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Probably one of the most striking examples of the close connections between global optimization processes and statistical physics is the simulated annealing method, inspired by the famous Monte Carlo algorithm devised by Metropolis et al.…

In physics, complex systems are often simplified into minimal, solvable models that retain only the core principles. In machine learning, layerwise linear models (e.g., linear neural networks) act as simplified representations of neural…

The linear Markov Decision Process (MDP) framework offers a principled foundation for reinforcement learning (RL) with strong theoretical guarantees and sample efficiency. However, its restrictive assumption-that both transition dynamics…

This article is concerned with learning and stochastic control in physical systems which contain unknown input signals. These unknown signals are modeled as Gaussian processes (GP) with certain parametrized covariance structures. The…

A major stumbling block for statistical physics and materials science has been the lack of a uni- versal principle that allows us to understand and predict elementary structural, morphological, and dynamical properties of non-equilibrium…

The physical significance of the stochastic processes associated to the generalized Gibbs ensembles is scrutinized here with special attention to the thermodynamic fluctuations of small systems. The contact with the environment produces an…

Latent-variable energy-based models (LVEBMs) assign a single normalized energy to joint pairs of observed data and latent variables, offering expressive generative modeling while capturing hidden structure. We recast maximum-likelihood…

These notes give a summary of techniques used in large deviation theory to study the fluctuations of time-additive quantities, called dynamical observables, defined in the context of Langevin-type equations, which model equilibrium and…

Context. Machine-Learning (ML) solves problems by learning patterns from data, with limited or no human guidance. In Astronomy, it is mainly applied to large observational datasets, e.g. for morphological galaxy classification. Aims. We…

The mean-field Langevin dynamics (MFLD) is a nonlinear generalization of the Langevin dynamics that incorporates a distribution-dependent drift, and it naturally arises from the optimization of two-layer neural networks via (noisy) gradient…

Generalized Langevin equations with non-linear forces and position-dependent linear friction memory kernels, such as commonly used to describe the effective dynamics of coarse-grained variables in molecular dynamics, are rigorously derived…

Systems exhibiting nonlinear dynamics, including but not limited to chaos, are ubiquitous across Earth Sciences such as Meteorology, Hydrology, Climate and Ecology, as well as Biology such as neural and cardiac processes. However, System…

Stochastic gradient Markov chain Monte Carlo (SG-MCMC) has become increasingly popular for simulating posterior samples in large-scale Bayesian modeling. However, existing SG-MCMC schemes are not tailored to any specific probabilistic…

The understanding of the statistical properties and of the dynamics of multistable systems is gaining more and more importance in a vast variety of scientific fields. This is especially relevant for the investigation of the tipping points…

Machine learning (ML) is transforming all areas of science. The complex and time-consuming calculations in molecular simulations are particularly suitable for a machine learning revolution and have already been profoundly impacted by the…

The Gaussian process (GP) is a popular statistical technique for stochastic function approximation and uncertainty quantification from data. GPs have been adopted into the realm of machine learning in the last two decades because of their…

One of the main questions regarding complex systems at large scales concerns the effective interactions and driving forces that emerge from the detailed microscopic properties. Coarse-grained models aim to describe complex systems in terms…

Latent variable models (LVMs) represent observed variables by parameterized functions of latent variables. Prominent examples of LVMs for unsupervised learning are probabilistic PCA or probabilistic SC which both assume a weighted linear…

Production machine learning (ML) systems fail silently -- not with crashes, but through wrong decisions. While observability is recognized as critical for ML operations, there is a lack empirical evidence of what practitioners actually…

Glassy polymers are central to engineering applications, yet their viscoelastic response over broad frequency and temperature ranges remains difficult to characterize. We extend non-affine deformation theory by incorporating a…