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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…
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…
Although major advances have been achieved over the past decades for the reduction and identification of linear systems, deriving nonlinear low-order models still is a chal- lenging task. In this work, we develop a new data-driven framework…
Data-driven methodologies are nowadays ubiquitous. Their rapid development and spread have led to applications even beyond the traditional fields of science. As far as dynamical systems and differential equations are concerned, neural…
Discovering governing Partial Differential Equations (PDEs) from sparse and noisy data is a challenging issue in data-driven scientific computing. Conventional sparse regression methods often suffer from two major limitations: (i) the…
In the study of complex dynamical systems, understanding and accurately modeling the underlying physical processes is crucial for predicting system behavior and designing effective interventions. Yet real-world systems exhibit pronounced…
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…
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…
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…
The Sparse Identification of Nonlinear Dynamics (SINDy) framework has been frequently used to discover parsimonious differential equations governing natural and physical systems. This includes recent extensions to SINDy that enable 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…
System inference for nonlinear dynamic models, represented by ordinary differential equations (ODEs), remains a significant challenge in many fields, particularly when the data are noisy, sparse, or partially observable. In this paper, we…
Real-world datasets for deep learning frequently suffer from the co-occurring challenges of class imbalance and label noise, hindering model performance. While methods exist for each issue, effectively combining them is non-trivial, as…
This paper addresses the problem of learning linear dynamical systems from noisy observations. In this setting, existing algorithms either yield biased parameter estimates or have large sample complexities. We resolve these issues by…
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…
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…
We study a class of fully-discrete schemes for the numerical approximation of solutions of stochastic Cahn--Hilliard equations with cubic nonlinearity and driven by additive noise. The spatial (resp. temporal) discretization is performed…
We introduce a novel method for training machine learning models in the presence of noisy labels, which are prevalent in domains such as medical diagnosis and autonomous driving and have the potential to degrade a model's generalization…
We introduce DeepMoD, a Deep learning based Model Discovery algorithm. DeepMoD discovers the partial differential equation underlying a spatio-temporal data set using sparse regression on a library of possible functions and their…
We propose a novel data-driven method called QENDy (Quadratic Embedding of Nonlinear Dynamics) that not only allows us to learn quadratic representations of highly nonlinear dynamical systems, but also to identify the governing equations.…