SymbolicNumericIntegration.jl
DataDrivenDiffEq.jl
| SymbolicNumericIntegration.jl | DataDrivenDiffEq.jl | |
|---|---|---|
| 1 | 3 | |
| 113 | 398 | |
| 0.0% | 0.3% | |
| 7.3 | 6.3 | |
| 2 days ago | 3 days ago | |
| Julia | Julia | |
| MIT License | MIT License |
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SymbolicNumericIntegration.jl
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[2201.12468] Symbolic-Numeric Integration of Univariate Expressions based on Sparse Regression
The repository associated with this paper is https://github.com/SciML/SymbolicNumericIntegration.jl.
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.
What are some alternatives?
SymbolicRegression.jl - Distributed High-Performance Symbolic Regression in Julia
18337 - 18.337 - Parallel Computing and Scientific Machine Learning
MuladdMacro.jl - This package contains a macro for converting expressions to use muladd calls and fused-multiply-add (FMA) operations for high-performance in the SciML scientific machine learning ecosystem
Catalyst.jl - Chemical reaction network and systems biology interface for scientific machine learning (SciML). High performance, GPU-parallelized, and O(1) solvers in open source software.
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
DifferentialEquations.jl - Multi-language suite for high-performance solvers of differential equations and scientific machine learning (SciML) components. Ordinary differential equations (ODEs), stochastic differential equations (SDEs), delay differential equations (DDEs), differential-algebraic equations (DAEs), and more in Julia.
Optimization.jl - Mathematical Optimization in Julia. Local, global, gradient-based and derivative-free. Linear, Quadratic, Convex, Mixed-Integer, and Nonlinear Optimization in one simple, fast, and differentiable interface.