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We study the convergence to equilibrium of an underdamped Langevin equation that is controlled by a linear feedback force. Specifically, we are interested in sampling the possibly multimodal invariant probability distribution of a Langevin…

Optimization and Control · Mathematics 2022-01-12 Tobias Breiten , Carsten Hartmann , Lara Neureither , Upanshu Sharma

Hyperparameter tuning is one of the essential steps to guarantee the convergence of machine learning models. We argue that intuition about the optimal choice of hyperparameters for stochastic gradient descent can be obtained by studying a…

Disordered Systems and Neural Networks · Physics 2025-12-12 Chanju Park , Biagio Lucini , Gert Aarts

The measured time series from complex systems are renowned for their intricate stochastic behavior, characterized by random fluctuations stemming from external influences and nonlinear interactions. These fluctuations take diverse forms,…

Statistical Mechanics · Physics 2025-03-19 Pyei Phyo Lin , Matthias Wächter , Joachim Peinke , M. Reza Rahimi Tabar

Pervasive across diverse domains, stochastic systems exhibit fluctuations in processes ranging from molecular dynamics to climate phenomena. The Langevin equation has served as a common mathematical model for studying such systems, enabling…

Statistical Mechanics · Physics 2025-05-01 Youngkyoung Bae , Seungwoong Ha , Hawoong Jeong

Conserved dynamical systems are generally considered to be critical. We study a class of critical routing models, equivalent to random maps, which can be solved rigorously in the thermodynamic limit. The information flow is conserved for…

Adaptation and Self-Organizing Systems · Physics 2013-01-10 Dimitrije Markovic , Andre Schuelein , Claudius Gros

This paper investigates the fundamental information-theoretic limits for the control and sensing of noiseless linear dynamical systems subject to a broad class of nonlinear observations. We analyze the interactions between the control and…

Systems and Control · Electrical Eng. & Systems 2026-01-21 Ming Li , Fan Liu , Yifeng Xiong , Jie Xu , Tao Liu

Extreme events occur across the natural, engineering, and socioeconomic sciences, where rare but high-impact episodes can lead to disproportionate consequences that pose major challenges for prediction and risk management. Existing studies…

Dynamical Systems · Mathematics 2026-05-22 Charlotte Moser , Nan Chen , Marios Andreou

Transformer-based models generate hidden states that are difficult to interpret. In this work, we analyze hidden states and modify them at inference, with a focus on motion forecasting. We use linear probing to analyze whether interpretable…

Machine Learning · Computer Science 2025-05-19 Omer Sahin Tas , Royden Wagner

Motivated by an application to empirical Bayes learning in high-dimensional regression, we study a class of Langevin diffusions in a system with random disorder, where the drift coefficient is driven by a parameter that continuously adapts…

Statistics Theory · Mathematics 2025-11-04 Zhou Fan , Justin Ko , Bruno Loureiro , Yue M. Lu , Yandi Shen

Recently, we proposed a method to estimate parameters of stochastic dynamics based on the linear response statistics. The method rests upon a nonlinear least-squares problem that takes into account the response properties that stem from the…

Numerical Analysis · Mathematics 2020-11-24 He Zhang , John Harlim , Xiantao Li

Networks of globally coupled, noise activated, bistable elements with connection time delays are considered. The dynamics of these systems is studied numerically using a Langevin description and analytically using (1) a Gaussian…

Statistical Mechanics · Physics 2009-11-11 Daniel Huber , Lev Tsimring

In this paper, we characterize the synchronization phenomenon of hyperchaotic scalar non-linear delay dynamics in a fully-developed chaos regime. Our results rely on the observation that, in that regime, the stationary statistical…

Chaotic Dynamics · Physics 2008-10-08 Adrian A. Budini

Scaling behavior is studied of several dominant eigenvalues of spectra of Markov matrices and the associated correlation times governing critical slowing down in models in the universality class of the two-dimensional Ising model. A scheme…

Condensed Matter · Physics 2009-10-30 M. P. Nightingale , H. W. J. Bloete

We study the most probable way an interface moves on a macroscopic scale from an initial to a final position within a fixed time in the context of large deviations for a stochastic microscopic lattice system of Ising spins with Kac…

Mathematical Physics · Physics 2017-03-08 P. Birmpa , N. Dirr , D. Tsagkarogiannis

Errors dynamics captures the evolution of the state errors between two distinct trajectories, that are governed by the same system rule but initiated or perturbed differently. In particular, state observer error dynamics analysis in matrix…

Systems and Control · Electrical Eng. & Systems 2023-12-21 Xinghan Li , Jianqi Chen , Han Zhang , Jieqiang Wei , Junfeng Wu

Understanding the dynamics of complex systems is a central task in many different areas ranging from biology via epidemics to economics and engineering. Unexpected behaviour of dynamic systems or even system failure is sometimes difficult…

Optimization and Control · Mathematics 2022-03-25 Dominik Kahl , Andreas Weber , Maik Kschischo

Many complex systems operating far from the equilibrium exhibit stochastic dynamics that can be described by a Langevin equation. Inferring Langevin equations from data can reveal how transient dynamics of such systems give rise to their…

Machine Learning · Statistics 2021-11-01 Mikhail Genkin , Owen Hughes , Tatiana A. Engel

Experimental measurements of physical systems often have a limited number of independent channels, causing essential dynamical variables to remain unobserved. However, many popular methods for unsupervised inference of latent dynamics from…

Machine Learning · Computer Science 2020-10-23 William Gilpin

We study the problem of system identification for stochastic continuous-time dynamics, based on a single finite-length state trajectory. We present a method for estimating the possibly unstable open-loop matrix by employing properly…

Machine Learning · Statistics 2025-09-30 Reza Sadeghi Hafshejani , Mohamad Kazem Shirani Fradonbeh

This paper considers the problem of closed-loop identification of linear scalar systems with Gaussian process noise, where the system input is determined by a deterministic state feedback policy. The regularized least-square estimate (LSE)…

Systems and Control · Electrical Eng. & Systems 2020-03-30 Ali Reza Pedram , Takashi Tanaka