Constructing High-Dimensional Non-Equilibrium Potential Landscapes Using a Variational Force Projection Approach

The core message of this article is to present EPR-Net, a novel and effective deep learning approach that tackles the crucial challenge of constructing potential landscapes for high-dimensional non-equilibrium steady-state (NESS) systems. EPR-Net leverages a 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, enabling simultaneous landscape construction and entropy production rate estimation.