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BP: Fachverband Biologische Physik

BP 20: Statistical Physics of Biological Systems I (joint session BP/DY)

BP 20.4: Vortrag

Mittwoch, 19. März 2025, 15:45–16:00, H44

Learning the Equilibrium Free Energy from Non-Equilibrium Steady States with Denoising Diffusion Models — •Daniel Nagel and Tristan Bereau — Institute for Theoretical Physics, Heidelberg University, 69120 Heidelberg, Germany

Estimating accurate free energy profiles is crucial for predicting the behavior of complex molecular systems. While biased molecular dynamics simulations enhance the sampling of rare events, extracting reliable free energy landscapes from these simulations remains challenging. On the other hand, stochastic thermodynamics, i.e. the concept of entropy production, provides valuable insights into the dynamics of complex systems in non-equilibrium states. However, its computational complexity, due to dependence on time-dependent probability distributions, limits its application to smaller systems.

This work presents a novel approach that combines stochastic thermodynamics with the established machine learning technique of denoising diffusion models to efficiently estimate free energy profiles from biased non-equilibrium steady states. By linking the diffusion and simulation times, we show that the training objective, known as the score, can be decomposed into a non-trivial conservative contribution from the equilibrium potential and a trivial non-conservative part determined by external driving forces. To showcase the effectiveness of our approach and its ability to learn equilibrium free energy profiles, we apply it to a driven toy model and a Martini force field molecular dynamics simulation of a small molecule biased through a lipid bilayer.

Keywords: free energy estimation; diffusion model; stochastic thermodynamics; molecular dynamics; machine learning