PORT-METRIPLECTIC NEURAL NETWORKS - Thermodynamics-Informed Machine Learning of Complex Physical Systems

Aug 4, 2026

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Port-metriplectic neural networks are developed for learning complex physical systems from data using the port-Hamiltonian formalism. The method enforces thermodynamic principles by construction, guaranteeing conservation of energy and non-negative entropy production. To achieve this, the port-Hamiltonian framework is modified into a port-metriplectic one, enabling deep network architectures that learn system physics in a decomposed, compositional manner through energy ports. The approach supports predictions at both partial and full-system scales and is evaluated with reported performance examples.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages9

Reading Time23 min

AccessFree to download

Introduction

Learned simulators and inductive biases

Port-Hamiltonian to port-metriplectic extension

Hamiltonian neural networks

Reversible dynamics as an inductive bias

arXiv :2211 .01873v3 [ cs .LG] 17 Feb 2023 PORT-METRIPLECTIC NEURAL NETWORKS: THERMODYNAMICS-INFORMED MACHINE LEARNING OF COMPLEX PHYSICAL SYSTEMS Quercus Hernández 1 , Alberto Badías2 , Francisco Chinesta3,4 , and Elías Cueto 1 1Aragon Institute of Engineering Research (I3A) . University of Zaragoza. Zaragoza, Spain. 2Higher Technical School of Industrial Engineering, Polytechnic University of Madrid. Madrid, Spain. 3ESI Group chair. PIMM Lab. ENSAM Institute of Technology. Paris, France. 4CNRS@CREATE LTD. Singapore. February 20, 2023 ABSTRACT We develop inductive biases for the machine learning of complex physical systems based on the portHamiltonian formalism. To satisfy by construction the principles of thermodynamics in the learned physics (conservation of energy, non-negative entropy production), we modify accordingly the portHamiltonian formalism so as to achieve a port-metriplectic one. We show that the constructed networks are able to learn the physics of complex systems by parts, thus alleviating the burden associated to the experimental characterization and posterior learning process of this kind of systems. Predictions can be done, however, at the scale of the complete system. Examples are shown on the performance of the proposed technique. 1 Introduction Recently, the possibility of developing learned simulators has attracted an important research activity in the computational mechanics community and beyond. By “learned simulators” we mean methodologies able to learn from data the dynamics of a physical system so as to perform accurate predictions about previously unseen situations without the burden associated to the construction of numerical models by means of ﬁnite elements, ﬁnite volumes or similar techniques [1, 2, 3] . Among their advantages we can cite that they are based on reusable architectures, can be optimized to work under really stringent real-time feedback rates, and are specially well suited for optimization and inverse problems. While original, black-box approaches showed great promise, both industry and academia are reluctant to generalize their use, since small modiﬁcations in the input data may cause nonsense results. This is at the origin of the development and employ of inductive biases during the learning process [3, 4] . An inductive bias allows the learning algorithm to prioritize one particular solution over any other [5] . This is particularly interesting for physical phenomena for which previous knowledge exists. Paul Dirac once said that [6] `The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difﬁculty is only that the exact application of these laws leads to equations much too complicated to be soluble. ' Therefore, in the presence of centuries of knowledge about virtually any physical phenomena, it is simply nonsense to ignore it and to favor theory-blind, black-box approaches. In this paper we develop a novel strategy based on the port-Hamiltonian formalism, which we extend so as to comply with the ﬁrst and second principles of thermodynamics by construction [7, 8, 9] . Port-Hamiltonian formalisms extend the well-known Hamiltonian (thus, conservative) physics to open systems and introduce the possibility of dissipation and control through external actuation within this theory. We show here, however, that general port-Hamiltonian systems do not comply a priori with the laws of thermodynamics and modify them so as to ensure this fulﬁllment. Based on this new formalism, which we call port-metriplectic, since it is at the same time metric and symplectic, we construct a deep neural network methodology to learn the physics of complex systems from data. The resulting port-metriplectic networks will comply by construction with the principles of thermodynamics—that can be enforced through hard or soft constraints—while they allow to analyze complex sy

FAQs

What problem do port-metriplectic neural networks address?

They address learning the physics of complex physical systems from data while avoiding the need for heavy experimental characterization and conventional numerical model construction.

How does the method ensure thermodynamic consistency?

It modifies the port-Hamiltonian formalism into a port-metriplectic one so that learned dynamics satisfy conservation of energy and non-negative entropy production by construction.

Can the networks learn physics by parts or only for the full system?

The constructed networks learn the physics of complex systems by parts, and predictions can also be performed at the scale of the complete system.

Aug 4, 2026

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