Neuro-symbolic partial differential equation solver
We present a highly scalable strategy for developing mesh-free neuro-symbolic partial differential equation solvers from existing numerical discretizations found in scientific computing. This strategy is unique in that it can be used to efficiently train neural network surrogate models for the solution functions and the differential operators, while retaining the accuracy and convergence properties of state-of-the-art numerical solvers. This neural bootstrapping method is based on minimizing residuals of discretized differential systems on a set of random collocation points with respect to the trainable parameters of the neural network, achieving unprecedented resolution and optimal scaling for solving physical and biological systems.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Neuro-Symbolic AI for Analytical Solutions of Differential Equations
Analytical solutions of differential equations offer exact insights into fundamental behaviors of physical processes. Their application, however, is limited as finding these solutions is difficult. To overcome this limit…
Differential equation solutionA Data-Free Symbolic Regression Approach for Solving Equations
Many equations arising in science currently cannot be solved by available analytical techniques and are therefore solved numerically, without yielding explicit symbolic expressions. Existing symbolic regression approache…
DEM-NeRF: A Neuro-Symbolic Method for Scientific Discovery through Physics-Informed Simulation
Neural networks have emerged as a powerful tool for modeling physical systems, offering the ability to learn complex representations from limited data while integrating foundational scientific knowledge. In particular, n…
Learning To Solve Differential Equations Across Initial Conditions
Recently, there has been a lot of interest in using neural networks for solving partial differential equations. A number of neural network-based partial differential equation solvers have been formulated which provide pe…
Large-scale Neural Solvers for Partial Differential Equations
Solving partial differential equations (PDE) is an indispensable part of many branches of science as many processes can be modelled in terms of PDEs. However, recent numerical solvers require manual discretization of the…
Distributed Computing