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A Julia package for Deep Backwards Stochastic Differential Equation (Deep BSDE) and Feynman-Kac methods to solve high-dimensional PDEs without the curse of dimensionality

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https://github.com/vboussange/HighDimPDE.jl/blob/main/src/DeepSplitting.jl#L110 This is hardcoded to Euler-Maruyama. This could potentially be improved by making this use StochasticDiffEq to generalize the time stepping algorithms which could be used. It would be interesting...

https://github.com/SciML/NeuralPDE.jl/issues/514

For now gradients `∇v_y,∇v_z` cannot be used in the nonlinear function ``` f(y,z,v_y,v_z,∇v_y,∇v_z, p, t) ``` Uncommenting those two line https://github.com/vboussange/HighDimPDE.jl/blob/21a25b7f13f15332a1b5872961315b7bcedc5a5b/src/DeepSplitting.jl#L92-L93 should make this work. Nonetheless, possibly because of issue...

This PR adds `HighDimPDE_reflect_outs`, another implementation of `HighDimPDE._reflect`/`HighDimPDE._reflect_GPU`, which computes `out` (`out1` and `out2`) along with `rtemp`/`rmin` exclusively from indices of `b` where it "lies outside the boundary of `[s,e]^d`"....

## Checklist - [x] Appropriate tests were added - [x] Any code changes were done in a way that does not break public API - [ ] All documentation related...

This sets everything up as built doc examples, splits tutorials from examples, adds more informative titles, and sets up buildkite

This pull request changes the compat entry for the `HighDimPDE` package from `2` to `2, 1` for package docs. This keeps the compat entries for earlier versions. Note: I have...

**Describe the bug 🐞** The format check fails because it tries to format the `docs/` directory. We should exclude it and limit to `src` and `test` directories only. **Expected behavior**...

bug