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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 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.
摘要：
我们介绍EPR-Net，一种新颖而有效的深度学习方法，解决了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潜在景观。EPR-Net利用了一个很好的数学事实，即所需的负电势梯度只是加权内积空间中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定熵生产率(EPR)密切相关，能够同时进行景观建设和EPR估算。我们为噪声小的系统引入了增强的学习策略，并扩展我们的框架，以统一的方式包括降维和状态相关的扩散系数情况。对基准问题的比较评估证明了更高的准确性，与现有方法相比，EPR-Net的有效性和鲁棒性。我们将我们的方法应用于挑战生物物理问题，例如八维(8D)极限环和52D多稳定性问题，它提供了准确的解决方案和对建筑景观的有趣见解。凭借其多功能性和强大功能，EPR-Net为生物物理学中的各种景观建设问题提供了有希望的解决方案。
