ODE-Specialized Physics-Informed Neural Solver

The ODE-specialized physics-informed neural network (PINN) solver is a method for the DifferentialEquations.jl common interface of ODEProblem, which generates the solution via a neural network. Thus the standard ODEProblem is used, but a new algorithm, NNODE, is used to solve the problem.

The algorithm type is:


where chain is a DiffEqFlux sciml_train-compatible Chain or FastChain representing a neural network, and opt is an optimization method for sciml_train. For more details, see the DiffEqFlux documentation on sciml_train.

Lagaris, Isaac E., Aristidis Likas, and Dimitrios I. Fotiadis. "Artificial neural networks for solving ordinary and partial differential equations." IEEE Transactions on Neural Networks 9, no. 5 (1998): 987-1000.