Related papers: Sparse Identification of Nonlinear Distributed-Del…

Dynamic graph neural networks have been widely used in modeling and representation learning of graph structure data. Current dynamic representation learning focuses on either discrete learning which results in temporal information loss or…

Power grid parameter estimation involves the estimation of unknown parameters, such as inertia and damping coefficients, using observed dynamics. In this work, we present a comparison of data-driven algorithms for the power grid parameter…

One way to understand time-series data is to identify the underlying dynamical system which generates it. This task can be done by selecting an appropriate model and a set of parameters which best fits the dynamics while providing the…

We develop data-driven dynamical models of the nonlinear aeroelastic effects on a long-span suspension bridge from sparse, noisy sensor measurements which monitor the bridge. Using the {\em sparse identification of nonlinear dynamics}…

Modeling and identification of high-dimensional stochastic processes is ubiquitous in many fields. In particular, there is a growing interest in modeling stochastic processes with simple and interpretable structures. In many applications,…

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…

Discrete-time linear time-varying (LTV) systems form a powerful class of models to approximate complex dynamical systems with nonlinear dynamics for the purpose of analysis, design and control. Motivated by inference of spatio-temporal…

This work presents a data-driven approach to the identification of spatial and temporal truncation errors for linear and nonlinear discretization schemes of Partial Differential Equations (PDEs). Motivated by the central role of truncation…

When the scale of communication networks has been growing rapidly in the past decades, it becomes a critical challenge to extract fast and accurate estimation of key state parameters of network links, e.g., transmission delays and dropped…

Dynamical systems are typically governed by a set of linear/nonlinear differential equations. Distilling the analytical form of these equations from very limited data remains intractable in many disciplines such as physics, biology, climate…

Latent stochastic differential equation (SDE) models are important tools for the unsupervised discovery of dynamical systems from data, with applications ranging from engineering to neuroscience. In these complex domains, exact posterior…

Modeling atmospheric chemistry is computationally expensive and limits the widespread use of atmospheric chemical transport models. This computational cost arises from solving high-dimensional systems of stiff differential equations.…

In future power systems, the detailed structure and dynamics may not always be fully known. This is due to an increasing number of distributed energy resources, such as photovoltaic generators, battery storage systems, heat pumps and…

This work addresses fundamental issues related to the structure and conditioning of linear time-delayed models of non-linear dynamics on an attractor. While this approach has been well-studied in the asymptotic sense (e.g. for infinite…

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…

A key task in the field of modeling and analyzing nonlinear dynamical systems is the recovery of unknown governing equations from measurement data only. There is a wide range of application areas for this important instance of system…

In this work, we revisit dictionary-based sparse regression, in particular, Sequential Threshold Least Squares (STLS), and propose a score-guided library selection to provide practical guidance for data-driven modeling, with emphasis on…

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…

In this paper, we study the system identification problem for sparse linear time-invariant systems. We propose a sparsity promoting block-regularized estimator to identify the dynamics of the system with only a limited number of input-state…

Time delay is ubiquitous in many experimental and real-world situations. It is often unclear whether time delay plays a significant role in observed phenomena, and if it does, how long the time lag really is. This would be invaluable…