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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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Hi, We have observed a strange issue where a GPU compilation error occurs (seemingly randomly) during training with BFGS: ``` ERROR: GPU compilation of MethodInstance for (::GPUArrays.var"#broadcast_kernel#26")(::CUDA.CuKernelContext, ::ComponentMatrix{Float64, CUDA.CuDeviceMatrix{Float64, 1},...

Evaluating the solution of an optimization procedure using ```julia discretization = PhysicsInformedNN(chain, QuadratureTraining()) prob = discretize(system, discretization) result = Optimization.solve(prob, BFGS()) discretization.phi([0.5], result.u) # Error here ``` yields the error...

I've noticed that this package is sucking up a lot of CI time. I will never argue for running fewer tests as I love good test coverage, and I understand...

Directional derivatives are currently calculated by first calculating all the variable derivs and then performing a weighted sum. This could be more efficient, especially with many dimensions. Actions to take:...

Currently something like u(x) - u(0) ~ sin(x) gets parsed as u(x) - u(x) ~ sin(x) when generating the loss function, because all instances of u(anything) are assumed to have...

Hi, Is there any way to define a PDE without having to manually write all the terms, maybe using a vector notation? Say if I have the heat equation in...

Solves high dimensional PDEs by deep neural networks. 1. #220 2. #201 3. #19

If anyone wants to rewrite NeuralPDE, I want to share some of my expectations here, some of which have been reflected in Sophon.jl. The following code is mostly pseudocode, used...

What is the current state of NNODE? It does not seem to be more widely used? My impression is that training is difficult when representing the entire continuous numerical solution...

Hi all, Many of you have reached out to me or @ChrisRackauckas about doing a GSoC related to NeuralPDE.jl, or PDE discretizers and we're both very happy to have you...