Deep Fluids: A Generative Network for Parameterized Fluid Simulations (1806.02071v2)

Abstract: This paper presents a novel generative model to synthesize fluid simulations from a set of reduced parameters. A convolutional neural network is trained on a collection of discrete, parameterizable fluid simulation velocity fields. Due to the capability of deep learning architectures to learn representative features of the data, our generative model is able to accurately approximate the training data set, while providing plausible interpolated in-betweens. The proposed generative model is optimized for fluids by a novel loss function that guarantees divergence-free velocity fields at all times. In addition, we demonstrate that we can handle complex parameterizations in reduced spaces, and advance simulations in time by integrating in the latent space with a second network. Our method models a wide variety of fluid behaviors, thus enabling applications such as fast construction of simulations, interpolation of fluids with different parameters, time re-sampling, latent space simulations, and compression of fluid simulation data. Reconstructed velocity fields are generated up to 700x faster than re-simulating the data with the underlying CPU solver, while achieving compression rates of up to 1300x.

Deep Fluids: A Comprehensive Synthesis of Parameterized Fluid Simulations Using Generative Networks

The paper "Deep Fluids: A Generative Network for Parameterized Fluid Simulations" presents an innovative approach to synthesizing fluid simulations through generative neural networks. The research focuses on training convolutional neural networks (CNNs) to generate fluid velocities based on a set of reduced parameters, thus significantly accelerating the simulation process and providing substantial data compression capabilities.

Key Contributions and Methodology

This research introduces a generative model optimized specifically for fluid dynamics, leveraging deep learning to synthesize plausible fluid simulations from parameters that describe fluid behaviors. The core contributions of the paper include:

1. Generative Model for Fluids: The paper proposes a novel generative CNN capable of fully synthesizing both 2-D and 3-D fluid velocities. The network is trained on discrete data representing various fluid behaviors such as turbulent flows and viscous liquids. By employing a novel loss function, the model ensures divergence-free velocity fields, a key requirement in simulating incompressible flows.
2. Data Compression and Performance Improvement: The trained network achieves remarkable data compression rates of up to 1300× compared to the original simulation datasets, which is two orders of magnitude greater than previously reported methods. Moreover, the model can generate reconstructed velocity fields up to 700 times faster than traditional CPU-based methods, making it viable for real-time applications such as gaming and virtual reality.
3. Interpolation and Extrapolation in Parameter Spaces: The generative model efficiently handles interpolation of fluid behaviors by exploring the parameter space, producing plausible intermediate fluid states that were not explicitly part of the training dataset. In addition, the paper extends the utility of its architecture by employing an encoder and latent space integration network to accommodate complex simulation scenarios with extended parameterizations.
4. Reduced-Order Modelling and Latent Space Simulations: The approach extends to reduced-order models by encoding simulation classes into a latent space, enabling the architecture to generate simulations in scenarios where computational resources are constrained. A latent space integration network further allows the advancement of these simulations in time without sacrificing accuracy.

Implications and Future Developments

The implications of this research are significant for both theoretical advancements in the modeling of fluid dynamics and practical applications in computational acceleration and data storage. The ability to interpolate and extrapolate fluid simulations enables more efficient prototyping and testing of physical phenomena in virtual environments. Furthermore, the demonstrated compression capabilities suggest that this approach could be transformative in industries requiring extensive fluid simulations, such as film production and interactive media.

Future developments in this area may focus on enhancing the quality of fine-scale structures in fluid reconstructions, potentially through adversarial training frameworks or improved regularization methods. Expanding the approach to accommodate heterogeneous fluid environments and more complex boundary conditions could also provide further versatility across different scientific and engineering domains.

In summary, "Deep Fluids" illustrates a significant step forward in leveraging generative models for efficient fluid simulation, combining deep learning strategies with the physical requirements of fluid dynamics. This paper provides a comprehensive basis for the continued exploration of machine learning applications within the field of computational physics, paving the way for more sophisticated and accessible simulation techniques.