Dynamic Discovery of PDEs

[finmod]

@AlCap23 In the docs and tutorials, could you give an example of PDE discoveries as in https://royalsocietypublishing.org/doi/10.1098/rspa.2020.0279 to demonstrate the versatility of DataDrivenDiffEq.

[AlCap23]

I've started on doing this, but I have to dig a little deeper to get the portioning right.

[AlCap23]

Just to write down what is missing to get the full stack working.

• [ ] Allow to pass in derivatives w.r.t. the states AND transform them accordingly to a numerical derivative via interpolation
• [ ] Split the Problem into Subproblems , which generalizes to train / test splits of problems. Alternatively one could allow to pass in an array of problems and search Pareto optimal solutions here.

It is not a long list, but this makes it a little bit harder. Especially the first one.

I've been using the same data as Rudy et. al. did, but the hard part is to find the right subset of data for such a big dataset with mostly zeros.