DataDrivenDiffEq.jl
OrdinaryDiffEq.jl
| DataDrivenDiffEq.jl | OrdinaryDiffEq.jl | |
|---|---|---|
| 3 | 3 | |
| 398 | 500 | |
| 0.3% | 0.6% | |
| 6.3 | 9.6 | |
| 6 days ago | 4 days ago | |
| Julia | Julia | |
| MIT License | GNU General Public License v3.0 or later |
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DataDrivenDiffEq.jl
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Equation based on point
If you are looking to infer the actual structure (not just parameters) of an ODE given some data, there is DataDrivenDiffEq.jl. https://github.com/SciML/DataDrivenDiffEq.jl
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[D] Has anyone worked with Physics Informed Neural Networks (PINNs)?
This is all not to mention the fact that PINNs are a notoriously computationally intensive approach, where it's pretty easy to show the differentiable solver approach of DiffEqFlux.jl achieves about a 10,000x speedup over another PINN package on parameter estimation of Lorenz equations, and while it scales to higher PDE dimensions well, it doesn't scale to larger systems of PDEs very well. You'll want to factor in a good chunk of training time, and of course increase that by a few orders of magnitude if your dynamics are stiff. Altogether, without knowing your exact problem it's hard to give a rough idea of how practical it would be, but if I tasked a beginning graduate student with trying this out on some of the biological PDEs I work with, then I would give them about 4-6 months to get something decent together.
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Parameter estimation on non linear time series analysis. [P]
And for reference implementations you can take a look at DataDrivenDiffEq.jl. All DMDs (that I know of) essentially work by building and solving a convex optimization.
OrdinaryDiffEq.jl
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Modern Numerical Solving methods
There has been a lot of research in Runge Kutta methods in the last couple decades which resulted in all kind of specialized Runge Kutta methods. You have high order ones, RK methods for stiff problems, embedded RK methods which benefit from adaprive step size control, RK-Nystrom methods for second order Problems, symplectic RK methods which preserve energy (eg. hamiltonian) ando so on. If you are interested in the numerics and the use cases I highly recommend checking out the Julia Libary OrdinaryDiffEq (https://github.com/SciML/OrdinaryDiffEq.jl). If you look into the documentation you find A LOT of implemented RK methods for all kind of use cases.
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Why Fortran is a scientific powerhouse
Project.toml or Manifest.toml? Every package has Project.toml which specifies bounds (https://github.com/SciML/OrdinaryDiffEq.jl/blob/master/Proje...). Every fully reproducible project has a Manifest that decrease the complete package state (https://github.com/SciML/SciMLBenchmarks.jl/blob/master/benc...).
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How do the Julia ODE solvers choose/select their initial steps? What formula do they use to estimate the appropriate initial step size?
Yes. If you want to see a robust version of the algorithm you can check out https://github.com/SciML/OrdinaryDiffEq.jl/blob/master/src/initdt.jl
What are some alternatives?
18337 - 18.337 - Parallel Computing and Scientific Machine Learning
Latexify.jl - Convert julia objects to LaTeX equations, arrays or other environments.
SymbolicNumericIntegration.jl - SymbolicNumericIntegration.jl: Symbolic-Numerics for Solving Integrals
auto-07p - AUTO is a publicly available software for continuation and bifurcation problems in ordinary differential equations originally written in 1980 and widely used in the dynamical systems community.
DiffEqBase.jl - The lightweight Base library for shared types and functionality for defining differential equation and scientific machine learning (SciML) problems
SciMLTutorials.jl - Tutorials for doing scientific machine learning (SciML) and high-performance differential equation solving with open source software.
NeuralPDE.jl - Physics-Informed Neural Networks (PINN) Solvers of (Partial) Differential Equations for Scientific Machine Learning (SciML) accelerated simulation
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
StochasticDiffEq.jl - Solvers for stochastic differential equations which connect with the scientific machine learning (SciML) ecosystem
SciMLBenchmarks.jl - Scientific machine learning (SciML) benchmarks, AI for science, and (differential) equation solvers. Covers Julia, Python (PyTorch, Jax), MATLAB, R