Repository: Freie Universit├Ąt Berlin, Math Department

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

Zhao, Yue and Zhang, Wei and Li, Tiejun (2024) EPR-Net: Constructing non-equilibrium potential landscape via a variational force projection formulation. National Science Review .

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Official URL: https://doi.org/10.1093/nsr/nwae052

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.

Item Type:Article
Subjects:Mathematical and Computer Sciences
Mathematical and Computer Sciences > Mathematics
Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
ID Code:3127
Deposited By: Lukas-Maximilian Jaeger
Deposited On:26 Feb 2024 11:52
Last Modified:26 Feb 2024 11:52

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