Related papers: Promoting global stability in data-driven models o…

Structural dynamics models with nonlinear stiffness appear, for example, when analyzing systems with nonlinear material behavior or undergoing large deformations. For complex systems, these models become too large for real-time applications…

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…

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…

We present a novel study on enhancing the capability of preserving the content in world models, focusing on a property we term World Stability. Recent diffusion-based generative models have advanced the synthesis of immersive and realistic…

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…

Steady plasma flows have been studied almost exclusively in systems with continuous symmetry or in open domains. In the absence of continuous symmetry, the lack of a conserved quantity makes the study of flows intrinsically challenging. In…

We prove conditions for global nonlinear stability of Oldroyd-B viscoelatic fluid flows in the Couette shear flow geometry. Global stability is inferred by analysing a new functional, called a perturbation entropy, to quantify the magnitude…

We propose a novel framework for learning stabilizable nonlinear dynamical systems for continuous control tasks in robotics. The key idea is to develop a new control-theoretic regularizer for dynamics fitting rooted in the notion of…

Sparse system identification is the data-driven process of obtaining parsimonious differential equations that describe the evolution of a dynamical system, balancing model complexity and accuracy. There has been rapid innovation in system…

In addition to providing high-profile successes in computer vision and natural language processing, neural networks also provide an emerging set of techniques for scientific problems. Such data-driven models, however, typically ignore…

Sparse identification of nonlinear dynamics (SINDy) has been widely used to discover the governing equations of a dynamical system from data. It uses sparse regression techniques to identify parsimonious models of unknown systems from a…

Dynamical systems with extreme events are difficult to capture with data-driven modeling, due to the relative scarcity of data within extreme events compared to the typical dynamics of the system, and the strong dependence of the long-time…

Modern societies have an abundance of data yet good system models are rare. Unfortunately, many of the current system identification and machine learning techniques fail to generalize outside of the training set, producing models that…

We propose a technique for the design and analysis of adaptation algorithms in dynamical systems. The technique applies both to systems with conventional Lyapunov-stable target dynamics and to ones of which the desired dynamics around the…

Building upon the technique that we developed earlier for perturbed sweeping processes with convex moving constraints and monotone vector fields (Kamenskii et al, Nonlinear Anal. Hybrid Syst. 30, 2018), the present paper establishes global…

In this effort we propose a data-driven learning framework for reduced order modeling of fluid dynamics. Designing accurate and efficient reduced order models for nonlinear fluid dynamic problems is challenging for many practical…

Identifying governing equations in physical and biological systems from datasets remains a long-standing challenge across various scientific disciplines, providing mechanistic insights into complex system evolution. Common methods like…

We present a data-driven approach to efficiently approximate nonlinear transient dynamics in solid-state systems. Our proposed machine-learning model combines a dimensionality reduction stage with a nonlinear vector autoregression scheme.…

In this paper, we establish the sufficient conditions guaranteeing global uniform exponential stability, or at least global asymptotic stability, of all solutions for nonlinear dynamical systems, also known as global incremental stability…

Interfacial fluctuations in a two-phase binary fluid mixture reveal signatures of underlying physical processes that occur within each phase and on a range of spatial and temporal scales. In this study, we investigate a model binary fluid…