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

作　　者：Yue Zhao Wei Zhang Tiejun Li 

机构地区：[1]Center for Data Science,Peking University,Beijing 100871,China [2]Zuse Institute Berlin,Berlin 14195,Germany [3]Department of Mathematics and Computer Science,Freie Universität Berlin,Berlin 14195,Germany [4]Laboratory of Mathematics and Applied Mathematics(LMAM)and School of Mathematical Sciences,Peking University,Beijing 100871,China [5]Center for Machine Learning Research,Peking University,Beijing 100871,China

出　　处：《National Science Review》2024年第7期129-141,共13页国家科学评论（英文版）

基　　金：support from the National Natural Science Foundational of China(11825102 and 12288101);the Ministry of Science and Technology of China(2021YFA1003301);supported by the Deutsche Forschungsgemeinschaft(DFG)under Germany’s Excellence Strategy,part of the Berlin Mathematics Research Centre MATH+(EXC-2046/1,390685689);the DFG through Grant CRC 1114‘Scaling Cascades in Complex Systems’(235221301).

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.

关 键 词：high-dimensional potential landscape non-equilibrium system entropy production rate dimensionality reduction deep learning 

分 类 号：TP333[自动化与计算机技术—计算机系统结构]