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Scalable Gradients for Stochastic Differential Equations

by   Xuechen Li, et al.

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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Code Repositories


Differentiable SDE solvers with GPU support and efficient sensitivity analysis.

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Code for "Infinitely Deep Bayesian Neural Networks with Stochastic Differential Equations"

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