Reduced-order modeling of unsteady fluid flow using neural network ensembles

TL;DR

This work tackles the challenge of efficient and accurate time-dependent reduced-order modeling for unsteady CFD by marrying convolutional autoencoders for spatial compression with an ensemble of LSTMs for latent-time forecasting. Bagging is used to form a robust LSTM ensemble that mitigates error propagation over long horizons at unseen designs. The CAE-eLSTM ROM is demonstrated on two incompressible laminar flows (lid-driven cavity and 2D cylinder) across two CFD solvers, delivering higher accuracy and stability than a single LSTM and achieving significant online speed-ups (approximately 9.4x and 27x, respectively). While the offline training cost is high, the approach is parallelizable and mesh-structure dependent, with future work extending to 3D, turbulence, and unstructured meshes to broaden applicability and efficiency.

Abstract

The use of deep learning has become increasingly popular in reduced-order models (ROMs) to obtain low-dimensional representations of full-order models. Convolutional autoencoders (CAEs) are often used to this end as they are adept at handling data that are spatially distributed, including solutions to partial differential equations. When applied to unsteady physics problems, ROMs also require a model for time-series prediction of the low-dimensional latent variables. Long short-term memory (LSTM) networks, a type of recurrent neural network useful for modeling sequential data, are frequently employed in data-driven ROMs for autoregressive time-series prediction. When making predictions at unseen design points over long time horizons, error propagation is a frequently encountered issue, where errors made early on can compound over time and lead to large inaccuracies. In this work, we propose using bagging, a commonly used ensemble learning technique, to develop a fully data-driven ROM framework referred to as the CAE-eLSTM ROM that uses CAEs for spatial reconstruction of the full-order model and LSTM ensembles for time-series prediction. When applied to two unsteady fluid dynamics problems, our results show that the presented framework effectively reduces error propagation and leads to more accurate time-series prediction of latent variables at unseen points.

Figures (13)

• Figure 1: Architecture of the encoder of a convolutional autoencoder (CAE) consisting of convolutional, pooling, and fully connected layers.
• Figure 2: Diagram of a single-layer LSTM neural network making a prediction one timestep ahead.
• Figure 3: An example of bootstrapping, where random subsets of the original dataset are chosen through sampling with replacement.
• Figure 4: Schematic of the online stage of the CAE-eLSTM ROM.
• Figure 5: Schematics describing the lid-driven cavity problem.