[Paper Review] Deep Learning for Reduced Order Modelling and Efficient Temporal Evolution of Fluid Simulations

Pranshu Pant, Ruchit Doshi+2 more|arXiv (Cornell University)|Jul 9, 2021

Model Reduction and Neural Networks80 references116 citations

TL;DR

This paper proposes DL-ROM, a deep learning framework that learns non-linear reduced-order representations of fluid flow simulations using 3D autoencoders and U-Net architectures. By projecting high-fidelity flow snapshots into a learned low-dimensional latent space, the model predicts future timesteps with up to 100x faster inference than traditional CFD solvers, achieving high reconstruction accuracy while minimizing error accumulation over time.

ABSTRACT

Reduced Order Modelling (ROM) has been widely used to create lower order, computationally inexpensive representations of higher-order dynamical systems. Using these representations, ROMs can efficiently model flow fields while using significantly lesser parameters. Conventional ROMs accomplish this by linearly projecting higher-order manifolds to lower-dimensional space using dimensionality reduction techniques such as Proper Orthogonal Decomposition (POD). In this work, we develop a novel deep learning framework DL-ROM (Deep Learning - Reduced Order Modelling) to create a neural network capable of non-linear projections to reduced order states. We then use the learned reduced state to efficiently predict future time steps of the simulation using 3D Autoencoder and 3D U-Net based architectures. Our model DL-ROM is able to create highly accurate reconstructions from the learned ROM and is thus able to efficiently predict future time steps by temporally traversing in the learned reduced state. All of this is achieved without ground truth supervision or needing to iteratively solve the expensive Navier-Stokes(NS) equations thereby resulting in massive computational savings. To test the effectiveness and performance of our approach, we evaluate our implementation on five different Computational Fluid Dynamics (CFD) datasets using reconstruction performance and computational runtime metrics. DL-ROM can reduce the computational runtimes of iterative solvers by nearly two orders of magnitude while maintaining an acceptable error threshold.

Motivation & Objective

• To overcome the limitations of linear reduced order models (ROMs) in capturing complex, non-linear fluid dynamics.
• To develop a deep learning-based framework that learns non-linear, low-dimensional embeddings of fluid flow states without requiring ground truth supervision.
• To enable efficient, real-time prediction of future flow states by temporally propagating in the learned latent space.
• To drastically reduce computational cost compared to iterative Navier-Stokes solvers while maintaining acceptable accuracy.
• To validate the method across diverse CFD datasets, including turbulent and vortex-dominated flows.

Proposed method

• The framework uses a 3D convolutional autoencoder to encode high-fidelity flow snapshots into a low-dimensional latent space, learning a non-linear manifold.
• A 3D U-Net architecture is employed as the decoder to reconstruct the full-order flow state from the latent representation with minimal error.
• The model takes 10 previous timesteps as input, each separated by 10 time steps, to predict the next flow state in the latent space.
• Latent state transitions are modeled via a temporal prediction head that propagates the reduced state forward in time without solving the Navier-Stokes equations.
• Hyperparameters such as latent dimension (optimized at 32) and temporal context length are tuned for reconstruction accuracy and efficiency.
• The method avoids LSTMs and instead uses a 3D convolutional recurrence mechanism to maintain spatial and temporal coherence.

Experimental results

Research questions

• RQ1 Can a deep learning-based ROM outperform traditional linear ROMs in capturing complex, non-linear fluid dynamics?
• RQ2 To what extent can a learned latent space enable accurate, long-term prediction of fluid flow evolution without iterative Navier-Stokes solves?
• RQ3 How does the DL-ROM framework compare in computational efficiency and reconstruction accuracy to conventional CFD solvers across diverse flow regimes?
• RQ4 Can the model maintain low error accumulation over multiple prediction steps in a closed-loop simulation?
• RQ5 What is the impact of flow complexity (e.g., vortex shedding, high gradients) on reconstruction fidelity?

Key findings

• DL-ROM reduces computational runtime of CFD simulations by nearly two orders of magnitude compared to iterative OpenFOAM solvers across three custom datasets (2D cylinder, 2D airfoil, 2D plate).
• The model achieves high reconstruction accuracy, with mean squared error (MSE) per pixel remaining low and decreasing gradually over 20 prediction iterations, indicating stable error propagation.
• The model accurately predicts complex flow structures such as von-Kármán vortex streets, even in regions with high flow gradients, though small errors emerge near obstructions.
• Reconstruction performance is suboptimal for datasets with fine-scale turbulent structures (e.g., 2D channel flow), where small flow features are lost during compression into the latent space.
• The framework successfully performs looped simulations over 20 timesteps without ground truth supervision, maintaining low MSE and stable predictions.
• The optimal latent dimension for reconstruction was found to be 32, balancing accuracy and computational efficiency.