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SciML / 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
https://mtk.sciml.ai/dev/
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Differential Equation Function Transformations #141

Open ChrisRackauckas opened 5 years ago

ChrisRackauckas commented 5 years ago

Basic things like http://www.math.mcgill.ca/jakobson/courses/ma261/lecture5.pdf

This can really help enforce conditions like non-negativity since if your space doesn't allow it, then the numerical solver can guarantee it won't happen if it solves for exp(x) instead of x.

stevengogogo commented 3 years ago

it won't happen if it solves for exp(x) instead of x

Do you have a sample equation that has the problem you mentioned and can be benefited from this method?

ChrisRackauckas commented 3 years ago

https://www.radford.edu/~thompson/vodef90web/problems/demosnodislin/Demos_MOL/DemoPolymer/nonnegative.pdf

The one on the bottom of page 4 should be good.