General Events - Department of Mathematics

Title: Variational Neural Networks for Observable Thermodynamics (V-NOTS)

Abstract: Much attention has recently been devoted to the data-based computing of physical system evolution. In such approaches, data from past trajectories is used to reconstruct equations of motion and/or predict future evolution of the system. However, a significant challenge arises when the available data does not correspond to the variables that actually define the system's full phase space. A simple example of this difficulty is a thrown rock: we can easily observe the position and velocity, but we cannot infer the momentum, which is mass times velocity, purely from observations. In this work, we focus on the case of dissipative dynamical systems, where the phase space consists of coordinates, momenta, and entropies. In general, while coordinates are observable, the associated momenta and entropies are not.

To address this difficulty, we develop Variational Neural Networks for Observable Thermodynamics (V-NOTS) that operate exclusively on observable variables. The novelty of the approach lies in the thermodynamic Lagrangian, coupled with the design of neural networks that inherently respect thermodynamic constraints, guaranteeing non-decreasing entropy evolution. We show that this structure-preserving network provides an efficient description of phase space evolution, achieving high accuracy with a limited number of data points and relatively few parameters. We address several non-trivial examples and show the fundamental limitations of the method due to ambiguity in the dynamics equations' signatures based on the observable variables.