Elvet -- a neural network-based differential equation and variational problem solver
This provides a tool for researchers and engineers to apply machine learning methods to mathematical problems, but it is incremental as it builds on existing neural network-based solvers.
The authors introduced Elvet, a Python package that uses neural networks to solve differential equations and variational problems, handling arbitrary systems and constraints by training neural networks to represent solutions.
We present Elvet, a Python package for solving differential equations and variational problems using machine learning methods. Elvet can deal with any system of coupled ordinary or partial differential equations with arbitrary initial and boundary conditions. It can also minimize any functional that depends on a collection of functions of several variables while imposing constraints on them. The solution to any of these problems is represented as a neural network trained to produce the desired function.