Deep operator learning speeds up sampling for complex stochastic systems
Deep operator learning for efficient sampling from invariant measures of stochastic differential equations
Machine Learning
Summary
Sampling from complex random systems described by stochastic differential equations (SDEs) is often slow and computationally expensive. The authors created a neural network-based sampler that learns how to generate samples from a wide range of these systems after initial training. This method then produces samples quickly for new problems without the usual long wait times. They also showed that their approach works well even for very high-dimensional problems where traditional methods fail.
What this means in practice
- •For financial modelers: Quickly produce sample paths from market models governed by complex SDEs to improve risk estimation accuracy.
- •For computational physicists: Simulate particle systems with interacting stochastic dynamics faster than traditional grid or sampling methods.
Authors
Lin Guo, Li Lei, Jingtong Zhang
Abstract
We introduce an amortized neural sampler that combines operator learning with flow methods for sampling. It maps SDE coefficient functions to pushforwards from a reference measure to the invariant measures, enabling efficient sampling across families of stochastic differential equations. Our framework shifts traditional sampling cost to an initial training phase, after which new SDE instances require only one encoder pass and a few ODE solver steps, independent of mixing time. To handle problems in high dimensions, we use Lagrangian trajectory sensors for the coefficient functions and cross attention in the architecture. We also theoretically establish the expressivity and resolution invariance of our framework. Experiments on 1D and 2D SDE families show competitive accuracy with substantial speedups over MCMC in regimes with slow mixing, transfer across sensor counts, and demonstration results on a 64D interacting particle SDE where traditional grid approaches are infeasible.