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Related papers: SINDy-BVP: Sparse Identification of Nonlinear Dyna…

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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

Learning identifiable representations and models from low-level observations is helpful for an intelligent spacecraft to complete downstream tasks reliably. For temporal observations, to ensure that the data generating process is provably…

Machine Learning · Computer Science 2024-12-05 Congxi Zhang , Yongchun Xie

Data-driven discovery of governing equations from data remains a fundamental challenge in nonlinear dynamics. Although sparse regression techniques have advanced system identification, they struggle with rational functions and noise…

Machine Learning · Computer Science 2025-11-17 Zitong Zhang , Hao Sun

The quantitative formulation of evolution equations is the backbone for prediction, control, and understanding of dynamical systems across diverse scientific fields. Besides deriving differential equations for dynamical systems based on…

Data Analysis, Statistics and Probability · Physics 2025-01-06 Tim W. Kroll , Oliver Kamps

The discovery of governing equations from scientific data has the potential to transform data-rich fields that lack well-characterized quantitative descriptions. Advances in sparse regression are currently enabling the tractable…

Other Statistics · Statistics 2022-06-08 Kathleen Champion , Bethany Lusch , J. Nathan Kutz , Steven L. Brunton

In the context of population dynamics, identifying effective model features, such as fecundity and mortality rates, is generally a complex and computationally intensive process, especially when the dynamics are heterogeneous across the…

Populations and Evolution · Quantitative Biology 2025-07-01 Rainey Lyons , Vanja Dukic , David M. Bortz

Recovering dynamical equations from observed noisy data is the central challenge of system identification. We develop a statistical mechanics approach to analyze sparse equation discovery algorithms, which typically balance data fit and…

Statistical Mechanics · Physics 2025-09-16 Andrei A. Klishin , Joseph Bakarji , J. Nathan Kutz , Krithika Manohar

Dynamical systems are typically governed by a set of linear/nonlinear differential equations. Distilling the analytical form of these equations from very limited data remains intractable in many disciplines such as physics, biology, climate…

Machine Learning · Computer Science 2021-05-18 Fangzheng Sun , Yang Liu , Hao Sun

The Weak-form Sparse Identification of Nonlinear Dynamics algorithm (WSINDy) has been demonstrated to offer coarse-graining capabilities in the context of interacting particle systems (https://doi.org/10.1016/j.physd.2022.133406). In this…

Computational Physics · Physics 2023-12-04 Daniel A. Messenger , Joshua W. Burby , David M. Bortz

Nonlinear dynamics are ubiquitous in science and engineering applications, but the physics of most complex systems is far from being fully understood. Discovering interpretable governing equations from measurement data can help us…

Machine Learning · Computer Science 2022-10-18 Luning Sun , Daniel Zhengyu Huang , Hao Sun , Jian-Xun Wang

We present a sparse sensing framework based on Dynamic Mode Decomposition (DMD) to identify flow regimes and bifurcations in large-scale thermo-fluid systems. Motivated by real-time sensing and control of thermal-fluid flows in buildings…

Dynamical Systems · Mathematics 2017-06-26 Boris Kramer , Piyush Grover , Petros Boufounos , Mouhacine Benosman , Saleh Nabi

Identifying the governing equations of a nonlinear dynamical system is key to both understanding the physical features of the system and constructing an accurate model of the dynamics that generalizes well beyond the available data. We…

Machine Learning · Computer Science 2022-08-16 Peter Y. Lu , Joan Ariño , Marin Soljačić

This study proposes a novel framework for learning the underlying physics of phenomena with moving boundaries. The proposed approach combines Ensemble SINDy and Peridynamic Differential Operator (PDDO) and imposes an inductive bias assuming…

Machine Learning · Computer Science 2023-03-29 A. C. Bekar , E. Haghighat , E. Madenci

Rheology plays a pivotal role in understanding the flow behavior of fluids by discovering governing equations that relate deformation and stress, known as constitutive equations. Despite the importance of these equations, current methods…

Soft Condensed Matter · Physics 2024-12-06 Takeshi Sato , Souta Miyamoto , Shota Kato

Spatiotemporal dynamics pervade the natural sciences, from the morphogen dynamics underlying patterning in animal pigmentation to the protein waves controlling cell division. A central challenge lies in understanding how controllable…

Pattern Formation and Solitons · Physics 2025-03-03 Matthew Ricci , Guy Pelc , Zoe Piran , Noa Moriel , Mor Nitzan

This paper considers parameter estimation for nonlinear state-space models, which is an important but challenging problem. We address this challenge by employing a variational inference (VI) approach, which is a principled method that has…

Machine Learning · Statistics 2022-09-15 Jarrad Courts , Adrian Wills , Thomas Schön , Brett Ninness

The recently proposed System Identification via Validation and Adaptation (SIVA) method allows system identification, uncertainty quantification, and model validation directly from data. Inspired by generative modeling, SIVA employs a…

Systems and Control · Electrical Eng. & Systems 2025-08-05 Cristian López , Jackson E. Herzlieb , Keegan J. Moore

We consider the problem of learning a realization of a partially observed bilinear dynamical system (BLDS) from noisy input-output data. Given a single trajectory of input-output samples, we provide a finite time analysis for learning the…

Machine Learning · Computer Science 2025-10-23 Yahya Sattar , Yassir Jedra , Maryam Fazel , Sarah Dean

Differential equations based on physical principals are used to represent complex dynamic systems in all fields of science and engineering. Through repeated use in both academics and industry, these equations have been shown to represent…

Methodology · Statistics 2022-09-08 Joshua S. North , Christopher K. Wikle , Erin M. Schliep

Estimating the governing equation parameter values is essential for integrating experimental data with scientific theory to understand, validate, and predict the dynamics of complex systems. In this work, we propose a new method for…

Dynamical Systems · Mathematics 2025-06-27 Cristian López , Keegan J. Moore