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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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Need https://github.com/jonniedie/ComponentArrays.jl/pull/164 to actually work

I am trying to solve the simple supported beam problem by PINNs. The problem can be described by 2-order of ODEs as following M"(x) = q(x) M(x=0)=0 M(x=L)=0 0Not working...

This pull request changes the compat entry for the `ComponentArrays` package from `0.12` to `0.12, 0.13`. This keeps the compat entries for earlier versions. Note: I have not tested your...

The goal of this PR is to extend the interface to accept `PDESystem`s that are initialized with array variables (#574) The changes so far occur in `symbolic_utilities.jl` and I expect...

With the recent update this should work now.

I am trying to solve a PDE with variables [t, z1, …, zn]. Here’s my code: ```Julia using Test, Flux, Optim, DiffEqFlux, Optimization using Random, NeuralPDE, DifferentialEquations using Statistics, Distributions,...

I have an inverse problem where the parameter function is a function of the solution, what is the correct way to implement it? ```julia using ModelingToolkit, NeuralPDE, Lux, Random, NNlib...

Very WIP, I'm pulling in and merging prototypes of the various components into the main repo. This depends on the adaptive reweighting stuff and so that should be finalized and...

- [ ] NNPDENS - [ ] NNPDEHan - [ ] [NNPDEHan_tests.jl](https://github.com/SciML/NeuralPDE.jl/blob/master/test/NNPDEHan_tests.jl) - [ ] [NNPDENS_tests.jl](https://github.com/SciML/NeuralPDE.jl/blob/master/test/NNPDENS_tests.jl) - [ ] [Solving a 100-dimensional Hamilton-Jacobi-Bellman Equation](https://neuralpde.sciml.ai/dev/examples/100_HJB/#Solving-a-100-dimensional-Hamilton-Jacobi-Bellman-Equation) tutorial - [ ] https://neuralpde.sciml.ai/dev/examples/blackscholes/ tutorial...

enhancement