memory overhead and inefficient execution of grid-based PDE operators. We present FlashPDE, a drop-in fused operator library for grid-based scientific machine learning. FlashPDE replaces fragmented PyTorch finite-difference execution with differentiable Triton kernels. Each operator integrates fused stencil evaluation, an analytic discrete-adjoint backward pass, and boundary-gradient correction within a unified PyTorch autograd.Function interface. The library provides 14 differentiable PDE operators covering 17 configurations across 1D--3D elliptic, parabo