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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…

Sparse Identification of Nonlinear Dynamics (SINDy) has been shown to successfully recover governing equations from data; however, this approach assumes the initial condition to be exactly known in advance and is sensitive to noise. In this…

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…

Accurately modeling the nonlinear dynamics of a system from measurement data is a challenging yet vital topic. The sparse identification of nonlinear dynamics (SINDy) algorithm is one approach to discover dynamical systems models from data.…

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 of partial differential equations from data is a potential breakthrough to solve the lack of physical equations in complex dynamic systems, but because numerical differentiation is ill-posed to noise data, noise has become…

In this paper, we address the challenge of deriving dynamical models from sparse and noisy data. High-quality data is crucial for symbolic regression algorithms; limited and noisy data can present modeling challenges. To overcome this, we…

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…

The accurate forecasting of complex, high-dimensional dynamical systems from observational data is a fundamental task across numerous scientific and engineering disciplines. A significant challenge arises from noise-corrupted measurements,…

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…

SINDy is a method for learning system of differential equations from data by solving a sparse linear regression optimization problem [Brunton et al., 2016]. In this article, we propose an extension of the SINDy method that learns systems of…

Fourier embedding has shown great promise in removing spectral bias during neural network training. However, it can still suffer from high generalization errors, especially when the labels or measurements are noisy. We demonstrate that…

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…

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…

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…

The sparse identification of nonlinear dynamics (SINDy) is a regression framework for the discovery of parsimonious dynamic models and governing equations from time-series data. As with all system identification methods, noisy measurements…

This paper presents an online algorithm for identification of partial differential equations (PDEs) based on the weak-form sparse identification of nonlinear dynamics algorithm (WSINDy). The algorithm is online in a sense that if performs…

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 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…

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)…