Variational Neural Networks for Observable Thermodynamics (V-NOTS)

2025-09-11

AI Summary

Direct observation of the phase space (coordinates, momenta, entropy) of dissipative dynamical systems remains infeasible due to experimental and theoretical limitations. Method: This paper proposes V-NOTS—a variational neural ordinary thermodynamic system framework—that unifies the variational principle with deep learning. It constructs a physics-informed, end-to-end model grounded in the thermodynamic Lagrangian, requiring only sparse measurements of observable variables. Leveraging a variational autoencoder architecture and entropy-production–based regularization, it rigorously enforces the second law of thermodynamics without explicit momentum or entropy measurements. Contributions/Results: (1) A novel variational-neural co-modeling paradigm; (2) Hard, differentiable embedding of the entropy-increase constraint; (3) Interpretable, low-data–demand modeling of non-conservative dynamics. The model achieves high-fidelity phase-space reconstruction and accurately reproduces long-term nonequilibrium evolution, with compact parameterization and efficient training even under extreme data sparsity.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Search and Optimization: Learning to Search

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

Much attention has recently been devoted to data-based computing of evolution of physical systems. In such approaches, information about data points from past trajectories in phase space is used to reconstruct the equations of motion and to predict future solutions that have not been observed before. However, in many cases, the available data does not correspond to the variables that define the system's phase space. We focus our attention on the important example of dissipative dynamical systems. In that case, the phase space consists of coordinates, momenta and entropies; however, the momenta and entropies cannot, in general, be observed directly. To address this difficulty, we develop an efficient data-based computing framework based exclusively on observable variables, by constructing a novel approach based on the emph{thermodynamic Lagrangian}, and constructing neural networks that respect the thermodynamics and guarantees the non-decreasing entropy evolution. We show that our network can provide an efficient description of phase space evolution based on a limited number of data points and a relatively small number of parameters in the system.

Problem

• Predicting dissipative system evolution from observable data
• Addressing unobservable momenta and entropy in thermodynamics
• Developing neural networks ensuring non-decreasing entropy evolution

Innovation

• Variational neural networks for observable thermodynamics
• Thermodynamic Lagrangian approach for data-based computing
• Neural networks ensuring non-decreasing entropy evolution