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DataDrivenDiffEq.jl reviews and mentions
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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.
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SciML/DataDrivenDiffEq.jl is an open source project licensed under MIT License which is an OSI approved license.
The primary programming language of DataDrivenDiffEq.jl is Julia.
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