Related papers: Data-Driven Modeling of Nonlinear Traveling Waves

This paper reports results on the classification of traveling wave solutions, including nonnegative weak sense, in the spatial 1D degenerate parabolic equation. These are obtained through dynamical systems theory and geometric approaches…

Machine learning (ML) has become a versatile tool for analyzing anomalous diffusion trajectories, yet most existing pipelines are trained on large collections of simulated data. In contrast, experimental trajectories, such as those from…

To fully understand, analyze, and determine the behavior of dynamical systems, it is crucial to identify their intrinsic modal coordinates. In nonlinear dynamical systems, this task is challenging as the modal transformation based on the…

We propose a machine learning framework to accelerate numerical computations of time-dependent ODEs and PDEs. Our method is based on recasting (generalizations of) existing numerical methods as artificial neural networks, with a set of…

We study traveling wave solutions of the nonlinear variational wave equation. In particular, we show how to obtain global, bounded, weak traveling wave solutions from local, classical ones. The resulting waves consist of monotone and…

Identifying the governing equations of a nonlinear dynamical system is key to both understanding the physical features of the system and constructing an accurate model of the dynamics that generalizes well beyond the available data. We…

We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…

Learning time-dependent partial differential equations (PDEs) that govern evolutionary observations is one of the core challenges for data-driven inference in many fields. In this work, we propose to capture the essential dynamics of…

We consider propagating, spatially localised waves in a class of equations that contain variational and non-variational terms. The dynamics of the waves is analysed through a collective coordinate approach. Motivated by the variational…

One of the main questions regarding complex systems at large scales concerns the effective interactions and driving forces that emerge from the detailed microscopic properties. Coarse-grained models aim to describe complex systems in terms…

Models for travelling waves in multi-fluid plasmas give essential insight into fully nonlinear wave structures in plasmas, not readily available from either numerical simulations or from weakly nonlinear wave theories. We illustrate these…

Harnessing data to discover the underlying governing laws or equations that describe the behavior of complex physical systems can significantly advance our modeling, simulation and understanding of such systems in various science and…

The geometries of surface wave modes are determined by the highly nontrivial interplay of capillarity and wetting effects at the boundaries of their domain. Aside from idealised scenarios, this commonly leads to unknown boundary conditions,…

In an era defined by rapid data evolution, traditional Machine Learning (ML) models often struggle to adapt to dynamic environments. Evolving Machine Learning (EML) has emerged as a pivotal paradigm, enabling continuous learning and…

Reaction-diffusion equations (RDEs) are often derived as continuum limits of lattice-based discrete models. Recently, a discrete model which allows the rates of movement, proliferation and death to depend upon whether the agents are…

The use of machine learning to predict wave dynamics is a topic of growing interest, but commonly-used deep learning approaches suffer from a lack of interpretability of the trained models. Here we present an interpretable machine learning…

Dispersive shock waves (DSWs), which connect states of different amplitude via a modulated wave train, form generically in nonlinear dispersive media subjected to abrupt changes in state. The primary tool for the analytical study of DSWs is…

Identifying dynamical systems from experimental data is a notably difficult task. Prior knowledge generally helps, but the extent of this knowledge varies with the application, and customized models are often needed. Neural ordinary…

We develop data-driven models to predict the dynamics of a freely settling sphere in a quiescent Newtonian fluid using experimentally obtained trajectories. Particle tracking velocimetry was used to obtain a comprehensive dataset of…

Machine learning (ML) is redefining what is possible in data-intensive fields of science and engineering. However, applying ML to problems in the physical sciences comes with a unique set of challenges: scientists want physically…