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Differentiability w.r.t. coefficients? #83

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ChrisRackauckas opened this issue Jan 12, 2021 · 0 comments
Open

Differentiability w.r.t. coefficients? #83

ChrisRackauckas opened this issue Jan 12, 2021 · 0 comments

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@ChrisRackauckas
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See #82 and SciML/DiffEqFlux.jl#380 (comment)

Essentially the issue is that in some cases differentiability w.r.t. the coefficients of the spline is needed for function fitting, like in SplineLayer of DiffEqFlux. Currently we just have DoesNotExist() which gives zero gradients in Zygote. While it's preferred to use the overload functions because they ensure numerical stability, on some interpolations it's okay, and those ones that are okay are just the most basic ones. So for now those are excluded from the derivative overload by #82 until analytical solutions for the coefficients are added, in which case we can add it right back when it's available. That fixes the DiffEqFlux tests while retaining the more numerically stable overloads on B-splines and such, which isn't the best solution because if you use the wrong interpolation you'll get zero'd gradients on the coefficients, but it's the best for now.

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