The review explores how control theory, optimal transport, probabilistic inference, non‑equilibrium thermodynamics, and machine learning are interconnected through the optimization of free‑energy‑like functionals under dynamical or statistical constraints. It presents a conceptual thread linking these five fields and illustrates the ideas with applications in reinforcement learning, variational inference, and generative modeling. The article is written for readers without prior familiarity, beginning with physics principles.
By Emmy Blumenthal, Nikolas Claussen, Benjamin Eysenbach, Catherine Ji, Gautam Reddy, Colin Scheibner, Benjamin Sorkin
Nonlinear GENERIC-Embedded Neural Networks (N-GENNs) are a deep learning framework designed to discover evolution equations for systems governed by the nonlinear GENERIC formalism. The method incorporates generalized gradient flows through convex dissipation potentials, allowing it to capture a wider range of thermodynamically consistent dynamics, including those with non‑quadratic dissipation potentials. Thermodynamic structure is enforced by construction, ensuring compliance with the first and second laws, and the approach is validated on a harmonic oscillator with a heat bath, an idealized chemical motor, and a one‑dimensional viscoplastic Perzyna model.
By Vojt\v{e}ch Votruba, Zequn He, Weilun Qiu, Celia Reina, Michal Pavelka
arXiv:2606. 09112v1 Announce Type: cross Abstract: The rapid evolution of artificial intelligence has led to substantial advances in deep neural networks.
By Chen-Rui Fan, Bo Lu, Xing-Yu Wu, Tie-Jun Wang, Chuan Wang
arXiv:2606. 15444v1 Announce Type: cross Abstract: In this paper we show that the physical learning methods known as coupled learning (CL) and equilibrium propagation (EP) conserve a mass-like quantity in the trainable parameters in the continuous-time, small-nudging limit.
By Joshua A. McGinnis, Adam G. Kline, Yoichiro Mori
arXiv:2607. 23940v1 Announce Type: new Abstract: Physics-Informed Neural Networks (PINNs) solve differential equations by minimizing the residual of a nonlinear operator over a neural parameterization of the solution.
By Pavlos Protopapas, Kaylee Vo
arXiv:2606. 15443v1 Announce Type: cross Abstract: Physical learning methods train physical networks to perform computational tasks using only local update rules, exploiting the physics of the system to handle the global transfer of information.
By Joshua A. McGinnis, Xinbo Li, Yoichiro Mori
arXiv:2607. 16177v1 Announce Type: new Abstract: Reinforcement learning (RL) has recently emerged as a promising feedback control strategy for nonlinear and complex dynamical systems.
By Matteo Tomasetto, Nicol\`o Botteghi, Gabriele Bruni, Andrea Manzoni
arXiv:2510. 16084v3 Announce Type: replace Abstract: Backpropagation learning algorithm, the workhorse of modern artificial intelligence, is notoriously difficult to implement in physical neural networks.
By Karol Sajnok, Micha{\l} Matuszewski
arXiv:2606. 30064v1 Announce Type: new Abstract: We introduce a data-driven probabilistic framework for learning systems based on Gibbs measures on hierarchical structures.
By L. U. Abdullaev, F. Herrera, U. A. Rozikov, M. V. Velasco
arXiv:2606. 04476v1 Announce Type: new Abstract: In this paper, we study the gradient descent dynamics for jointly training both layers of a one-hidden-layer ReLU network to fit a linear target function.
By Berk Tinaz, Changzhi Xie, Mahdi Soltanolkotabi
arXiv:2607. 20152v1 Announce Type: cross Abstract: Active Inference (AIF) frames adaptive behavior as the minimization of expected free energy (EFE), combining epistemic and pragmatic objectives within a single variational principle.
By Nikola Milosevic, Nicol\'as Hinrichs, Nico Scherf
The paper introduces the Physics-Informed Stochastic Configuration Machine (PI‑SCM), a backpropagation‑free neural network designed for solving nonlinear differential equations. By analytically evaluating local Jacobians, PI‑SCM linearizes the physical loss, enabling optimal weight determination through generalized linear least squares and avoiding iterative nonlinear optimization. The authors present a progressive algorithmic suite—PI‑SC‑I, PI‑SC‑II, and PI‑SC‑III—prove their universal approximation properties, and show through experiments that PI‑SCM achieves high‑fidelity predictions and parameter identification while accelerating training by orders of magnitude compared to standard PINNs.
By Yuehao Song (School of Automation, Central South University, Changsha, China), Zhong Chen (School of Automation, Central South University, Changsha, China), Lihui Cen (School of Automation, Central South University, Changsha, China), Liang Wu (Johns Hopkins University, Baltimore, USA), Kai Zhang (State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing, China)