A tool to use neural networks to approximate arbitrary functions (currently ) by specifying a domain and one or multiple residuals for (parts of) the domain.
Can be used especially for the approximation of solutions of partial differential equations.
Based on PyTorch.
Approximate an explicitly given function.
Approximate a piecewise given function.
Approximate the solution of an initial-boundary value problem governed by the conservation equation by using its residual.
Approximate a solution of an initial-boundary value problem governed by Laplace's equation:
Uses StepsDiscretization to ensure that start and endpoints of domain are in the discretized domain, this is important for boundary conditions.
Pretraining is used to first fit the neural network to the boundary conditions, then to the PDE.
Approximate the heat equation:
Approximate the Richardson-Richards equation in the setup described by Michael A. Celia, Efthimios T. Bouloutas and Rebecca L. Zarba in 1990.
The RRE:
with constitutive equation:
