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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/469

I’m trying to solve the dynamics of a massive particle on gravitational force by PINNs. The below code is inspired by an example in the documentation of NeuralPDE package. The...

I am trying to solve the equations for a fully developed laminar flow in a channel (continuity and x-momentum NSE equation) but my PINN code is unable to drive down...

Hi, Is there an alternative way to describe the PDE to solve that doesn't require the use of ModelingToolkit or Symbolics? For example, if I were to need to write:...

Interactive visualization of results would be a convenient tool for analysis Makie.jl looks suitable for this https://github.com/JuliaPlots/Makie.jl examples: http://juliaplots.org/MakieReferenceImages/gallery/index.html ![example](https://user-images.githubusercontent.com/1010467/81500379-2e8cfa80-92d2-11ea-884a-7069d401e5d0.gif) two simple cases: iteration number slider ->(prediction and error in...

good first issue

```julia julia> s = NeuralPDE.generate_quasi_random_points(300, [[-1.0,-2.0],[1.0,2.0]], Float64, LatinHypercubeSample()) 2×300 Matrix{Float64}: -1.08 -1.33333 -1.86 -1.49333 … -1.54667 -1.66667 -1.47333 1.35667 1.53667 1.84333 1.07333 1.28 1.66667 1.24667 julia> scatter(s[1,:],s[2,:]) ``` ```julia julia>...

I think that the objective functions/loss functions used for `GridTraining` and `StochasticTraining` generated in [ode_solve.jl](https://github.com/SciML/NeuralPDE.jl/blob/master/src/ode_solve.jl) "get squared" before they are passed to `OptimizationFunction`, meaning, the function $(\sum_i \ell_i^2)^2$ is passed...

I just realized that the recent PR #604 did not fix anything. As `Phi` is a mutable field of immutable `PhysicsInformedNN`. The related source code is a bit messy. Adapting...