Related papers: LES-SINDy: Laplace-Enhanced Sparse Identification …
The explicit governing equation is one of the simplest and most intuitive forms for characterizing physical laws. However, directly discovering partial differential equations (PDEs) from data poses significant challenges, primarily in…
A major challenge in the study of dynamical systems is that of model discovery: turning data into models that are not just predictive, but provide insight into the nature of the underlying dynamical system that generated the data. This…
Sparse Identification of Nonlinear Dynamics (SINDy) has become a standard methodology for inferring governing equations of dynamical systems from observed data using statistical modeling. However, classical SINDy approaches rely on…
Lithium-ion batteries (LIBs) are utilized as a major energy source in various fields because of their high energy density and long lifespan. During repeated charging and discharging, the degradation of LIBs, which reduces their maximum…
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…
Spatiotemporal dynamics pervade the natural sciences, from the morphogen dynamics underlying patterning in animal pigmentation to the protein waves controlling cell division. A central challenge lies in understanding how controllable…
The parametric greedy latent space dynamics identification (gLaSDI) framework has demonstrated promising potential for accurate and efficient modeling of high-dimensional nonlinear physical systems. However, it remains challenging to handle…
This paper addresses identification of sparse linear and noise-driven continuous-time state-space systems, i.e., the right-hand sides in the dynamical equations depend only on a subset of the states. The key assumption in this study, is…
Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve…
Dynamical systems modeling is a core pillar of scientific inquiry across natural and life sciences. Increasingly, dynamical system models are learned from data, rendering identifiability a paramount concept. For systems that are not…
A parametric adaptive physics-informed greedy Latent Space Dynamics Identification (gLaSDI) method is proposed for accurate, efficient, and robust data-driven reduced-order modeling of high-dimensional nonlinear dynamical systems. In the…
In this study, we investigate the performance of the sparse identification of nonlinear dynamics (SINDy) algorithm and the neural ordinary differential equations (ODEs) in identification of the underlying mechanisms of open ocean Lagrangian…
Many low-mass stars like the Sun host periodic, oscillatory magnetic fields that lead to variable levels of stellar activity, driving space weather that affects the habitability and detection of exoplanets. Owing to the intrinsic difficulty…
Understanding the decisions made by deep neural networks is essential in high-stakes domains such as medical imaging and autonomous driving. Yet, these models often lack transparency, particularly in computer vision.…
Discovering the partial differential equations underlying spatio-temporal datasets from very limited and highly noisy observations is of paramount interest in many scientific fields. However, it remains an open question to know when model…
The simulation of many complex phenomena in engineering and science requires solving expensive, high-dimensional systems of partial differential equations (PDEs). To circumvent this, reduced-order models (ROMs) have been developed to speed…
Obtaining predictive low-order models is a central challenge in fluid dynamics. Data-driven frameworks have been widely used to obtain low-order models of aerodynamic systems; yet, resulting models tend to yield predictions that grow…
Identifying network dynamics is a critical yet challenging task to to understand the mechanism of real-world social systems. There are two types of algorithms, and one requires the knowledge of self-dynamics function, interactive function,…
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…
Accurate numerical solutions of partial differential equations are essential in many scientific fields but often require computationally expensive solvers, motivating reduced-order models (ROMs). Latent Space Dynamics Identification (LaSDI)…