Fig. 1: Overall workflow of the proposed approach.
From: Constructing custom thermodynamics using deep learning
Given a complex system described by X, the goal is to model the behavior of macroscopic coordinates of interest Z*. We construct closure coordinates \(\hat{{\boldsymbol{Z}}}\) and closed (dynamical) equation on the combined reduced coordinates \({\boldsymbol{Z}}=({\boldsymbol{{Z}}}^{* },\hat{\boldsymbol{{Z}}})\). The classical ideal-gas law is an illustration of this process (top). For general non-equilibrium, dynamic systems (bottom), carrying out this workflow from theoretical analysis is challenging. Our machine learning method (middle) addresses this by simultaneously constructing the closure coordinates using PCA-ResNet (Methods), and governing equations on reduced coordinates using the S-OnsagerNet with drift term −(M(Z) + W(Z))∇V(Z) and noise term σ(Z) (see equation (2)).
