Zhao Yue, Zhang Wei, Li Tiejun
Center for Data Science, Peking University, Beijing 100871, China.
Zuse Institute Berlin, Berlin 14195, Germany.
Natl Sci Rev. 2024 Feb 20;11(7):nwae052. doi: 10.1093/nsr/nwae052. eCollection 2024 Jul.
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.
我们提出了EPR-Net，这是一种新颖且有效的深度学习方法，用于解决生物物理学中的一个关键挑战：为高维非平衡稳态系统构建势能面。EPR-Net利用了一个很好的数学事实，即在加权内积空间中，所需的负势能梯度简单地是基础动力学驱动力的正交投影。值得注意的是，我们的损失函数与稳态熵产生率（EPR）有着密切的联系，能够同时进行势能面构建和EPR估计。我们为小噪声系统引入了一种增强学习策略，并以统一的方式将我们的框架扩展到包括降维和状态依赖扩散系数的情况。在基准问题上的比较评估表明，与现有方法相比，EPR-Net具有更高的准确性、有效性和鲁棒性。我们将我们的方法应用于具有挑战性的生物物理问题，如八维（8D）极限环和52维多稳定性问题，这些问题为构建的势能面提供了准确的解决方案和有趣的见解。凭借其通用性和强大功能，EPR-Net为生物物理学中各种势能面构建问题提供了一个有前途的解决方案。
