Re-posted from: http://www.stochasticlifestyle.com/integrating-equation-solvers-with-probabilistic-programming-through-differentiable-programming/
Part of the COMPUTATIONAL ABSTRACTIONS FOR PROBABILISTIC AND DIFFERENTIABLE PROGRAMMING WORKSHOP
Abstract: Many probabilistic programming languages (PPLs) attempt to integrate with equation solvers (differential equations, nonlinear equations, partial differential equations, etc.) from the inside, i.e. the developers of the PPLs like Stan provide differential equation solver choices as part of the suite. However, as equation solvers are an entire discipline to themselves with many active development communities and subfields, this places an immense burden on PPL developers to keep up with the changing landscape of tens of thousands of independent researchers. In this talk we will explore how Julia PPLs such as Turing.jl support of equation solvers from the outside, i.e. how the tools of differentiable programming allows equation solver libraries to be compatible with PPLs without requiring any co-development between the communities. We will discuss how this has enabled many advanced methods, such as adaptive solvers for stochastic differential equations and nonlinear tearing of differential-algebraic equations, to be integrated into the Turing.jl environment with no development effort required, and how this enables many workflows in scientific machine learning (SciML).
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