Deep Learning for Reduced Order Modelling and Efficient Temporal Evolution of Fluid Simulations

TL;DR

This paper introduces DL-ROM, a deep learning framework that non-linearly reduces the complexity of fluid simulations, enabling fast and accurate future state predictions without solving expensive Navier-Stokes equations.

Contribution

The work develops a novel neural network-based ROM that surpasses traditional linear methods by enabling non-linear projections and efficient temporal evolution prediction.

Findings

Reduces CFD simulation runtimes by nearly 100x

Maintains acceptable accuracy in fluid flow reconstructions

Operates without ground truth supervision

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.