NeuralPDE.jl
dolfinx
NeuralPDE.jl | dolfinx | |
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10 | 18 | |
905 | 658 | |
1.4% | 2.7% | |
9.7 | 9.6 | |
2 days ago | 4 days ago | |
Julia | C++ | |
GNU General Public License v3.0 or later | GNU Lesser General Public License v3.0 only |
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NeuralPDE.jl
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Automatically install huge number of dependency?
The documentation has a manifest associated with it: https://docs.sciml.ai/NeuralPDE/dev/#Reproducibility. Instantiating the manifest will give you all of the exact versions used for the documentation build (https://github.com/SciML/NeuralPDE.jl/blob/gh-pages/v5.7.0/assets/Manifest.toml). You just ]instantiate folder_of_manifest. Or you can use the Project.toml.
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from Wolfram Mathematica to Julia
PDE solving libraries are MethodOfLines.jl and NeuralPDE.jl. NeuralPDE is very general but not very fast (it's a limitation of the method, PINNs are just slow). MethodOfLines is still somewhat under development but generates quite fast code.
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IA et Calcul scientifique dans Kubernetes avec le langage Julia, K8sClusterManagers.jl
GitHub - SciML/NeuralPDE.jl: Physics-Informed Neural Networks (PINN) and Deep BSDE Solvers of Differential Equations for Scientific Machine Learning (SciML) accelerated simulation
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[D] ICLR 2022 RESULTS ARE OUT
That doesn't mean there's no use case for PINNs, we wrote a giant review-ish kind of thing on NeuralPDE.jl to describe where PINNs might be useful. It's just... not the best for publishing. It's things like, (a) where you have not already optimized a classical method, (b) need something that's easy to generate solvers for different cases without too much worry about stability, (c) high dimensional PDEs, and (d) surrogates over parameters. (c) and (d) are the two "real" uses cases you can actually publish about, but they aren't quite good for (c) (see mesh-free methods from the old radial basis function literature in comparison) or (d) (there are much faster surrogate techniques). So we are continuing to work on them for (a) and (b) as an interesting option as part of a software suite, but that's not the kind of thing that's really publishable so I don't think we plan to ever submit that article anywhere.
- [N] Open Colloquium by Prof. Max Welling: "Is the next deep learning disruption in the physical sciences?"
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[D] What are some ideas that are hyped up in machine learning research but don't actually get used in industry (and vice versa)?
Did this change at all with the advent of Physics Informed Neural Networks? The Julia language has some really impressive tools for that use case. https://github.com/SciML/NeuralPDE.jl
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[Research] Input Arbitrary PDE -> Output Approximate Solution
PDEs are difficult because you don't have a simple numerical definition over all PDEs because they can be defined by arbitrarily many functions. u' = Laplace u + f? Define f. u' = g(u) * Laplace u + f? Define f and g. Etc. To cover the space of PDEs you have to go symbolic at some point, and make the discretization methods dependent on the symbolic form. This is precisely what the ModelingToolkit.jl ecosystem is doing. One instantiation of a discretizer on this symbolic form is NeuralPDE.jl which takes a symbolic PDESystem and generates an OptimizationProblem for a neural network which represents the solution via a Physics-Informed Neural Network (PINN).
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[D] Has anyone worked with Physics Informed Neural Networks (PINNs)?
NeuralPDE.jl fully automates the approach (and extensions of it, which are required to make it solve practical problems) from symbolic descriptions of PDEs, so that might be a good starting point to both learn the practical applications and get something running in a few minutes. As part of MIT 18.337 Parallel Computing and Scientific Machine Learning I gave an early lecture on physics-informed neural networks (with a two part video) describing the approach, how it works and what its challenges are. You might find those resources enlightening.
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Doing Symbolic Math with SymPy
What is great about ModelingToolkit.jl is how its used in practical ways for other packages. E.g. NeuralPDE.jl.
Compared to SymPy, I feel that it is less of a "how do I integrate this function" package and more about "how can I build this DSL" framework.
https://github.com/SciML/NeuralPDE.jl
dolfinx
- What's your main programming language?
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rodin alternatives - mfem and FreeFem-sources
7 projects | 8 Mar 2023
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Learn PDE constrained optimization
One thing that is a pain when learning this stuff is that actually performing the optimization requires a good understanding of the numerical discretization of PDEs. Finite elements are a natural choice because it is very easy to characterize the adjoint with this formulation. There are some good free tools that you can use to actually learn and do some computations yourself. The first is hIPPYlib (paper, code), which is built on top of FEniCS (link), for which there are many good tutorials. Beware trying to install this on Windows though. You will need to work in Docker or in Ubuntu via Windows Linux Subsystem.
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Open source FEA tools instead of ANSYS Workbench and APDL
If you're ok with coding, fenics is a solid place to start. Also if you're comfortable with coding, openfoam is FVM, rather than FEM, but it can handle solidmechanics.
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Eighty Years of the Finite Element Method: Birth, Evolution, and Future
> FEniCs made FEM so easy
https://fenicsproject.org/
Indeed, was blown away when I saw it for the first time over a decade ago, compared to the convoluted C++ FEM libraries I had seen before that.
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Best Python package(s) to solve PDEs numerically?
Have you looked at FEniCS? Pretty much everything else I'm aware of is probably overkill (e.g., MOOSE in C++, HYPRE's Python bindings, etc.)
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Open-source FEA software
FEniCSx is quite good.
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The Julia language has a number of correctness flaws
You mean Python? For many research tasks it's fine. High level libraries let you define your computation in a minimal amount of code. FEniCS is a great example of this - underneath it compiles the abstracted high level stuff to calls to low-level libraries that do the heavy lifting. For many applications you can just write vectorized code with Numpy that performs well, or use Numba to JIT what you can't vectorize. For some tasks, however, you need interfaces that don't exist in the high level libraries, and that was the case for me.
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What's a good book to learn to numerically solve ODEs and PDEs in python?
I just came across FEniCSX. I’m not sure if it’s what you want but here’s the description:
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Okay, let's end this Tabs vs Space debate once and for all
Fenics: Very popular finite element framework “UseTab: Never” https://github.com/FEniCS/dolfinx/blob/main/.clang-format
What are some alternatives?
deepxde - A library for scientific machine learning and physics-informed learning
Gridap.jl - Grid-based approximation of partial differential equations in Julia
SymPy - A computer algebra system written in pure Python
mfem - Lightweight, general, scalable C++ library for finite element methods
ModelingToolkit.jl - An acausal modeling framework for automatically parallelized scientific machine learning (SciML) in Julia. A computer algebra system for integrated symbolics for physics-informed machine learning and automated transformations of differential equations
taichi - Productive, portable, and performant GPU programming in Python.
ReservoirComputing.jl - Reservoir computing utilities for scientific machine learning (SciML)
AMDGPU.jl - AMD GPU (ROCm) programming in Julia
pykokkos - Performance portable parallel programming in Python.
18337 - 18.337 - Parallel Computing and Scientific Machine Learning
libmesh - libMesh github repository