Tangent Schrödinger Bridge method improves predictions of stochastic system responses
Tangent Schrödinger Bridge Matching: Learning Stochastic Transport with Mechanistic Sensitivities
Machine Learning
Summary
Predicting how systems with randomness respond to changes, like in fluid flow or reactions, usually needs expensive simulations. The authors created Tangent Schrödinger Bridge Matching, a method that learns from outcomes and their sensitivities to parameters to better predict these responses. This method not only matches what is observed but also predicts how the system reacts to changes more accurately than previous approaches. They tested it on various complex models, showing it improves predictions and helps make better decisions, such as choosing the right fluid viscosity.
What this means in practice
- •For computational fluid dynamics engineers: Enhance selection of fluid properties like viscosity by predicting system responses with better accuracy and reduced error in simulations.
- •For chemical process modelers: Improve forecast of reaction-diffusion systems’ responses to parameter changes using learned sensitivity-aware stochastic transports.
Authors
Jowaria Khan, Elizabeth Bondi-Kelly
Abstract
Predicting how stochastic systems respond to changes in viscosity, reaction rates, or external forces requires costly simulations, motivating reusable learned models. Yet matching observed outcome distributions does not ensure accurate intervention responses. We introduce Tangent Schrödinger Bridge Matching (Tangent-SBM), which learns stochastic transports from endpoint observations and mechanistic sensitivities. It propagates parameter derivatives alongside trajectories and supervises them against supplied targets. For average-response targets, single-rollout squared error also penalizes response variability; our objective uses two independent rollouts to match the mean without this additional penalty. We establish conditions under which sensitivity accuracy bounds finite-change prediction error and decision regret. Across Gaussian, stochastic double-well, PDEBench reaction--diffusion, and stochastic Navier--Stokes systems, Tangent-SBM improves sensitivity and finite-change prediction over matched conditional-bridge baselines while maintaining comparable endpoint and distributional accuracy. Controls examine target correctness, response objectives, and simulator-budget allocation. To test decision usefulness, we evaluate calibrated viscosity selection in Navier--Stokes: Tangent-SBM reduces tracking error relative to taking no action on every evaluated task.