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While modern representation learning relies heavily on global error signals, decentralized algorithms driven by local interactions offer a fundamental distributed alternative. However, the macroscopic convergence properties of these…

Machine Learning · Computer Science 2026-04-21 Zilin Li , Weiwei Xu , Xuchun Tong , Xuanbo Lu , Xuanqi Zhao

Obtaining system parameters and reconstructing the full flow state from limited velocity observations using conventional fluid dynamics solvers can be prohibitively expensive. Here we employ machine learning algorithms to overcome the…

Fluid Dynamics · Physics 2024-10-17 Vladimir Parfenyev , Mark Blumenau , Ilia Nikitin

We consider systems under uncertainty whose dynamics are partially unknown. Our aim is to study satisfaction of temporal logic properties by trajectories of such systems. We express these properties as signal temporal logic formulas and…

Systems and Control · Electrical Eng. & Systems 2020-05-12 Ali Salamati , Sadegh Soudjani , Majid Zamani

Discovering governing equations from data, in particular high dimensional data, is challenging in various fields of science and engineering, and it has potential to revolutionise the science and technology in this big data era. This paper…

Fluid Dynamics · Physics 2024-01-12 X. Lin , D. Xiao , F. Fang

In this paper, we consider the data-driven discovery of stable dynamical models with a single equilibrium. The proposed approach uses a basis-function parameterization of the differential equations and the associated Lyapunov function. This…

Systems and Control · Electrical Eng. & Systems 2026-04-10 Zhe Li , Ilias Mitrai

A dynamical systems approach to turbulence envisions the flow as a trajectory through a high-dimensional state space transiently visiting the neighbourhoods of unstable simple invariant solutions (E. Hopf, Commun. Appl. Maths 1, 303, 1948).…

Fluid Dynamics · Physics 2023-11-15 Jacob Page , Peter Norgaard , Michael P. Brenner , Rich R. Kerswell

Despite the significant recent progress in deep generative models, the underlying structure of their latent spaces is still poorly understood, thereby making the task of performing semantically meaningful latent traversals an open research…

Machine Learning · Computer Science 2023-07-04 Yue Song , T. Anderson Keller , Nicu Sebe , Max Welling

Empirical researchers increasingly use upstream machine-learning (ML) methods to construct proxies for latent target variables from complex, unstructured data. A naive plug-in use of such proxies in downstream econometric models, however,…

Econometrics · Economics 2026-04-14 Lixiong Li

Deriving governing equations of complex physical systems based on first principles can be quite challenging when there are certain unknown terms and hidden physical mechanisms in the systems. In this work, we apply a deep learning…

Plasma Physics · Physics 2022-12-06 Wenjie Cheng , Haiyang Fu , Liang Wang , Chuanfei Dong , Yaqiu Jin , Mingle Jiang , Jiayu Ma , Yilan Qin , Kexin Liu

Hidden variable graphical models can sometimes imply constraints on the observable distribution that are more complex than simple conditional independence relations. These observable constraints can falsify assumptions of the model that…

Methodology · Statistics 2026-05-12 Michael C. Sachs , Erin E. Gabriel , Robin J. Evans , Arvid Sjölander

Recently, many reinforcement learning techniques were shown to have provable guarantees in the simple case of linear dynamics, especially in problems like linear quadratic regulators. However, in practice, many reinforcement learning…

Machine Learning · Computer Science 2020-06-30 Abraham Frandsen , Rong Ge

We introduce a data-driven method and shows its skills for spatiotemporal prediction of high-dimensional chaotic dynamics and turbulence. The method is based on a finite-dimensional approximation of the Koopman operator where the…

Fluid Dynamics · Physics 2019-09-04 Mohammad Amin Khodkar , Pedram Hassanzadeh , Athanasios Antoulas

Data assimilation (DA) aims at optimally merging observational data and model outputs to create a coherent statistical and dynamical picture of the system under investigation. Indeed, DA aims at minimizing the effect of observational and…

Data Analysis, Statistics and Probability · Physics 2022-01-05 Yumeng Chen , Alberto Carrassi , Valerio Lucarini

With the advent of modern data collection and storage technologies, data-driven approaches have been developed for discovering the governing partial differential equations (PDE) of physical problems. However, in the extant works the model…

Machine Learning · Statistics 2019-05-28 Haibin Chang , Dongxiao Zhang

Conservation laws are an inherent feature in many systems modeling real world phenomena, in particular, those modeling biological and chemical systems. If the form of the underlying dynamical system is known, linear algebra and algebraic…

Numerical Analysis · Mathematics 2024-03-11 Tracey Oellerich , Maria Emelianenko

Exploring the intersection of deterministic and stochastic dynamics, this paper delves into Lagrangian discovery for conservative and non-conservative systems under stochastic excitation. Traditional Lagrangian frameworks, adept at…

Dynamical Systems · Mathematics 2024-02-28 Tapas Tripura , Satyam Panda , Budhaditya Hazra , Souvik Chakraborty

Sequential modelling of high-dimensional data is an important problem that appears in many domains including model-based reinforcement learning and dynamics identification for control. Latent variable models applied to sequential data…

Machine Learning · Computer Science 2023-01-23 Oliver Limoyo , Trevor Ablett , Jonathan Kelly

The study presents a general framework for discovering underlying Partial Differential Equations (PDEs) using measured spatiotemporal data. The method, called Sparse Spatiotemporal System Discovery ($\text{S}^3\text{d}$), decides which…

We develop a data-driven framework for learning and correcting non-autonomous vehicle dynamics. Physics-based vehicle models are often simplified for tractability and therefore exhibit inherent model-form uncertainty, motivating the need…

Machine Learning · Computer Science 2025-12-02 Nguyen Ly , Caroline Tatsuoka , Jai Nagaraj , Jacob Levy , Fernando Palafox , David Fridovich-Keil , Hannah Lu

In fluid physics, data-driven models to enhance or accelerate solution methods are becoming increasingly popular for many application domains, such as alternatives to turbulence closures, system surrogates, or for new physics discovery. In…