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Scientific machine learning (SciML) benchmarks, AI for science, and (differential) equation solvers. Covers Julia, Python (PyTorch, Jax), MATLAB, R

Results 114 SciMLBenchmarks.jl issues
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Added the MTK version of [transistor amplifier problem](https://archimede.uniba.it/~testset/problems/transamp.php), from #359 I'm not sure how the solvers are set up, so everything below line 58 (`tspan = (0.0, 0.2)`) is from...

Howdy, I see ODE benchmarks for specific ODE problems, but I was curious if for a general linear system: x'=A(t)x if i) you've ploted N (size of ode system), versus...

https://discourse.julialang.org/t/am-i-going-about-solving-this-pde-system-the-right-way/74621/9

https://frankschae.github.io/post/high-weak/ @frankschae

https://archimede.dm.uniba.it/~testset/testsetivpsolvers/?page_id=26#DAE Edit: URL changed to https://archimede.uniba.it/~testset/testsetivpsolvers/?page_id=26#DAE - [x] [Chemical Akzo Nobel](https://archimede.dm.uniba.it/~testset/problems/chemakzo.php) - [ ] [Andrews' squeezing mechanism problem](https://archimede.dm.uniba.it/~testset/problems/andrews.php) - [x] [Transistor amplifier problem](https://archimede.dm.uniba.it/~testset/problems/transamp.php) - [ ] [Charge-pump problem](https://archimede.dm.uniba.it/~testset/problems/pump.php) - [...

https://easychair.org/publications/paper/mc5T https://github.com/verivital/daev/tree/master/daev/examples

https://archimede.dm.uniba.it/~testset/testsetivpsolvers/?page_id=26#ODE - [ ] [Ring Modulator](https://archimede.dm.uniba.it/~testset/problems/ringmod.php) - [ ] [Medical Akzo Nobel problem](https://archimede.dm.uniba.it/~testset/problems/medakzo.php) - [ ] [EMEP problem](https://archimede.dm.uniba.it/~testset/problems/emep.php) - [ ] [E5](https://archimede.dm.uniba.it/~testset/problems/e5.php) - [ ] [Beam](https://archimede.dm.uniba.it/~testset/problems/beam.php)

Parts of the PINN solver benchmarks are not compiling https://benchmarks.sciml.ai/html/PINNErrorsVsTime/allen_cahn_et.html

Would be great to have a benchmark for IDE PINNs.

Was done in SciMLTutorials in https://github.com/SciML/SciMLTutorials.jl/pull/445, https://github.com/SciML/SciMLTutorials.jl/pull/446, + https://github.com/SciML/SciMLTutorials.jl/pull/448 . But it's not clear it's worth the effort for this repo.