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The combination of machine learning (ML) and sparsity-promoting techniques is enabling direct extraction of governing equations from data, revolutionizing computational modeling in diverse fields of science and engineering. The discovered…

Neural networks offer highly expressive turbulence closures, yet their complexity obscures the physical mechanisms they aim to model, and their computational cost can limit their tractability. To address these limitations, we introduce a…

Identifying the governing equations of a dynamical system is one of the most important tasks for scientific modeling. However, this procedure often requires high-quality spatio-temporal data uniformly sampled on structured grids. In this…

Uncertainty quantification during atmospheric chemistry modeling is computationally expensive as it typically requires a large number of simulations using complex models. As large-scale modeling is typically performed with simplified…

The discovery of governing differential equations from data is an open frontier in machine learning. The sparse identification of nonlinear dynamics (SINDy) \citep{brunton_discovering_2016} framework enables data-driven discovery of…

The sparse identification of nonlinear dynamical systems (SINDy) is a data-driven technique employed for uncovering and representing the fundamental dynamics of intricate systems based on observational data. However, a primary obstacle in…

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…

We propose a probabilistic model discovery method for identifying ordinary differential equations (ODEs) governing the dynamics of observed multivariate data. Our method is based on the sparse identification of nonlinear dynamics (SINDy)…

Automated data-driven modeling, the process of directly discovering the governing equations of a system from data, is increasingly being used across the scientific community. PySINDy is a Python package that provides tools for applying the…

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…

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…

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…

Many dynamical systems exhibit oscillatory behavior that can be modeled with differential equations. Recently, these equations have increasingly been derived through data-driven methods, including the transparent technique known as Sparse…

We propose a fast probabilistic framework for identifying differential equations governing the dynamics of observed data. We recast the SINDy method within a Bayesian framework and use Gaussian approximations for the prior and likelihood to…

Kolmogorov-Arnold networks (KANs) have arisen as a potential way to enhance the interpretability of machine learning. However, solutions learned by KANs are not necessarily interpretable, in the sense of being sparse or parsimonious. Sparse…

Nonlinear system identification often involves a fundamental trade-off between interpretability and flexibility, often requiring the incorporation of physical constraints. We propose a unified data-driven framework that combines the…

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…

Discovering governing equations of complex dynamical systems directly from data is a central problem in scientific machine learning. In recent years, the sparse identification of nonlinear dynamics (SINDy) framework, powered by heuristic…

Model parsimony is an important \emph{cognitive bias} in data-driven modelling that aids interpretability and helps to prevent over-fitting. Sparse identification of nonlinear dynamics (SINDy) methods are able to learn sparse…

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…