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Related papers: Weak SINDy For Partial Differential Equations

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Symbolic Regression (SR) is a widely studied field of research that aims to infer symbolic expressions from data. A popular approach for SR is the Sparse Identification of Nonlinear Dynamical Systems (SINDy) framework, which uses sparse…

Distilling physical laws autonomously from data has been of great interest in many scientific areas. The sparse identification of nonlinear dynamics (SINDy) and its variations have been developed to extract the underlying governing…

Systems and Control · Electrical Eng. & Systems 2022-09-08 Adam Purnomo , Mitsuhiro Hayashibe

In this work we study the asymptotic consistency of the weak-form sparse identification of nonlinear dynamics algorithm (WSINDy) in the identification of differential equations from noisy samples of solutions. We prove that the WSINDy…

Numerical Analysis · Mathematics 2022-11-30 Daniel A. Messenger , David M. Bortz

We present a statistical learning framework for robust identification of partial differential equations from noisy spatiotemporal data. Extending previous sparse regression approaches for inferring PDE models from simulated data, we address…

Numerical Analysis · Mathematics 2019-07-19 Suryanarayana Maddu , Bevan L. Cheeseman , Ivo F. Sbalzarini , Christian L. Müller

Identifying dynamical systems characterized by nonlinear parameters presents significant challenges in deriving mathematical models that enhance understanding of physics. Traditional methods, such as Sparse Identification of Nonlinear…

Machine Learning · Computer Science 2025-08-12 Siva Viknesh , Younes Tatari , Chase Christenson , Amirhossein Arzani

Robust physics (e.g., governing equations and laws) discovery is of great interest for many engineering fields and explainable machine learning. A critical challenge compared with general training is that the term and format of governing…

Numerical Analysis · Mathematics 2021-02-15 Zhiming Zhang , Yongming Liu

A general framework for recovering drift and diffusion dynamics from sampled trajectories is presented for the first time for stochastic delay differential equations. The core relies on the well-established SINDy algorithm for the sparse…

Numerical Analysis · Mathematics 2025-08-06 Dimitri Breda , Dajana Conte , Raffaele D'Ambrosio , Ida Santaniello , Muhammad Tanveer

Identifying from observation data the governing differential equations of a physical dynamics is a key challenge in machine learning. Although approaches based on SINDy have shown great promise in this area, they still fail to address a…

Machine Learning · Computer Science 2025-10-22 Fayad Ali Banna , Antoine Caradot , Eduardo Brandao , Jean-Philippe Colombier , Rémi Emonet , Marc Sebban

Identification of nonlinear dynamical systems has been popularized by sparse identification of the nonlinear dynamics (SINDy) via the sequentially thresholded least squares (STLS) algorithm. Many extensions SINDy have emerged in the…

Machine Learning · Computer Science 2023-08-04 Shawn L. Kiser , Mikhail Guskov , Marc Rébillat , Nicolas Ranc

Identifying Ordinary Differential Equations (ODEs) from measurement data requires both fitting the dynamics and assimilating, either implicitly or explicitly, the measurement data. The Sparse Identification of Nonlinear Dynamics (SINDy)…

Dynamical Systems · Mathematics 2024-05-07 Jacob Stevens-Haas , Yash Bhangale , Aleksandr Aravkin , Nathan Kutz

We introduce Weak-PDE-LEARN, a Partial Differential Equation (PDE) discovery algorithm that can identify non-linear PDEs from noisy, limited measurements of their solutions. Weak-PDE-LEARN uses an adaptive loss function based on weak forms…

Machine Learning · Computer Science 2023-09-12 Robert Stephany , Christopher Earls

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

Governing equations are essential to the study of nonlinear dynamics, often enabling the prediction of previously unseen behaviors as well as the inclusion into control strategies. The discovery of governing equations from data thus has the…

Dynamical Systems · Mathematics 2021-04-30 Alejandro Carderera , Sebastian Pokutta , Christof Schütte , Martin Weiser

We perform a sparse identification of nonlinear dynamics (SINDy) for low-dimensionalized complex flow phenomena. We first apply the SINDy with two regression methods, the thresholded least square algorithm (TLSA) and the adaptive Lasso…

Fluid Dynamics · Physics 2021-12-08 Kai Fukami , Takaaki Murata , Kai Zhang , Koji Fukagata

Data-driven identification of differential equations is an interesting but challenging problem, especially when the given data are corrupted by noise. When the governing differential equation is a linear combination of various differential…

Numerical Analysis · Mathematics 2023-04-05 Mengyi Tang , Wenjing Liao , Rachel Kuske , Sung Ha Kang

This work leverages laser vibrometry and the weak form of the sparse identification of nonlinear dynamics (WSINDy) for partial differential equations to learn macroscale governing equations from full-field experimental data. In the…

Numerical Analysis · Mathematics 2024-10-01 Abigail C. Schmid , Alireza Doostan , Fatemeh Pourahmadian

The growing integration of renewable energy sources has significantly reduced grid inertia, making modern power systems more vulnerable to instabilities. Accurate estimation of dynamic parameters such as inertia constants and damping…

Dynamical Systems · Mathematics 2025-12-08 Aiman Mushtaq Purra , Danish Rafiq

Sparse identification of nonlinear dynamics (SINDy) is a data-driven framework for estimating classical nonlinear dynamical systems from time-series data. In this approach, system dynamics is represented as a linear combination of a…

Quantum Physics · Physics 2026-02-17 Yusei Tateyama , Yuzuru Kato

We present AC-SINDy, a compositional extension of the Sparse Identification of Nonlinear Dynamics (SINDy) framework that replaces explicit feature libraries with a structured representation based on arithmetic circuits. Rather than…

Machine Learning · Computer Science 2026-04-22 Peter Racioppo

Sparse Identification of Nonlinear Dynamics (SINDy) is a powerful method for discovering parsimonious governing equations from data, but it often requires expert tuning of candidate libraries. We propose an LLM-aided SINDy pipeline that…

Systems and Control · Electrical Eng. & Systems 2026-02-10 Linyu Lin