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Physics-Informed Neural Networks (PINN) Solvers of (Partial) Differential Equations for Scientific Machine Learning (SciML) accelerated simulation

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https://github.com/SciML/NeuralPDE.jl/issues/818 describes a problem with complex numbers. We can add it properly in NeuralPDE and also have an example explaining it.

## Checklist - [ ] Appropriate tests were added - [ ] Any code changes were done in a way that does not break public API - [ ] All...

NeuralPDE develops its loss function in two steps: 1. Develop a data-free loss function $\ell(x, \theta)$ from each equation/boundary condition in the `PDESystem`. This is the role of NeuralPDE's parser....

This pull request changes the compat entry for the `ModelingToolkit` package from `8.33` to `8.33, 9` for package docs. This keeps the compat entries for earlier versions. Note: I have...

This pull request changes the compat entry for the `ModelingToolkit` package from `8` to `8, 9`. This keeps the compat entries for earlier versions. Note: I have not tested your...

The current setup was written before we had all the useful tools present in Symbolics.jl, this PR takes advantage of these and the PDE helper functions present in PDEBase

MWE: Running one of the tests in `NNODE_tests.jl`, ```julia using Flux using Random, NeuralPDE using OrdinaryDiffEq, Statistics import OptimizationOptimisers Random.seed!(100) # Run a solve on scalars linear = (u, p,...

## Checklist - [ ] Tests - [ ] Current API dosent break? - [ ] Documentation - [ ] The new code follows the [contributor guidelines](https://github.com/SciML/.github/blob/master/CONTRIBUTING.md), in particular the...

Hello SciML team ! I have been using NeuralPDE for a few months as part of my thesis. The challenge I am facing is the need to solve both inverse...