Combining Extended Convolutional Autoencoders and Reservoir Computing for Accurate Reduced-Order Predictions of Atmospheric Flows

TL;DR

This work proposes to reduce the computational cost with a Reduced Order Model (ROM) that combines Extended Convolutional Autoencoders (E-CAE) and Reservoir Computing (RC) that accurately reconstructs and predicts the future system dynamics with errors below 6% in 2D and 8% in 3D, while significantly reducing the computational cost of a full-order simulation.

Abstract

Forecasting atmospheric flows with traditional discretization methods, also called full order methods (e.g., finite element methods or finite volume methods), is computationally expensive. We propose to reduce the computational cost with a Reduced Order Model (ROM) that combines Extended Convolutional Autoencoders (E-CAE) and Reservoir Computing (RC). Thanks to an extended network depth, the E-CAE encodes the high-resolution data coming from the full order method into a compact latent representation and can decode it back into high-resolution with 75% lower reconstruction error than standard CAEs. The compressed data are fed to an RC network, which predicts their evolution. The advantage of RC networks is a reduced computational cost in the training phase compared to conventional predictive models. We assess our data-driven ROM through well-known 2D and 3D benchmarks for atmospheric flows. We show that our ROM accurately reconstructs and predicts the future system dynamics with errors below 6% in 2D and 8% in 3D, while significantly reducing the computational cost of a full-order simulation. Compared to other ROMs available in the literature, such as Dynamic Mode Decomposition and Proper Orthogonal Decomposition with Interpolation, our ROM is as efficient but more accurate. Thus, it is a promising alternative to high-dimensional atmospheric simulations.

Figures (12)

• Figure 1: CAE architecture with encorder and decoder that feature $L$ layers. For each layer $l$, with $l = 1, \dots, L$, $N_f^l$ is the number of applied filters.
• Figure 2: Encoder architecture of the E-CAE with $L$ layers. For each layer $l$, with $l = 1, \dots, L$, we apply $n_f$ sets of $N_f^l$ filters.
• Figure 3: Sketch of the three main components of an RC architecture: input layer, reservoir node, and output layer. With $\bm{W}_{in}$, $\bm{W}_{res}$ and $\bm{W}_{out}$, we denote the weight matrices that define the interactions among the components.
• Figure 4: Rising thermal bubble: Time evolution of latent spaces for the different training-to-validation (T-to-V) dataset ratios listed in Tab. \ref{['tab:sensitivity_analysis']}. The blue and orange dashed curves show the ground truth and the reconstructed/predicted latent spaces, respectively. The red dashed line indicates the time instance where prediction starts.
• Figure 5: Rising thermal bubble: Time evolution of error \ref{['eq:l2Error']} for different training-to-validation (T-to-V) dataset ratios listed in Tab. \ref{['tab:sensitivity_analysis']}: $60\% - 40\%$ (blue curve), $40\% - 60\%$ (yellow curve) and $80\% - 20\%$ (green curve). The dashed vertical lines indicate the start of prediction phase for each case. The inset provides a zoomed-in view of green curve in normal scale.

Theorems & Definitions (1)

• Remark 3.1