Scalable Gradients for Stochastic Differential Equations

Code

• github.com/google-research/torchsde
  OfficialIn paperpytorch★ 1,708
• github.com/xwinxu/bayesian-sde
  jax★ 173
• github.com/xwinxu/bayesde
  jax★ 173
• github.com/JFagin/latent_SDE
  pytorch★ 2

Abstract

The adjoint sensitivity method scalably computes gradients of solutions to ordinary differential equations. We generalize this method to stochastic differential equations, allowing time-efficient and constant-memory computation of gradients with high-order adaptive solvers. Specifically, we derive a stochastic differential equation whose solution is the gradient, a memory-efficient algorithm for caching noise, and conditions under which numerical solutions converge. In addition, we combine our method with gradient-based stochastic variational inference for latent stochastic differential equations. We use our method to fit stochastic dynamics defined by neural networks, achieving competitive performance on a 50-dimensional motion capture dataset.

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Reproductions