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This work is concerned with uncertainty quantification in reduced-order dynamical system identification. Reduced-order models for system dynamics are ubiquitous in design and control applications and recent efforts focus on their…

First principles modeling of physical systems has led to significant technological advances across all branches of science. For nonlinear systems, however, small modeling errors can lead to significant deviations from the true, measured…

System identification plays a crucial role in physics and machine learning for discovering governing equations directly from data. A powerful approach is the Sparse Identification of Nonlinear Dynamics (SINDy) method, which assumes that…

Dynamical systems provide a mathematical framework for understanding complex physical phenomena. The mathematical formulation of these systems plays a crucial role in numerous applications; however, it often proves to be quite intricate.…

The theory of slow invariant manifolds (SIMs) is the foundation of various model-order reduction techniques for dissipative dynamical systems with multiple time-scales, e.g. in chemical kinetic models. The construction of SIMs and many…

We introduce Fourier Weak SINDy, a minimal noise-robust and interpretable derivative-free equation learning method that combines weak-form sparse equation learning with spectral density estimation for data-driven test function selection. By…

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…

Research in modern data-driven dynamical systems is typically focused on the three key challenges of high dimensionality, unknown dynamics, and nonlinearity. The dynamic mode decomposition (DMD) has emerged as a cornerstone for modeling…

This work proposes an iterative sparse-regularized regression method to recover governing equations of nonlinear dynamical systems from noisy state measurements. The method is inspired by the Sparse Identification of Nonlinear Dynamics…

Discovery of dynamical systems from data forms the foundation for data-driven modeling and recently, structure-preserving geometric perspectives have been shown to provide improved forecasting, stability, and physical realizability…

We present a versatile framework that employs Physics-Informed Neural Networks (PINNs) to discover the entropic contribution that leads to the constitutive equation for the extra-stress in rheological models of polymer solutions. In this…

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…

Modeling real-world spatio-temporal data is exceptionally difficult due to inherent high dimensionality, measurement noise, partial observations, and often expensive data collection procedures. In this paper, we present Sparse…

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,…

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…

We consider the data-driven discovery of governing equations from time-series data in the limit of high noise. The algorithms developed describe an extensive toolkit of methods for circumventing the deleterious effects of noise in the…

This work designs a scalable, parameter-aware sparse regression framework for discovering interpretable partial differential equations and subgrid-scale closures from multi-parameter simulation data. Building on SINDy (Sparse Identification…

The formulation of rheological constitutive equations -- models that relate internal stresses and deformations in complex fluids -- is a critical step in the engineering of systems involving soft materials. While data-driven models provide…

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…

Data-driven discovery of governing equations has advanced significantly in recent years; however, existing methods often struggle in multiscale systems where dynamically significant terms may have small coefficients. Therefore, we propose…