We present a novel yet simple deep learning approach, dubbed EPR-Net, for constructing the potential landscape of high-dimensional non-equilibrium steady state (NESS) systems. The key idea of our approach is to utilize the fact that the negative potential gradient is the orthogonal projection of the driving force in a weighted Hilbert space with respect to the steady-state distribution. The constructed loss function also coincides with the entropy production rate (EPR) formula in NESS theory. This approach can be extended to dealing with dimensionality reduction and state-dependent diffusion coefficients in a unified fashion. The robustness and effectiveness of the proposed approach are demonstrated by numerical studies of several high-dimensional biophysical models with multi-stability, limit cycle, or strange attractor with non-vanishing noise.
翻译:我们提出了一个新颖而简单的深层次学习方法,称为EMPR-Net,用于构建高维非平衡稳定状态(NESS)系统的潜在景观。我们方法的关键理念是利用以下事实:负潜在梯度是加权Hilbert空间动力对稳定状态分布的正方位预测。构建的损失函数也与 NESS 理论中的恒温生产率(EPR)公式相吻合。这一方法可以推广到以统一的方式处理维度减少和以国家为依存的传播系数。拟议方法的稳健性和有效性表现在对多个高维生物物理模型进行的数字研究上,这些模型具有多稳定性、极限循环,或具有非消散噪音的奇异吸引器。