Data-driven modeling of nonlinear traveling waves

Presented is a data-driven machine learning framework for modeling traveling wave spatiotemporal dynamics. The presented based on the steadily propagating ansatz, u(x,t)=U(?=x?ct+a). For known evolution equations, this coordinate transformation reduces governing partial differential equations to set of coupled ordinary (ODEs) in ?. Although waves are readily observed many physical systems, underlying may be unknown. these instances, dynamical system can modeled empirically with neural ODEs. ideas applied several systems that admit waves. Examples include fronts, pulses, and wavetrains restricted one-way propagation single spatial dimension. Last, applicability real-world an exploration rotating detonation