Integrate Radial and Kriging with samplings

[ludoro]

• [x] Random sampling
• [x] Uniform sampling
• [x] Sparse grid sampling
• [x] Sobol sampling
• [x] (Monte Carlo) Importance sampling
• [x] Latin Hypercube
• [x] Low-discrepancy sampling: https://en.wikipedia.org/wiki/Low-discrepancy_sequence
• [x] https://www.mdpi.com/1996-1073/12/10/1906/pdf
• [x] https://cseweb.ucsd.edu/~dstefan/pubs/dalal:2008:low.pdf
• [ ] https://arxiv.org/pdf/1703.05312.pdf
• [x] https://pdfs.semanticscholar.org/d1b6/97574a16c43f0b93253a1d23e36fed6575f3.pdf
• [x] https://www.sciencedirect.com/science/article/pii/S1364815214001698
• [x] https://www.researchgate.net/publication/228261680_Low-Discrepancy_Sequences_Monte_Carlo_Simulation_of_Option_Prices
• [x] https://journals.aps.org/pre/abstract/10.1103/PhysRevE.96.022314
• [x] Minimum Interpolation Surface (MIS) https://www.sciencedirect.com/science/article/pii/S1364815214001698

[ChrisRackauckas]

Indeed having sampling procedures is necessary for making this useful. It would be good to create an interface for general sampling, and then getting all of these under the same roof.

[ChrisRackauckas]

Maybe something like sample(f,SobolSampler()).

[ludoro]

I suppose f is the function/solution of the Differential equation we want to approximate?

[ChrisRackauckas]

Indeed. It's any x to scalar function. So not a full differential equation over time, let's take that off the table for now, but the evaluation of a cost function on the differential equation solution (for example, distance from data) is perfectly reasonable.

[ludoro]

Closing this because the samplings in the links are already implemented, but opening another separate issue for https://arxiv.org/pdf/1703.05312.pdf which is another surrogate I want to implement