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.
arXiv:2602. 03670v2 Announce Type: replace-cross Abstract: Equilibrium Propagation (EP) is a physics-inspired learning algorithm that uses stationary states of a dynamical system both for inference and learning.
arXiv:2604.14765v2 Announce Type: replace Abstract: We present a geometric framework for Reinforcement Learning (RL) that views policies as maps into the Wasserstein space of action probabilities. Fi...
arXiv:2606. 30064v1 Announce Type: new Abstract: We introduce a data-driven probabilistic framework for learning systems based on Gibbs measures on hierarchical structures.
We introduce a data-driven probabilistic framework for learning systems based on Gibbs measures on hierarchical structures. Unlike standard empirical risk minimization, where a dataset is used to identify a single optimal parameter, our approach transforms the empirical loss function into an interaction potential defining an energy-based model.
arXiv:2601. 21284v2 Announce Type: replace-cross Abstract: Diffusion models have emerged as powerful generative tools for modeling complex data distributions, yet their purely data-driven nature limits applicability in engineering and scientific problems where physical laws must be respected.
arXiv:2608. 02844v1 Announce Type: cross Abstract: We develop a class of diffusion-based stochastic particle optimisation methods for loss functions with intractable gradients.
arXiv:2509.26364v3 Announce Type: replace Abstract: The Schr\"odinger bridge problem is concerned with finding a stochastic dynamical system bridging two marginal distributions that minimises a certa...
arXiv:2609.17736v1 Announce Type: cross Abstract: Most molecular transitions occur on timescales far beyond direct molecular dynamics simulations. The committor, the probability that a configuration...
arXiv:2603. 11249v4 Announce Type: replace Abstract: Accurate prediction of phase equilibria remains a central challenge in chemical engineering.
arXiv:2608. 12624v1 Announce Type: new Abstract: Structure-preserving machine learning embeds physical structure directly into model architectures, yet uncertainty quantification (UQ) for such hard-constrained models remains limited because standard UQ methods may violate the encoded admissibility conditions, require architectural modifications, or impose substantial computational costs.
arXiv:2505. 06589v2 Announce Type: replace-cross Abstract: Modern machine learning repeatedly manipulates probability measures: empirical datasets, generated samples, latent distributions, class-conditional laws, particle systems, weights of wide networks and attention patterns.
The paper presents a differentiable hybrid modelling framework that combines a JAX finite volume population balance solver with learnable neural network components. This approach learns constitutive laws and initial conditions directly from experimental data, improving the fidelity of transport models in chemical engineering. The framework’s differentiability also enables optimisation of experimental settings for desired process outcomes.