Conditional Score-Based Modeling of Effective Langevin Dynamics

2026-06-16 · Source: stat.ML updates on arXiv.org · Field: Science & Research — Mathematics & Computational Sciences, Physical Sciences & Chemistry, Engineering & Applied Sciences · Depth: Expert, extended

Summary

A new data-driven calibration method introduces conditional score-based modeling for effective Langevin dynamics, addressing challenges in estimating drift and diffusion coefficients for stochastic reduced-order models. This approach establishes a novel relationship between model coefficients and the conditional score of the finite-time transition density, defined as the gradient of the logarithm of the transition density with respect to the initial state. The method constrains the drift and diffusion structure directly from finite-lag statistics, avoiding computationally expensive or unreliable techniques like trajectory differentiation, state-space partitioning, or repeated model integration. It formulates the problem as a least-squares fit over stationary lagged pairs. Validated on analytically tractable and data-driven nonequilibrium diffusions, the inferred models preserve invariant statistics and accurately reproduce finite-lag dynamical correlations, offering a scalable route for learning stochastic reduced-order models.

Key takeaway

For research scientists developing reduced-order models for complex dynamical systems, this conditional score-based framework offers a robust alternative to traditional calibration methods. You can directly infer state-dependent mobility from finite-lag data, ensuring accurate reproduction of both invariant statistics and crucial temporal correlations. This approach avoids costly simulations and unreliable short-time derivative estimates, enabling more scalable and precise model construction for high-dimensional or sparsely sampled systems.

Key insights

A novel conditional score-based method directly infers stochastic model mobility from finite-lag data, preserving statistics and dynamics.

Principles

• Stochastic reduced models must match invariant statistics and finite-lag dynamics.
• Conditional scores link finite-lag transition statistics to state-dependent mobility.
• Nonlinear observables are crucial for identifying state-dependent mobility corrections.

Method

Estimate stationary and conditional scores from data. Formulate a least-squares problem to fit mobility by matching observed lagged correlation derivatives, avoiding forward simulation.

In practice

• Use denoising score matching to estimate stationary and conditional scores.
• Employ nonlinear observables (e.g., "x^alpha" for "alpha != 1") to constrain state-dependent mobility.

Topics

• Stochastic Reduced-Order Models
• Langevin Dynamics
• Conditional Score Functions
• Denoising Score Matching
• Lagged Correlation Functions
• Koopman Operator Theory

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.