Related papers: VENI, VINDy, VICI: a generative reduced-order mode…

Recent advances in the field of data-driven dynamics allow for the discovery of ODE systems using state measurements. One approach, known as Sparse Identification of Nonlinear Dynamics (SINDy), assumes the dynamics are sparse within a…

The Sparse Identification of Nonlinear Dynamics (SINDy) is a method for discovering nonlinear dynamical system models from data. Quantifying uncertainty in SINDy models is essential for assessing their reliability, particularly in…

Identifying nonlinear dynamics and characterizing noise from data is critical across science and engineering for understanding and modeling the behavior of the systems accurately. The modified sparse identification of nonlinear dynamics…

Accurate numerical solutions of partial differential equations are essential in many scientific fields but often require computationally expensive solvers, motivating reduced-order models (ROMs). Latent Space Dynamics Identification (LaSDI)…

Sparse regression has emerged as a popular technique for learning dynamical systems from temporal data, beginning with the SINDy (Sparse Identification of Nonlinear Dynamics) framework proposed by arXiv:1509.03580. Quantifying the…

Sparse model identification enables the discovery of nonlinear dynamical systems purely from data; however, this approach is sensitive to noise, especially in the low-data limit. In this work, we leverage the statistical approach of…

The Weak-form Estimation of Non-linear Dynamics (WENDy) framework is a recently developed approach for parameter estimation and inference of systems of ordinary differential equations (ODEs). Prior work demonstrated WENDy to be robust,…

Solving partial differential equations (PDEs) is a required step in the simulation of natural and engineering systems. The associated computational costs significantly increase when exploring various scenarios, such as changes in initial or…

Reduced Order Models (ROMs) form essential tools across engineering domains by virtue of their function as surrogates for computationally intensive digital twinning simulators. Although purely data-driven methods are available for ROM…

Discovering governing equations from observational data remains a fundamental challenge in scientific modeling, particularly when the underlying mathematical structure is unknown. Traditional sparse identification methods like SINDy excel…

Reduced-order models (ROMs) can efficiently simulate high-dimensional physical systems but lack robust uncertainty quantification methods. Existing approaches are frequently architecture- or training-specific, which limits flexibility and…

We develop an unsupervised machine learning algorithm for the automated discovery and identification of traveling waves in spatio-temporal systems governed by partial differential equations (PDEs). Our method uses sparse regression and…

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…

With the rapid increase of available data for complex systems, there is great interest in the extraction of physically relevant information from massive datasets. Recently, a framework called Sparse Identification of Nonlinear Dynamics…

Phase mixing is a fundamental kinetic process that governs dissipation and stability in collisionless plasmas, but its inherent filamentation in velocity space creates major challenges for both high-fidelity simulations and reduced-order…

The data-driven recovery of the unknown governing equations of dynamical systems has recently received an increasing interest. However, the identification of governing equations remains challenging when dealing with noisy and partial…

Sparse system identification is the data-driven process of obtaining parsimonious differential equations that describe the evolution of a dynamical system, balancing model complexity and accuracy. There has been rapid innovation in system…

We develop a data-driven model discovery and system identification technique for spatially-dependent boundary value problems (BVPs). Specifically, we leverage the sparse identification of nonlinear dynamics (SINDy) algorithm and group…

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…

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…