[Paper Review] Compressed Convolutional LSTM: An Efficient Deep Learning framework to Model High Fidelity 3D Turbulence

Arvind Mohan, Don Daniel+2 more|arXiv (Cornell University)|Feb 28, 2019

Model Reduction and Neural Networks44 references59 citations

TL;DR

The authors introduce Compressed ConvLSTM (CC-LSTM) that combines a convolutional autoencoder with ConvLSTM to learn a low-dimensional attractor of 3D turbulence and generate spatio-temporal flow realizations efficiently, validated by physics-based diagnostics.

ABSTRACT

High-fidelity modeling of turbulent flows is one of the major challenges in computational physics, with diverse applications in engineering, earth sciences and astrophysics, among many others. The rising popularity of high-fidelity computational fluid dynamics (CFD) techniques like direct numerical simulation (DNS) and large eddy simulation (LES) have made significant inroads into the problem. However, they remain out of reach for many practical three-dimensional flows characterized by extremely large domains and transient phenomena. Therefore designing efficient and accurate data-driven generative approaches to model turbulence is a necessity. We propose a novel training approach for dimensionality reduction and spatio-temporal modeling of the three-dimensional dynamics of turbulence using a combination of Convolutional autoencoder and the Convolutional LSTM neural networks. The quality of the emulated turbulent fields is assessed with rigorous physics-based statistical tests, instead of visual assessments. The results show significant promise in the training methodology to generate physically consistent turbulent flows at a small fraction of the computing resources required for DNS.

Motivation & Objective

• Motivate the need for data-driven, low-cost high-fidelity turbulence modeling in engineering and geoscience applications.
• Develop a scalable framework that learns a low-dimensional attractor for 3D turbulent flows.
• Demonstrate a training strategy that jointly compresses data and models spatio-temporal dynamics.
• Assess physical fidelity of generated turbulence using physics-based diagnostics rather than visual inspection.

Proposed method

• Use a convolutional autoencoder (CAE) to compress 3D turbulence snapshots into a latent space.
• Extend ConvLSTM to 3D to model spatio-temporal evolution in the latent space.
• Train CC-LSTM in two steps: CAE-based dimensionality reduction followed by latent-space temporal modeling with ConvLSTM.
• Dynamically decompress latent predictions back to the original 3D field using the CAE decoder.
• Adopt a cyclic seeding approach to generate long time predictions from short forecast hops.

Experimental results

Research questions

• RQ1 Can CC-LSTM accurately capture 3D turbulence dynamics in a reduced latent space while preserving key spatial correlations?
• RQ2 Do physics-based diagnostics (e.g., energy spectrum, velocity gradient statistics, Q-R plane) indicate physically consistent turbulence in reconstructed fields?
• RQ3 How does the CAE-based compression affect reconstruction quality and predictive stability over time?

Key findings

• CC-LSTM achieves massive parameter reduction by operating in a compressed latent space without sacrificing essential spatial correlations.
• The CAE+ConvLSTM pipeline can generate physically consistent turbulent fields at a fraction of DNS computational cost.
• Physics-based diagnostics show the compressed representations reproduce energy spectra and velocity-gradient statistics reasonably well for HIT and ScalarHIT datasets.
• Compression ratios up to z=125 for HIT and z=20 for ScalarHIT demonstrate effective dimensionality reduction with acceptable fidelity in reconstructed fields.
• The approach enables long-time predictions by seeding and cyclic prediction, while maintaining training tractability on a single GPU.