Reduced order modeling with shallow recurrent decoder networks

Overview

SHallow REcurrent Decoder-based Reduced Order Model (SHRED-ROM) is an ultra-hyperreduced order modeling framework aiming at reconstructing high-dimensional data from limited sensor measurements in multiple scenarios. Thanks to the composition of a Long-Short Term Memory network (LSTM) and a Shallow Decoder Network (SDN), SHRED-ROM is capable of

Reconstructing high-dimensional data (such as synthetic or video data) from sparse sensor measurements in new scenarios unseen during training, regardless of sensor placement,

Dealing with both physical, geometrical and time-dependent parametric dependencies, while being agnostic to the paraemter values,

Estimating unknown parameters,

Coping with both fixed or mobile sensors.

Importantly, computational efficiency and memory usage are enhanced by reducing the dimensionality of full-order snapshots, allowing for compressive training of the networks, with minimal hyperparameter tuning and laptop-level computing.

Contents

GoPro_video*.gif  -->  videos of flows around an oscillating cylinder at different inflow conditions

KuramotoSivashinsky_data.npz  -->  time-dependent state, whose dynamics is described by the 1D Kuramoto-Sivashinsky equation, for different viscosity and initial condition frequencies. The corresponding parameters are also provided

Pinball_data.npz  -->  time-dependent densities, whose dynamics is described by the advection-diffusion partial differential equation, for different velocities of the rotating cylinders. The corresponding parameters and the transport term, which is computed through steady Navier-Stokes equations, are also provided

FlowAroundObstacle_data.npz  -->  time-dependent velocities and pressures, whose dynamics is described in terms of unsteady Navier-Stokes equations, for different obstacle geometries, inflow intensities and constant angles of attack. The corresponding parameters are also provided

FlowAroundObstacle_UnsteadyParam_data.npz  -->  time-dependent velocities and pressures, whose dynamics is described in terms of unsteady Navier-Stokes equations, for different obstacle geometries, inflow intensities and time-dependent angles of attack. The corresponding parameters are also provided

*.zip  -->  mesh, sensor indices and trained neural networks for code reproducibility