Lie Point Symmetry and Physics-Informed Networks
Symmetries have been leveraged to improve the generalization of neural networks through different mechanisms from data augmentation to equivariant architectures. However, despite their potential, their integration into neural solvers for partial differential equations (PDEs) remains largely unexplored. We explore the integration of PDE symmetries, known as Lie point symmetries, in a major family of neural solvers known as physics-informed neural networks (PINNs). We propose a loss function that informs the network about Lie point symmetries in the same way that PINN models try to enforce the underlying PDE through a loss function. Intuitively, our symmetry loss ensures that the infinitesimal generators of the Lie group conserve the PDE solutions.. Effectively, this means that once the network learns a solution, it also learns the neighbouring solutions generated by Lie point symmetries. Empirical evaluations indicate that the inductive bias introduced by the Lie point symmetries of the PDEs greatly boosts the sample efficiency of PINNs.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Symmetry-Constrained Multi-Scale Physics-Informed Neural Networks for Graphene Electronic Band Structure Prediction
Accurate prediction of electronic band structures in two-dimensional materials remains a fundamental challenge, with existing methods struggling to balance computational efficiency and physical accuracy. We present the S…
Computational EfficiencySymmetry-Reduced Physics-Informed Learning of Tensegrity Dynamics
Tensegrity structures possess intrinsic geometric symmetries that govern their dynamic behavior. However, most existing physics-informed neural network (PINN) approaches for tensegrity dynamics do not explicitly exploit …
Computational EfficiencyLie Point Symmetry and Physics Informed Networks
Symmetries have been leveraged to improve the generalization of neural networks through different mechanisms from data augmentation to equivariant architectures. However, despite their potential, their integration into n…
Data AugmentationInductive BiasSymmetry group based domain decomposition to enhance physics-informed neural networks for solving partial differential equations
Domain decomposition provides an effective way to tackle the dilemma of physics-informed neural networks (PINN) which struggle to accurately and efficiently solve partial differential equations (PDEs) in the whole domain…
Generalized Lie Symmetries in Physics-Informed Neural Operators
Physics-informed neural operators (PINOs) have emerged as powerful tools for learning solution operators of partial differential equations (PDEs). Recent research has demonstrated that incorporating Lie point symmetry in…