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We describe a simple stochastic method, so-called Langevin approach, which enables one to extract evolution equations of stochastic variables from a set of measurements. Our method is parameter-free and it is based on the nonlinear Langevin…
A Generalized Langevin Equation with exponential memory is proposed for the dynamics of a massive intruder in a dense granular fluid. The model reproduces numerical correlation and response functions, violating the equilibrium Fluctuation…
Stochastic Gradient Langevin Dynamics (SGLD) is a popular variant of Stochastic Gradient Descent, where properly scaled isotropic Gaussian noise is added to an unbiased estimate of the gradient at each iteration. This modest change allows…
In stochastic quantisation, quantum mechanical expectation values are computed as averages over the time history of a stochastic process described by a Langevin equation. Complex stochastic quantisation, though theoretically not rigorously…
A complete understanding of physical systems requires models that are accurate and obeys natural conservation laws. Recent trends in representation learning involve learning Lagrangian from data rather than the direct discovery of governing…
A novel framework for the analysis of observation statistics on time discrete linear evolutions in Banach space is presented. The model differs from traditional models for stochastic processes and, in particular, clearly distinguishes…
Agent-based models typically treat systems in isolation, discarding environmental coupling as either computationally prohibitive or dynamically irrelevant. We demonstrate that this neglect misses essential physics: environmental degrees of…
We present a novel learning framework that consistently embeds underlying physics while bypassing a significant drawback of most modern, data-driven coarse-grained approaches in the context of molecular dynamics (MD), i.e., the availability…
Probabilistic graphical models (PGMs) are widely used to discover latent structure in data, but their success hinges on selecting an appropriate model design. In practice, model specification is difficult and often requires iterative…
We propose a scalable, approximate inference hypernetwork framework for a general model of history-dependent processes. The flexible data model is based on a neural ordinary differential equation (NODE) representing the evolution of…
We develop interacting particle algorithms for learning latent variable models with energy-based priors. To do so, we leverage recent developments in particle-based methods for solving maximum marginal likelihood estimation (MMLE) problems.…
Standard GPs offer a flexible modelling tool for well-behaved processes. However, deviations from Gaussianity are expected to appear in real world datasets, with structural outliers and shocks routinely observed. In these cases GPs can fail…
Understanding and predicting the glassy dynamics of polymers remain fundamental challenges in soft matter physics. While the Elastically Collective Nonlinear Langevin Equation (ECNLE) theory has been successful in describing relaxation…
Generalized Langevin equations (GLEs) can be systematically derived via dimensional reduction from high-dimensional microscopic systems. For linear models the derivation can either be based on projection operator techniques such as the…
Dynamical systems that evolve continuously over time are ubiquitous throughout science and engineering. Machine learning (ML) provides data-driven approaches to model and predict the dynamics of such systems. A core issue with this approach…
The Generalized Langevin Equation, in history, arises as a natural fix for the rather traditional Langevin equation when the random force is no longer memoryless. It has been proved that with fractional Gaussian noise (fGn) mostly…
There remains an open question about the usefulness and the interpretation of Machine learning (MLE) approaches for discrimination of spatial patterns of brain images between samples or activation states. In the last few decades, these…
This paper presents a general neural network framework for solving quantum few-body systems, extending prior methods to handle diverse particle masses, interaction types, and system configurations. Our architecture, which combines an…
Machine learning has proven to be a valuable tool to approximate functions in high-dimensional spaces. Unfortunately, analysis of these models to extract the relevant physics is never as easy as applying machine learning to a large dataset…
Many living and complex systems exhibit second order emergent dynamics. Limited experimental access to the configurational degrees of freedom results in data that appears to be generated by a non-Markovian process. This poses a challenge in…