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

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.

arXiv commentAccepted for publication in National Science Review

References in corpus (15)

• Normalizing Flows: An Introduction and Review of Current Methods
• A Mean Field View of the Landscape of Two-Layers Neural Networks
• Stochastic gene expression as a many body problem
• Nonequilibrium Physics in Biology
• Stochastic Dynamical Structure (SDS) of Nonequilibrium Processes in the Absence of Detailed Balance. II: construction of SDS with nonlinear force and multiplicative noise
• Data-Driven Collective Variables for Enhanced Sampling
• DeePCG: constructing coarse-grained models via deep neural networks
• Coarse Graining Molecular Dynamics with Graph Neural Networks
• Epigenetics as a first exit problem
• Neural networks-based variationally enhanced sampling
• Mesoscopic Nonequilibrium Thermodynamics of Single Macromolecules and Dynamic Entropy-Energy Compensation
• Optimal Path to Epigenetic Switching
• Realization of Waddington's Metaphor: Potential Landscape, Quasi-potential, A-type Integral and Beyond
• Landscapes of Non-gradient Dynamics Without Detailed Balance: Stable Limit Cycles and Multiple Attractors
• A Data Driven Method for Computing Quasipotentials

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