NeuralPDE

Physics-Informed Neural Networks (PINN) Solvers of (Partial) Differential Equations for Scientific Machine Learning (SciML) accelerated simulation

https://github.com/sciml/neuralpde.jl

Science Score: 64.0%

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Low similarity (13.1%) to scientific vocabulary

Keywords

differential-equations differentialequations machine-learning neural-differential-equations neural-network neural-networks ode ordinary-differential-equations partial-differential-equations pde pinn scientific-ai scientific-machine-learning scientific-ml sciml

Keywords from Contributors

sde dae numerical dde stochastic-differential-equations julialang delay-differential-equations neural-ode computer-algebra matrix-exponential

Last synced: 6 months ago · JSON representation ·

Repository

Physics-Informed Neural Networks (PINN) Solvers of (Partial) Differential Equations for Scientific Machine Learning (SciML) accelerated simulation

Basic Info

Host: GitHub
Owner: SciML
License: other
Language: Julia
Default Branch: master
Homepage: https://docs.sciml.ai/NeuralPDE/stable/
Size: 570 MB

Statistics

Stars: 1,110
Watchers: 35
Forks: 221
Open Issues: 133
Releases: 81

Topics

Created almost 9 years ago · Last pushed 6 months ago

Metadata Files

Readme License Citation

README.md

NeuralPDE

NeuralPDE.jl is a solver package which consists of neural network solvers for partial differential equations using physics-informed neural networks (PINNs). This package utilizes neural stochastic differential equations to solve PDEs at a greatly increased generality compared with classical methods.

Installation

Assuming that you already have Julia correctly installed, it suffices to install NeuralPDE.jl in the standard way, that is, by typing ] add NeuralPDE. Note: to exit the Pkg REPL-mode, just press Backspace or Ctrl + C.

Tutorials and Documentation

For information on using the package, see the stable documentation. Use the in-development documentation for the version of the documentation, which contains the unreleased features.

Features

Physics-Informed Neural Networks for ODE, SDE, RODE, and PDE solving
Ability to define extra loss functions to mix xDE solving with data fitting (scientific machine learning)
Automated construction of Physics-Informed loss functions from a high level symbolic interface
Sophisticated techniques like quadrature training strategies, adaptive loss functions, and neural adapters to accelerate training
Integrated logging suite for handling connections to TensorBoard
Handling of (partial) integro-differential equations and various stochastic equations
Specialized forms for solving ODEProblems with neural networks
Compatibility with Flux.jl and Lux.jl for all of the GPU-powered machine learning layers available from those libraries.
Compatibility with NeuralOperators.jl for mixing DeepONets and other neural operators (Fourier Neural Operators, Graph Neural Operators, etc.) with physics-informed loss functions

Example: Solving 2D Poisson Equation via Physics-Informed Neural Networks

```julia using NeuralPDE, Lux, ModelingToolkit, Optimization, OptimizationOptimisers import DomainSets: Interval, infimum, supremum

@parameters x y @variables u(..) Dxx = Differential(x)^2 Dyy = Differential(y)^2

2D PDE

eq = Dxx(u(x, y)) + Dyy(u(x, y)) ~ -sin(pi * x) * sin(pi * y)

Boundary conditions

bcs = [u(0, y) ~ 0.0, u(1, y) ~ 0, u(x, 0) ~ 0.0, u(x, 1) ~ 0]

Space and time domains

domains = [x ∈ Interval(0.0, 1.0), y ∈ Interval(0.0, 1.0)]

Discretization

dx = 0.1

Neural network

dim = 2 # number of dimensions chain = Lux.Chain(Dense(dim, 16, Lux.σ), Dense(16, 16, Lux.σ), Dense(16, 1))

discretization = PhysicsInformedNN(chain, QuadratureTraining())

@named pdesystem = PDESystem(eq, bcs, domains, [x, y], [u(x, y)]) prob = discretize(pdesystem, discretization)

callback = function (p, l) println("Current loss is: $l") return false end

res = Optimization.solve(prob, ADAM(0.1); callback = callback, maxiters = 4000) prob = remake(prob, u0 = res.minimizer) res = Optimization.solve(prob, ADAM(0.01); callback = callback, maxiters = 2000) phi = discretization.phi ```

And some analysis:

```julia xs, ys = [infimum(d.domain):(dx / 10):supremum(d.domain) for d in domains] analyticsolfunc(x, y) = (sin(pi * x) * sin(pi * y)) / (2pi^2)

upredict = reshape([first(phi([x, y], res.minimizer)) for x in xs for y in ys], (length(xs), length(ys))) ureal = reshape([analyticsolfunc(x, y) for x in xs for y in ys], (length(xs), length(ys))) diffu = abs.(upredict .- u_real)

using Plots p1 = plot(xs, ys, ureal, linetype = :contourf, title = "analytic"); p2 = plot(xs, ys, upredict, linetype = :contourf, title = "predict"); p3 = plot(xs, ys, diff_u, linetype = :contourf, title = "error"); plot(p1, p2, p3) ```

Citation

If you use NeuralPDE.jl in your research, please cite this paper:

bib @article{zubov2021neuralpde, title={NeuralPDE: Automating Physics-Informed Neural Networks (PINNs) with Error Approximations}, author={Zubov, Kirill and McCarthy, Zoe and Ma, Yingbo and Calisto, Francesco and Pagliarino, Valerio and Azeglio, Simone and Bottero, Luca and Luj{\'a}n, Emmanuel and Sulzer, Valentin and Bharambe, Ashutosh and others}, journal={arXiv preprint arXiv:2107.09443}, year={2021} }

Owner

Name: SciML Open Source Scientific Machine Learning
Login: SciML
Kind: organization
Email: contact@chrisrackauckas.com

Website: https://sciml.ai
Twitter: SciML_Org
Repositories: 170
Profile: https://github.com/SciML

Open source software for scientific machine learning

Citation (CITATION.bib)

@misc{https://doi.org/10.48550/arxiv.2107.09443,
  doi = {10.48550/ARXIV.2107.09443},
  url = {https://arxiv.org/abs/2107.09443},
  author = {Zubov, Kirill and McCarthy, Zoe and Ma, Yingbo and Calisto, Francesco and Pagliarino, Valerio and Azeglio, Simone and Bottero, Luca and Luján, Emmanuel and Sulzer, Valentin and Bharambe, Ashutosh and Vinchhi, Nand and Balakrishnan, Kaushik and Upadhyay, Devesh and Rackauckas, Chris},
  keywords = {Mathematical Software (cs.MS), Symbolic Computation (cs.SC), FOS: Computer and information sciences, FOS: Computer and information sciences},  
  title = {NeuralPDE: Automating Physics-Informed Neural Networks (PINNs) with Error Approximations},
  publisher = {arXiv},
  year = {2021},
  copyright = {Creative Commons Attribution Non Commercial Share Alike 4.0 International}
}

GitHub Events

Total

Create event: 37
Commit comment event: 2
Release event: 6
Issues event: 16
Watch event: 128
Delete event: 33
Issue comment event: 109
Push event: 145
Pull request event: 98
Pull request review event: 81
Pull request review comment event: 88
Fork event: 22

Last Year

Create event: 37
Commit comment event: 2
Release event: 6
Issues event: 16
Watch event: 128
Delete event: 33
Issue comment event: 109
Push event: 145
Pull request event: 98
Pull request review event: 81
Pull request review comment event: 88
Fork event: 22

Committers

Last synced: 10 months ago

All Time

Total Commits: 2,278
Total Committers: 64
Avg Commits per committer: 35.594
Development Distribution Score (DDS): 0.711

Past Year

Commits: 247
Committers: 10
Avg Commits per committer: 24.7
Development Distribution Score (DDS): 0.543

Top Committers

Name	Email	Commits
KirillZubov	k**3@g**m	658
Chris Rackauckas	a**s@c**m	464
Astitva Aggarwal	a**t@g**m	373
ashutosh-b-b	a**3@g**m	159
Sathvik Bhagavan	s**n@j**m	119
Gabriel Birnbaum	g**m@g**m	86
CompatHelper Julia	c**y@j**g	55
MilkshakeForReal	y**u@u**a	48
github-actions[bot]	4****]	39
dependabot[bot]	4****]	29
Zoe McCarthy	z**2@g**m	29
Samedh Desai	s**i@S**l	24
ayushinav	a**t@g**m	21
Zing	z**2@g**m	19
ashutosh-b-b	a**3@g**m	17
Samedh Desai	s**i@s**m	14
akaysh	k**1@g**m	14
ArnoStrouwen	a**n@t**e	13
xtalax	a**y@g**m	11
Anant Thazhemadam	a**m@g**m	8
Kirill	k**l@K**l	7
Rohit Singh Rathaur	4****N	4
Chris de Graaf	me@c****v	4
Kanav Gupta	3****9	4
Hendrik Ranocha	r****a	3
abhro	5****o	3
Vaibhav Kumar Dixit	v**t@g**m	3
maja.k.gwozdz@gmail.com	m**z@g**m	3
Léo de Souza	l**a@m**u	3
Léo de Souza	4****a	3
and 34 more...

Committer Domains (Top 20 + Academic)

mit.edu: 2 chrisrackauckas.com: 1 juliahub.com: 1 julialang.org: 1 ucalgary.ca: 1 samedhs-mbp.mynetworksettings.com: 1 telenet.be: 1 cdg.dev: 1 minesparis.psl.eu: 1 alum.mit.edu: 1 juliacomputing.com: 1 31-39-92.wireless.csail.mit.edu: 1 samedhs-mbp.lan: 1 ethz.ch: 1 mail.com: 1 79.234.20.172.in-addr.arpa: 1 c02g73vamd6r.tld: 1 simons-rock.edu: 1 uchicago.edu: 1

Issues and Pull Requests

Last synced: 6 months ago

All Time

Total issues: 117
Total pull requests: 402
Average time to close issues: 6 months
Average time to close pull requests: about 2 months
Total issue authors: 64
Total pull request authors: 42
Average comments per issue: 5.16
Average comments per pull request: 1.57
Merged pull requests: 235
Bot issues: 1
Bot pull requests: 158

Past Year

Issues: 16
Pull requests: 110
Average time to close issues: 17 days
Average time to close pull requests: 12 days
Issue authors: 10
Pull request authors: 14
Average comments per issue: 0.88
Average comments per pull request: 0.65
Merged pull requests: 69
Bot issues: 1
Bot pull requests: 60

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Top Authors

Issue Authors

ChrisRackauckas (12)
nicholaskl97 (6)
AstitvaAggarwal (6)
YichengDWu (5)
KirillZubov (4)
xtalax (4)
geriatricvibes (3)
Runfa-Zhang (3)
sathvikbhagavan (3)
zoemcc (3)
marcofrancis (3)
avik-pal (3)
michaeljehan (2)
finmod (2)
affans (2)

Pull Request Authors

github-actions[bot] (103)
sathvikbhagavan (63)
dependabot[bot] (55)
ChrisRackauckas (36)
AstitvaAggarwal (29)
ArnoStrouwen (10)
KirillZubov (9)
hippyhippohops (8)
ayushinav (8)
xtalax (7)
sdesai1287 (6)
abhro (6)
thazhemadam (6)
avik-pal (6)
YichengDWu (5)

Top Labels

Issue Labels

bug (21) new_algorithm (9) question (9) good first issue (3) enhancement (2) help wanted (2) documentation (1)

Pull Request Labels

dependencies (55) github_actions (6)

Packages

Total packages: 2
Total downloads:
- julia 184 total

Total dependent packages: 3
(may contain duplicates)
Total dependent repositories: 0
(may contain duplicates)
Total versions: 71

juliahub.com: NeuralPDE

Physics-Informed Neural Networks (PINN) Solvers of (Partial) Differential Equations for Scientific Machine Learning (SciML) accelerated simulation

Homepage: https://docs.sciml.ai/NeuralPDE/stable/
Documentation: https://docs.juliahub.com/General/NeuralPDE/stable/
License: MIT
Latest release: 5.20.0
published 8 months ago

Versions: 70
Dependent Packages: 3
Dependent Repositories: 0
Downloads: 184 Total

Rankings

Forks count: 0.4%

Stargazers count: 0.5%

Average: 6.0%

Dependent repos count: 9.9%

Dependent packages count: 13.2%

Last synced: 6 months ago

juliahub.com: NeuralPDELogging

Physics-Informed Neural Networks (PINN) Solvers of (Partial) Differential Equations for Scientific Machine Learning (SciML) accelerated simulation

Homepage: https://docs.sciml.ai/NeuralPDE/stable/
Documentation: https://docs.juliahub.com/General/NeuralPDELogging/stable/
License: MIT
Latest release: 0.1.0
published over 6 years ago

Versions: 1
Dependent Packages: 0
Dependent Repositories: 0

Rankings

Forks count: 0.4%

Stargazers count: 0.5%

Dependent repos count: 9.9%

Average: 12.4%

Dependent packages count: 38.9%

Last synced: 6 months ago

Dependencies

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