EPR-Net: Constructing non-equilibrium potential landscape via a variational force projection formulation

TL;DR

EPR-Net is a deep learning method that constructs potential landscapes for high-dimensional non-equilibrium systems, simultaneously estimating entropy production rate with high accuracy and robustness.

Contribution

It introduces a variational force projection framework that effectively constructs landscapes and estimates entropy production rate in complex biophysical systems.

Findings

Outperforms existing methods in accuracy and robustness

Successfully applied to 8D and 52D biophysical problems

Provides insights into high-dimensional non-equilibrium landscapes

Abstract

We present EPR-Net, a novel and effective deep learning approach that tackles a crucial challenge in biophysics: constructing potential landscapes for high-dimensional non-equilibrium steady-state (NESS) systems. EPR-Net leverages a nice mathematical fact that the desired negative potential gradient is simply the orthogonal projection of the driving force of the underlying dynamics in a weighted inner-product space. Remarkably, our loss function has an intimate connection with the steady entropy production rate (EPR), enabling simultaneous landscape construction and EPR estimation. We introduce an enhanced learning strategy for systems with small noise, and extend our framework to include dimensionality reduction and state-dependent diffusion coefficient case in a unified fashion. Comparative evaluations on benchmark problems demonstrate the superior accuracy, effectiveness, and robustness of EPR-Net compared to existing methods. We apply our approach to challenging biophysical problems, such as an 8D limit cycle and a 52D multi-stability problem, which provide accurate solutions and interesting insights on constructed landscapes. With its versatility and power, EPR-Net offers a promising solution for diverse landscape construction problems in biophysics.