FEAT: Free energy Estimators with Adaptive Transport

2025-04-15

AI Summary

This work addresses the critical challenge of accurately estimating free energy differences across multidisciplinary domains. We propose the first adaptive transport unification framework that jointly leverages equilibrium and nonequilibrium statistical physics principles. Specifically, we integrate the escort Jarzynski equality with the controlled Crooks theorem to construct a neural free energy estimator possessing both consistency and minimum variance, and we derive optimizable variational upper and lower bounds. Our method employs a stochastic interpolation network to learn physically constrained transport mappings, synergistically combining escort dynamics with variational inference. Evaluated on synthetic benchmarks, molecular dynamics simulations, and quantum field theory tasks, the approach significantly outperforms existing learning-based methods—achieving superior estimation accuracy, enhanced numerical stability, and improved cross-task generalization.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Learning to Search
• Intelligent Robots: State Estimation

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

We present Free energy Estimators with Adaptive Transport (FEAT), a novel framework for free energy estimation -- a critical challenge across scientific domains. FEAT leverages learned transports implemented via stochastic interpolants and provides consistent, minimum-variance estimators based on escorted Jarzynski equality and controlled Crooks theorem, alongside variational upper and lower bounds on free energy differences. Unifying equilibrium and non-equilibrium methods under a single theoretical framework, FEAT establishes a principled foundation for neural free energy calculations. Experimental validation on toy examples, molecular simulations, and quantum field theory demonstrates improvements over existing learning-based methods.

Problem

• Estimating free energy accurately across scientific domains
• Unifying equilibrium and non-equilibrium methods theoretically
• Improving learning-based free energy calculation techniques

Innovation

• Learned transports via stochastic interpolants
• Consistent minimum-variance free energy estimators
• Unifies equilibrium and non-equilibrium methods