English
Related papers

Related papers: Bayesian autoencoders for data-driven discovery of…

200 papers

The moment quantities associated with the nonlinear Schrodinger equation offer important insights towards the evolution dynamics of such dispersive wave partial differential equation (PDE) models. The effective dynamics of the moment…

Pattern Formation and Solitons · Physics 2024-06-10 Su Yang , Shaoxuan Chen , Wei Zhu , P. G. Kevrekidis

Inferring higher-order interaction structure from observations of dynamics is a central challenge in complex systems, particularly when data are scarce, noisy, or concentrated in lower-dimensional regions of state space. We develop…

Physics and Society · Physics 2026-05-07 Katerina Tang , Vivek Srikrishnan , Jackson Kulik

Vortex-induced vibrations (VIV) remain a canonical yet complex manifestation of fluid-structure interactions, where coupled nonlinear dynamics govern the motion of bluff bodies. For several years, we have relied on traditional reduced-order…

Fluid Dynamics · Physics 2026-03-31 Haimi Jha , Hibah Saddal , Chandan Bose

This paper presents a machine learning framework for Bayesian systems identification from noisy, sparse and irregular observations of nonlinear dynamical systems. The proposed method takes advantage of recent developments in differentiable…

Machine Learning · Computer Science 2020-04-21 Yibo Yang , Mohamed Aziz Bhouri , Paris Perdikaris

The SINDy algorithm has been successfully used to identify the governing equations of dynamical systems from time series data. In this paper, we argue that this makes SINDy a potentially useful tool for causal discovery and that existing…

Machine Learning · Computer Science 2023-01-02 Andrew O'Brien , Rosina Weber , Edward Kim

In the study of complex dynamical systems, understanding and accurately modeling the underlying physical processes is crucial for predicting system behavior and designing effective interventions. Yet real-world systems exhibit pronounced…

Machine Learning · Statistics 2025-07-15 Ridwan Olabiyi , Han Hu , Ashif Iquebal

Data normalisation, a common and often necessary preprocessing step in engineering and scientific applications, can severely distort the discovery of governing equations by magnitudebased sparse regression methods. This issue is…

Machine Learning · Computer Science 2026-03-06 Jay Raut , Daniel N. Wilke , Stephan Schmidt

The data-driven discovery of dynamics via machine learning is currently pushing the frontiers of modeling and control efforts, and it provides a tremendous opportunity to extend the reach of model predictive control. However, many leading…

Optimization and Control · Mathematics 2019-03-06 Eurika Kaiser , J. Nathan Kutz , Steven L. Brunton

The SINDy algorithm has been successfully used to identify the governing equations of dynamical systems from time series data. However, SINDy assumes the user has prior knowledge of the variables in the system and of a function library that…

Machine Learning · Computer Science 2024-01-25 Andrew O'Brien

A novel approach is presented for discovering PDEs that govern the motion of satellites in space. The method is based on SINDy, a data-driven technique capable of identifying the underlying dynamics of complex physical systems from time…

Machine Learning · Computer Science 2023-11-17 João Funenga , Marta Guimarães , Henrique Costa , Cláudia Soares

Data-driven discovery of model equations is a powerful approach for understanding the behavior of dynamical systems in many scientific fields. In particular, the ability to learn mathematical models from data would benefit systems biology,…

Machine Learning · Computer Science 2025-11-04 G. Pillonetto , A. Giaretta , A. Aravkin , M. Bisiacco , T. Elston

In this paper, we address the challenge of deriving dynamical models from sparse and noisy data. High-quality data is crucial for symbolic regression algorithms; limited and noisy data can present modeling challenges. To overcome this, we…

Machine Learning · Computer Science 2024-10-14 Junette Hsin , Shubhankar Agarwal , Adam Thorpe , Luis Sentis , David Fridovich-Keil

The Sparse Identification of Nonlinear Dynamics (SINDy) algorithm can be applied to stochastic differential equations to estimate the drift and the diffusion function using data from a realization of the SDE. The SINDy algorithm requires…

Numerical Analysis · Mathematics 2024-01-29 Mathias Wanner , Igor Mezić

In recent years, identification of nonlinear dynamical systems from data has become increasingly popular. Sparse regression approaches, such as Sparse Identification of Nonlinear Dynamics (SINDy), fostered the development of novel governing…

Machine Learning · Statistics 2022-03-21 Alexandre Cortiella , Kwang-Chun Park , Alireza Doostan

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…

The ability to discover physical laws and governing equations from data is one of humankind's greatest intellectual achievements. A quantitative understanding of dynamic constraints and balances in nature has facilitated rapid development…

Dynamical Systems · Mathematics 2016-04-27 Steven L. Brunton , Joshua L. Proctor , J. Nathan Kutz

We present a weak formulation and discretization of the system discovery problem from noisy measurement data. This method of learning differential equations from data fits into a new class of algorithms that replace pointwise derivative…

Numerical Analysis · Mathematics 2022-05-03 Daniel A. Messenger , David M. Bortz

The Sparse Identification of Nonlinear Dynamics (SINDy) framework has been frequently used to discover parsimonious differential equations governing natural and physical systems. This includes recent extensions to SINDy that enable the…

Numerical Analysis · Mathematics 2026-01-21 Mohammed Alanazi , Majid Bani-Yaghoub

Complex systems in physics, chemistry, and biology that evolve over time with inherent randomness are typically described by stochastic differential equations (SDEs). A fundamental challenge in science and engineering is to determine the…

Machine Learning · Computer Science 2024-10-23 Qunxi Zhu , Bolin Zhao , Jingdong Zhang , Peiyang Li , Wei Lin

We introduce a Bayesian system identification (SysID) framework for jointly estimating robot's state trajectories and physical parameters with high accuracy. It embeds physically consistent inverse dynamics, contact and loop-closure…

Robotics · Computer Science 2026-02-19 Sergi Martinez , Steve Tonneau , Carlos Mastalli