Generalized physics-informed learning through language-wide differentiable programming

Copyright © 2020, for this paper by its authors. Scientific computing is increasingly incorporating the advancements in machine learning to allow for data-driven physics-informed modeling approaches. However, re-targeting existing scientific computing workloads to machine learning frameworks is both costly and limiting, as scientific simulations tend to use the full feature set of a general purpose programming language. In this manuscript we develop an infrastructure for incorporating deep learning into existing scientific computing code through Differentiable Programming (∂P). We describe a ∂P system that is able to take gradients of full Julia programs, making Automatic Differentiation a first class language feature and compatibility with deep learning pervasive. Our system utilizes the one-language nature of Julia package development to augment the existing package ecosystem with deep learning, supporting almost all language constructs (control flow, recursion, mutation, etc.) while generating high-performance code without requiring any user intervention or refactoring to stage computations. We showcase several examples of physics-informed learning which directly utilizes this extension to existing simulation code: neural surrogate models, machine learning on simulated quantum hardware, and data-driven stochastic dynamical model discovery with neural stochastic differential equations