Related papers: Model selection for hybrid dynamical systems via s…

Decision formation in perceptual decision-making involves sensory evidence accumulation instantiated by the temporal integration of an internal decision variable towards some decision criterion or threshold, as described by sequential…

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…

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…

This paper investigates the problem of identifying state-dependent switching systems, a class of hybrid dynamical systems that combine multiple linear or nonlinear modes. We propose two broad classes of switching systems: switching linear…

We present a pragmatic approach to the sparse identification of nonlinear dynamics for systems with discrete delays. It relies on approximating the underlying delay model with a system of ordinary differential equations via pseudospectral…

Hybrid modelling enhances the accuracy and predictive capability of dynamic models by integrating first principles with data-driven methods, effectively mitigating epistemic uncertainties inherent in mechanistic approaches. However, hybrid…

Recovering dynamical equations from observed noisy data is the central challenge of system identification. We develop a statistical mechanics approach to analyze sparse equation discovery algorithms, which typically balance data fit and…

In applications of nonlinear and complex dynamical systems, a common situation is that the system can be measured but its structure and the detailed rules of dynamical evolution are unknown. The inverse problem is to determine the system…

Distilling physical laws autonomously from data has been of great interest in many scientific areas. The sparse identification of nonlinear dynamics (SINDy) and its variations have been developed to extract the underlying governing…

In many problems of data-driven modeling for dynamical systems, the governing equations are not known a priori and must be selected phenomenologically from a large set of candidate interactions and basis functions. In such situations, point…

Poincar\'e maps are an integral aspect to our understanding and analysis of nonlinear dynamical systems. Despite this fact, the construction of these maps remains elusive and is primarily left to simple motivating examples. In this…

Discovering the governing equations of a dynamical system from observed trajectories provides deeper insight into its structure than mere prediction of future states. We present a data-driven approach to model discovery based on…

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…

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…

The ability to discover physical laws and governing equations from data is one of humankind's greatest intellectual achievements. A quantitative understanding of dynamic constraints and balances in nature has facilitated rapid development…

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…

The dynamic mode decomposition (DMD) is a data-driven method used for identifying the dynamics of complex nonlinear systems. It extracts important characteristics of the underlying dynamics using measured time-domain data produced either by…

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…

Equation discovery methods enable modelers to combine domain-specific knowledge and system identification to construct models most suitable for a selected modeling task. The method described and evaluated in this paper can be used as a…

Accurate models are essential for design, performance prediction, control, and diagnostics in complex engineering systems. Physics-based models excel during the design phase but often become outdated during system deployment due to changing…