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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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Adapted from paper - https://arxiv.org/pdf/2007.14527.pdf Treating Issue #501 Issues 1. Still not completely sure if values used in struct are to be calculated in the struct or somewhere else 2....

Adds inverse dirichlet adaptive loss function to address [#500](https://github.com/SciML/NeuralPDE.jl/issues/500)

This is just safer, @zoemcc

enhancement
good first issue

I'm working on a systematic expansion and review of the tests for PINNs: - [ ] Many PINN tests compare to the analytic solution but only using a test like:...

enhancement

```julia @parameters t @variables i(..) Di = Differential(t) Ii = Integral(t in DomainSets.ClosedInterval(0, t)) ``` it is only processing a simple expression with the variable of NN ```julia Ii(i(t)) ```...

bug

We use `generate_training_sets` to set up models with GridTraining. I managed to find a few breaking points in generate_training sets while playing with some more complex models. 1. dif is...

enhancement

create a bunch of tests covering the parser to keep track of that the symbolic part is working correctly MWE ```julia @parameters x @variables u(..) Dx = Differential(x) eq =...

enhancement

Say I defined and solved a PDE with NeuralPDE and I have the result. I want to do things with that result beyond plotting it in a space. It would...

enhancement

DiffEqOperator has a lot of good convergence tests for pde. It would be nice to cover with this tests NeuralPDE. https://github.com/SciML/DiffEqOperators.jl/tree/master/test/MOL

enhancement

As the next step in the development of the symbolic representation of geometry of PINNs is follow tasks: - [ ] ConstrainedEquation #176 - [ ] polar coordinates - [...

geometry