Latent Space Physics: Towards Learning the Temporal Evolution of Fluid Flow

By Steffen Wiewel, Moritz Becher, Nils Thürey. 2018

321 citations recorded by the source corpus.

We propose a method for the data‐driven inference of temporal evolutions of physical functions with deep learning. More specifically, we target fluid flow problems, and we propose a novel LSTM‐based approach to predict the changes of the pressure field 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.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition, Statistical and Nonlinear Physics, AI for Physical Sciences

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Citations in the corpus

Neural Ordinary Differential Equations (2018, neutral): “One can train feed-forward or recurrent neural networks to approximate a differential equation (Raissi and Karniadakis, 2018; Raissi et al., 2018a; Long et al., 2017), with applications such as ﬂ uid simulation (Wiewel et al., 2018).”
Toward Causal Representation Learning (2021, background): “One interesting aspect is physics simulation with neural networks [94], which can substantially increase the efﬁciency of hand-engineered simulators [104], [143], [211], [265], [269].”
Learning to Simulate Complex Physics with Graph Networks (2020, background): “, (Ladickỳ et al., 2015; Wiewel et al., 2019) learn parts of a fluid simulator for faster prediction.”
Transformer for Partial Differential Equations' Operator Learning (2022, methodology): “Therefore, once the encoding from observation space to the latent space is done, the system can evolve in time using Recurrent Neural Networks (RNNs) such as LSTM (Wiewel et al., 2019) or even linear propagators based on the assumptions of learning Koopman operator (Morton et al., 2018; Li et al., 2”
Digital Twin: Values, Challenges and Enablers From a Modeling Perspective (2019, methodology): “…replacement of equations with ML algorithms for gaining computational efﬁciency when generalization is not a necessity (e.g., we refer to [318]–[325] and references cited therein for speeding up numerical solvers for real-time applications) can be used in the context of digital twin when the…”
PDE-Net 2.0: Learning PDEs from Data with A Numeric-Symbolic Hybrid Deep Network (2018, background): “An interesting fact is that some popular networks in computer vision, such as ResNet[15, 16], have close relationship with ODEs/PDEs and can be naturally merged with traditional computational mathematics in various tasks [17, 18, 19, 20, 21, 22, 23, 24, 25, 26].”
Towards Physics-informed Deep Learning for Turbulent Flow Prediction (2019, methodology): “[31] proposed a method for the data-driven inference of temporal evolutions of physical functions with deep learning.”
Lagrangian Fluid Simulation with Continuous Convolutions (2020, background): “…to accelerate the expensive pressure correction step of grid-based solvers, while other works have focused on super-resolution (Xie et al., 2018), learning time evolution via the Koopman operator (Morton et al., 2018), and learning reduced representations (Wiewel et al., 2019; Kim et al., 2019).”
Learning Mesh-Based Simulation with Graph Networks (2020, background): “Short run times are also a desirable property for fluid simulation in visualization and graphics [41, 37, 42].”
Learning to Optimize: A Primer and A Benchmark (2021, methodology): “One can train feed-forward or recurrent neural networks to approximate PDEs, with applications such as fluid simulation [229].”
Deep Fluids: A Generative Network for Parameterized Fluid Simulations (2018, methodology): “An LSTM-based method for predicting changes of the pressure ﬁeld for multiple subsequent time steps has been presented by [WBT18], resulting in signiﬁcant speed-ups of the pressure solver.”