Data-Driven Modeling of Nonlinear Traveling Waves

Abstract

Presented is a data-driven Machine Learning (ML) framework for the identification and modeling of traveling wave spatiotemporal dynamics. The presented framework is based on the steadily-propagating traveling wave ansatz, $u(x,t)=U(\xi =x-ct+a)$. For known evolution equations, this coordinate transformation reduces governing partial differential equations (PDEs) to a set of coupled ordinary differential equations (ODEs) in the traveling wave coordinate $\xi$. Although traveling waves are readily observed in many physical systems, the underlying governing equations may be unknown. For these instances, the traveling wave ODEs can be (i) identified in an interpretable manner through an implementation of sparse regression techniques or (ii) modeled empirically with neural ODEs. Presented are these methods applied to several physical systems that admit traveling waves. Examples include traveling wave fronts, pulses, and wavetrains restricted to one-wave wave propagation in a single spatial dimension.

References in corpus (8)

• Discovering governing equations from data: Sparse identification of nonlinear dynamical systems
• Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations
• Collapse and Revival of the Matter Wave Field of a Bose-Einstein Condensate
• A wildland fire model with data assimilation
• Learning dominant physical processes with data-driven balance models
• Modeling Thermodynamic Trends of Rotating Detonation Engines
• Dimensionality Reduction and Reduced Order Modeling for Traveling Wave Physics
• Mode-Locked Rotating Detonation Waves: Experiments and a Model Equation

Cited by in corpus (2)

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