Symbolically Solving Partial Differential Equations using Deep Learning
We describe a neural-based method for generating exact or approximate solutions to differential equations in the form of mathematical expressions. Unlike other neural methods, our system returns symbolic expressions that can be interpreted directly. Our method uses a neural architecture for learning mathematical expressions to optimize a customizable objective, and is scalable, compact, and easily adaptable for a variety of tasks and configurations. The system has been shown to effectively find exact or approximate symbolic solutions to various differential equations with applications in natural sciences. In this work, we highlight how our method applies to partial differential equations over multiple variables and more complex boundary and initial value conditions.
Code (0)
등록된 구현이 없습니다.
Tasks
Deep LearningSimilar Papers 제목 키워드 기반
A neural method for symbolically solving partial differential equations
We describe a neural-based method for generating exact or approximate solutions to differential equations in the form of mathematical expressions. Unlike other neural methods, our system returns symbolic expressions that…
Hyena Neural Operator for Partial Differential Equations
Numerically solving partial differential equations typically requires fine discretization to resolve necessary spatiotemporal scales, which can be computationally expensive. Recent advances in deep learning have provided…
Forward-Backward Stochastic Neural Networks: Deep Learning of High-dimensional Partial Differential Equations
Classical numerical methods for solving partial differential equations suffer from the curse dimensionality mainly due to their reliance on meticulously generated spatio-temporal grids. Inspired by modern deep learning b…
One-Shot Transfer Learning of Physics-Informed Neural Networks
Solving differential equations efficiently and accurately sits at the heart of progress in many areas of scientific research, from classical dynamical systems to quantum mechanics. There is a surge of interest in using P…
Transfer LearningA Discussion on Solving Partial Differential Equations using Neural Networks
Can neural networks learn to solve partial differential equations (PDEs)? We investigate this question for two (systems of) PDEs, namely, the Poisson equation and the steady Navier--Stokes equations. The contributions of…
Ensemble Learning