Related papers: ADAM-SINDy: An Efficient Optimization Framework fo…

Data-driven discovery of governing equations from data remains a fundamental challenge in nonlinear dynamics. Although sparse regression techniques have advanced system identification, they struggle with rational functions and noise…

We evaluate the robustness of a probabilistic formulation of system identification (ID) to sparse, noisy, and indirect data. Specifically, we compare estimators of future system behavior derived from the Bayesian posterior of a learning…

Equation discovery methods hold promise for extracting knowledge from physics-related data. However, existing approaches often require substantial prior information that significantly reduces the amount of knowledge extracted. In this…

The Weak-form Sparse Identification of Nonlinear Dynamics algorithm (WSINDy) has been demonstrated to offer coarse-graining capabilities in the context of interacting particle systems (https://doi.org/10.1016/j.physd.2022.133406). In this…

Nonlinear dynamic models are widely used for characterizing functional forms of processes that govern complex biological pathway systems. Over the past decade, validation and further development of these models became possible due to data…

We extend the data-driven method of Sparse Identification of Nonlinear Dynamics (SINDy) developed by Brunton et al, Proc. Natl. Acad. Sci USA 113 (2016) to the case of delay differential equations (DDEs). This is achieved in a bilevel…

Identification of the particle interaction potential is a challenging and important task in dusty plasma, colloids, and smart materials as it allows the characterization of structure formation and helps predict phase transitions. With the…

Identifying parameters in a system of nonlinear, ordinary differential equations is vital for designing a robust controller. However, if the system is stochastic in its nature or if only noisy measurements are available, standard…

We present a weak formulation and discretization of the system discovery problem from noisy measurement data. This method of learning differential equations from data fits into a new class of algorithms that replace pointwise derivative…

Discovering compact governing equations from experimental observations is one of the defining objectives of quantitative science, yet practical discovery pipelines routinely fail when measurements are noisy, relevant state variables are…

Inferring physical laws from data is a central challenge in science and engineering, including but not limited to healthcare, physical sciences, biosciences, social sciences, sustainability, climate, and robotics. Deep networks offer…

Large scale dynamical systems (e.g. many nonlinear coupled differential equations) can often be summarized in terms of only a few state variables (a few equations), a trait that reduces complexity and facilitates exploration of behavioral…

Sparse identification of nonlinear dynamical systems is a topic of continuously increasing significance in the dynamical systems community. Here we explore it at the level of lattice nonlinear dynamical systems of many degrees of freedom.…

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…

Periodic orbits are among the simplest non-equilibrium solutions to dynamical systems, and they play a significant role in our modern understanding of the rich structures observed in many systems. For example, it is known that embedded…

Air pollution, particularly particulate matter (PM2.5), poses significant risks to public health and the environment, necessitating accurate prediction and continuous monitoring for effective air quality management. However, air quality…

Quantum feature maps offer expressive embeddings for classical learning tasks, and augmenting sparse identification of nonlinear dynamics (SINDy) with such features is a natural but unexplored direction. We introduce \textbf{Q-SINDy}, a…

We develop a principled mathematical framework for controlling nonlinear, networked dynamical systems. Our method integrates dimensionality reduction, bifurcation theory and emerging model discovery tools to find low-dimensional subspaces…

Recently, we have demonstrated that our approach is a highly effective tool while analysing complex phenomena existing in networks of coupled nonlinear systems. In the present article we present the results of our investigations into a…

The multiscale and turbulent nature of Earth's atmosphere has historically rendered accurate weather modeling a hard problem. Recently, there has been an explosion of interest surrounding data-driven approaches to weather modeling, which in…