Latent-space Physics: Towards Learning the Temporal Evolution of Fluid Flow (1802.10123v3)

Abstract: We propose a method for the data-driven inference of temporal evolutions of physical functions with deep learning. More specifically, we target fluid flows, i.e. Navier-Stokes problems, and we propose a novel LSTM-based approach to predict the changes of pressure fields over time. The central challenge in this context is the high dimensionality of Eulerian space-time data sets. We demonstrate for the first time that dense 3D+time functions of physics system can be predicted within the latent spaces of neural networks, and we arrive at a neural-network based simulation algorithm with significant practical speed-ups. We highlight the capabilities of our method with a series of complex liquid simulations, and with a set of single-phase buoyancy simulations. With a set of trained networks, our method is more than two orders of magnitudes faster than a traditional pressure solver. Additionally, we present and discuss a series of detailed evaluations for the different components of our algorithm.

• The paper introduces a method using CNN autoencoders and LSTMs to predict the temporal evolution of fluid flow by learning dynamics in a low-dimensional latent space.
• This approach achieves roughly two orders of magnitude speedup over traditional solvers while maintaining high accuracy, demonstrated by PSNR exceeding 64 for pressure predictions.
• The findings pave the way for faster computational fluid dynamics simulations, enable new inverse problem investigations, and are scalable to higher resolutions with suitable data.

Latent Space Physics: Predicting Temporal Fluid Flow Evolution with Neural Networks

The paper under review introduces a methodological advancement in the domain of physics-informed machine learning, specifically focusing on the temporal evolution of fluid flow problems through learned latent spaces. Authored by S. Wiewel, M. Becher, and N. Thuerey from the Technical University of Munich, the research demonstrates a novel computational paradigm leveraging Long Short-Term Memory (LSTM) neural networks combined with a Convolutional Neural Network (CNN) based autoencoder to predict the evolution of pressure fields governed by the Navier-Stokes equations.

The crux of the paper is the development of a technique that reduces the dimensionality of high-dimensional, space-time datasets typical in fluid dynamics simulations, thereby allowing efficient data-driven forecasting. By encoding the physical system states into a reduced latent space with a CNN, and predicting temporal changes using LSTMs, the method achieves remarkable reductions in runtime compared to traditional solvers, reporting speed improvements on the order of two magnitudes. This efficiency gain is particularly evident when tackling large, complex simulations involving fluids with intricate dynamics.

The significance of the methods is highlighted in the context of complex liquid and single-phase buoyancy simulations. The proposed approach not only significantly outpaces conventional solvers in terms of computational speed but also maintains a reasonable degree of predictive accuracy. The paper notes average PSNR (Peak Signal-to-Noise Ratio) metrics exceeding 64 for pressure predictions, a testament to the efficacy of the method in maintaining fidelity to the physical system's evolution. Moreover, the paper explores variational autoencoders as a means to enforce latent space normalization, although the results suggest limited improvement in predictive accuracy over non-variational approaches.

The implications of these findings are manifold. Practically, the methodology presents an opportunity to dramatically accelerate simulations in computational fluid dynamics, a field notorious for its intensive computational load. Theoretically, the ability to encode dynamic systems in latent spaces presents new avenues for investigating inverse problems, where identifying system inputs based on output states is of interest.

Looking ahead, this paper paves the way for further exploration into the optimization of LSTM architectures specifically tailored for physical systems, as well as the integration of such neural networks in multi-physics simulations involving coupled systems. The inherent scalability of the approach promises applicability to high-resolution simulations, contingent on the availability of commensurately detailed training datasets.

In summary, this research represents a noteworthy step in merging deep learning with physics-based modeling for fluid flow predictions, suggesting profound implications for both scientific inquiry and industrial applications where rapid and reliable simulations are required. The paper invites future research to harness the full potential of neural networks in the modeling of complex dynamic systems, further bridging the gap between computational efficiency and physical accuracy.