# Learning Stochastic Thermodynamics Directly from Correlation and Trajectory-Fluctuation Currents

arXiv: https://arxiv.org/abs/2504.19007 · HTML: https://mlsanity.com/paper/2504.19007/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 57 references that are in the map.
- First posted on arXiv 26 Apr 2025.

## Builds on (most cited first, 6 of 6)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Predicting Many Properties of a Quantum System from Very Few Measurements](https://mlsanity.com/paper/2002.08953/) (2020)
- [Deep learning probability flows and entropy production rates in active matter](https://mlsanity.com/paper/2309.12991/) (2023)
- [Learning entropy production via neural networks](https://mlsanity.com/paper/2003.04166/) (2020)
- [Inferring the Langevin Equation with Uncertainty via Bayesian Neural Networks](https://mlsanity.com/paper/2402.01338/) (2024)

## Built on by (most cited first, 1 of 1)

- [First-Order Trajectory Matching: Fast Ensemble Predictions of Chaotic, Turbulent, Stochastic Systems](https://mlsanity.com/paper/2606.11138/) (2026)

## Abstract (arXiv)

Markedly increased computational power and data acquisition have led to growing interest in data-driven inverse dynamics problems. These seek to answer a fundamental question: What can we learn from time series measurements of a complex dynamical system? For small systems interacting with external environments, the effective dynamics are inherently stochastic, making it crucial to properly manage noise in data. Here, we explore this for systems obeying Langevin dynamics and, using currents, we construct a learning framework for stochastic modeling. Currents have recently gained increased attention for their role in bounding entropy production (EP) from thermodynamic uncertainty relations (TURs). We introduce a fundamental relationship between the cumulant currents there and standard machine-learning loss functions. Using this, we derive loss functions for several key thermodynamic functions directly from the system dynamics without the (common) intermediate step of deriving a TUR. These loss functions reproduce results derived both from TURs and other methods. More significantly, they open a path to discover new loss functions for previously inaccessible quantities. Notably, this includes access to per-trajectory entropy production, even if the observed system is driven far from its steady-state. We also consider higher order estimation. Our method is straightforward and unifies dynamic inference with recent approaches to entropy production estimation. Taken altogether, this reveals a deep connection between diffusion models in machine learning and entropy production estimation in stochastic thermodynamics.