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Automatic differentiation would be useful so we don't have to implement linearizations or Jacobians of complicated analytic functions. Examples where autodiff would help:
Jacobians and Hessians of coordinate maps. As a first step we can use autodiff just to test our implementations of map Jacobians. That's a good testbed for adding autodiff support to the code.
Second metric derivatives. Currently we compute Ricci quantities numerically on the grid because they are so painful to compute analytically for Kerr-Schild. Autodiff might help.
Linearization of elliptic equations. These are needed for the Newton-Raphson algorithm, but often painful to derive and implement, in particular for complicated equations (XCTS, beyond GR, BNS ID, ...).
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I have played with the library https://github.com/autodiff/autodiff a bit in a toy repo. This seems like it could be useful so we don't have to implement things ourselves. However, I think doing only forward mode autodiff is okay-ish if we have to do it ourselves. I believe we can quite easily extend autodiff to support the blaze SIMD types would should allow autodiff to work.
Automatic differentiation would be useful so we don't have to implement linearizations or Jacobians of complicated analytic functions. Examples where autodiff would help:
The text was updated successfully, but these errors were encountered: