Tangent Schrödinger Bridge Matching: Learning Stochastic Transport with Mechanistic Sensitivities

2026-10-02

AI Summary

This study addresses the challenge that predicting interventions on stochastic system parameters relies on costly simulations, while existing models tend to degenerate into merely matching observational distributions by neglecting mechanistic sensitivity. To overcome this, we propose Tangent Schrödinger Bridge Matching, which pioneers the incorporation of mechanistic sensitivity supervision into the bridge matching framework. By jointly learning trajectories and parameter derivatives, combined with a dual-independent sampling objective to optimize mean responses, our approach eliminates estimation bias. We further establish theoretical bounds linking sensitivity precision to decision regret. Evaluated on PDE reaction-diffusion and Navier-Stokes fluid simulations, the proposed method significantly enhances parameter sensitivity estimation and counterfactual prediction accuracy. It rigorously preserves endpoint distribution consistency while effectively reducing tracking error in viscosity selection tasks.

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.

Problem

• Stochastic systems
• Mechanistic sensitivities
• Schrödinger Bridge Matching
• Intervention response
• Parameter derivatives

Innovation

• Tangent Schrödinger Bridge Matching
• mechanistic sensitivities
• stochastic transport
• parameter derivatives
• decision regret