A Physics-Informed, Deep Double Reservoir Network for Forecasting Boundary Layer Velocity
arxiv(2023)
摘要
When a fluid flows over a solid surface, it creates a thin boundary layer
where the flow velocity is influenced by the surface through viscosity, and can
transition from laminar to turbulent at sufficiently high speeds. Understanding
and forecasting the fluid dynamics under these conditions is one of the most
challenging scientific problems in fluid dynamics. It is therefore of high
interest to formulate models able to capture the nonlinear spatio-temporal
velocity structure as well as produce forecasts in a computationally efficient
manner. Traditional statistical approaches are limited in their ability to
produce timely forecasts of complex, nonlinear spatio-temporal structures which
are at the same time able to incorporate the underlying flow physics. In this
work, we propose a model to accurately forecast boundary layer velocities with
a deep double reservoir computing network which is capable of capturing the
complex, nonlinear dynamics of the boundary layer while at the same time
incorporating physical constraints via a penalty obtained by a Partial
Differential Equation (PDE). Simulation studies on a one-dimensional viscous
fluid demonstrate how the proposed model is able to produce accurate forecasts
while simultaneously accounting for energy loss. The application focuses on
boundary layer data on a water tunnel with a PDE penalty derived from an
appropriate simplification of the Navier-Stokes equations, showing forecasts
improved by 33.7
velocity fluctuation, respectfully, against non physics-informed methods.
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