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

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外文摘要：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 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 the 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 eight-dimensional(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.

外文关键词：

high-dimensional potential landscapenon-equilibrium systementropy production ratedimensionality reductiondeep learning

作者：

Yue Zhao、Wei Zhang、Tiejun Li

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作者单位：

Center for Data Science,Peking University,Beijing 100871,China

Zuse Institute Berlin,Berlin 14195,Germany

Department of Mathematics and Computer Science,Freie Universität Berlin,Berlin 14195,Germany

Laboratory of Mathematics and Applied Mathematics(LMAM)and School of Mathematical Sciences,Peking University,Beijing 100871,China

Center for Machine Learning Research,Peking University,Beijing 100871,China

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基金：

National Natural Science Foundational of ChinaNational Natural Science Foundational of ChinaMinistry of Science and Technology of ChinaDeutsche Forschungsgemeinschaft(DFG)under Germanys Excellence StrategyBerlin Mathematics Research Centre MATH+Berlin Mathematics Research Centre MATH+DFG through Grant CRC 1114'Scaling Cascades in Complex Systems'

项目编号：

11825102122881012021YFA1003301EXC-2046/1390685689235221301

出版年：

2024

DOI：

10.1093/nsr/nwae052

国家科学评论(英文版)

CSTPCD

ISSN：

年,卷(期)：2024.11(7)