# Learning entropy production via neural networks

arXiv: https://arxiv.org/abs/2003.04166 · HTML: https://mlsanity.com/paper/2003.04166/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Mar 2020.

## Built on by (most cited first, 10 of 10)

- [Foundation Inference Models for Markov Jump Processes](https://mlsanity.com/paper/2406.06419/) (2024)
- [Inferring the Langevin Equation with Uncertainty via Bayesian Neural Networks](https://mlsanity.com/paper/2402.01338/) (2024)
- [Using Entropy Measures for Monitoring the Evolution of Activity Patterns](https://mlsanity.com/paper/2210.01736/) (2022)
- [Learning Stochastic Thermodynamics Directly from Correlation and Trajectory-Fluctuation Currents](https://mlsanity.com/paper/2504.19007/) (2025)
- [Inferring entropy production in many-body systems using nonequilibrium maximum entropy](https://mlsanity.com/paper/2505.10444/) (2025)
- [Attaining entropy production and dissipation maps from Brownian movies via neural networks](https://mlsanity.com/paper/2106.15108/) (2021)
- [Information Theory Inspired Pattern Analysis for Time-series Data](https://mlsanity.com/paper/2302.11654/) (2023)
- [Optimal Computation from Fluctuation Responses](https://mlsanity.com/paper/2510.03900/) (2025)
- [Reconciling Causality and Non-Equilibrium Thermodynamics with Hamiltonian Causal Models](https://mlsanity.com/paper/2606.04822/) (2026)
- [A Path-Space Formulation of Prediction in World Models: From a Single Action to Prediction, Planning, and Irreversibility](https://mlsanity.com/paper/2606.28751/) (2026)

## Abstract (arXiv)

This Letter presents a neural estimator for entropy production, or NEEP, that estimates entropy production (EP) from trajectories of relevant variables without detailed information on the system dynamics. For steady state, we rigorously prove that the estimator, which can be built up from different choices of deep neural networks, provides stochastic EP by optimizing the objective function proposed here. We verify the NEEP with the stochastic processes of the bead-spring and discrete flashing ratchet models, and also demonstrate that our method is applicable to high-dimensional data and can provide coarse-grained EP for Markov systems with unobservable states.