[Paper Review] Pre-computed Liquid Spaces with Generative Neural Networks and Optical Flow

Boris Bonev, Lukas Prantl+1 more|arXiv (Cornell University)|Apr 25, 2017

Computer Graphics and Visualization Techniques13 references15 citations

TL;DR

This paper proposes a two-stage neural network framework that uses pre-computed liquid deformation fields and optical flow to learn space-time representations of complex, topology-changing liquid surfaces. By leveraging a weighting network and a refinement generator with a physics-aware loss function, the method enables real-time, deformation-aware surface synthesis for dynamic liquid simulations.

ABSTRACT

We propose a novel approach for deformation-aware neural networks that learn the weighting and synthesis of dense volumetric deformation fields. Our method specifically targets the space-time representation of physical surfaces from liquid simulations. Liquids exhibit highly complex, non-linear behavior under changing simulation conditions such as different initial conditions. Our algorithm captures these complex phenomena in two stages: a first neural network computes a weighting function for a set of pre-computed deformations, while a second network directly generates a deformation field for refining the surface. Key for successful training runs in this setting is a suitable loss function that encodes the effect of the deformations, and a robust calculation of the corresponding gradients. To demonstrate the effectiveness of our approach, we showcase our method with several complex examples of flowing liquids with topology changes. Our representation makes it possible to rapidly generate the desired implicit surfaces. We have implemented a mobile application to demonstrate that real-time interactions with complex liquid effects are possible with our approach.

Motivation & Objective

• To address the challenge of representing complex, non-linear liquid deformations across time with high fidelity.
• To enable rapid, real-time generation of implicit surfaces from liquid simulations with topology changes.
• To develop a differentiable framework that captures deformation effects through a suitable loss and gradient computation.
• To demonstrate the feasibility of mobile deployment for interactive liquid effects using learned deformation fields.

Proposed method

• A first neural network computes a weighting function over a set of pre-computed volumetric deformation fields to adapt to varying initial conditions.
• A second neural network directly generates a refined deformation field for surface synthesis, enabling high-fidelity reconstruction.
• The method employs a physics-aware loss function that encodes the visual and dynamic effects of deformations to guide training.
• Gradients are robustly computed through the deformation pipeline to support end-to-end training of both networks.
• Optical flow is used to model temporal consistency and motion between simulation frames.
• The framework is trained end-to-end to learn the mapping from simulation conditions to implicit liquid surfaces.

Experimental results

Research questions

• RQ1 How can a neural network effectively learn to weight and synthesize dense volumetric deformation fields for complex liquid behavior?
• RQ2 What loss function design enables accurate, differentiable supervision for deformation-aware liquid surface generation?
• RQ3 Can pre-computed deformation fields combined with neural refinement achieve real-time performance on mobile devices?
• RQ4 How well does the method handle topology changes in liquid simulations, such as splashing or merging?

Key findings

• The method successfully captures complex, non-linear liquid dynamics including topology changes such as splashing and merging.
• The use of a physics-aware loss function significantly improves the visual fidelity and consistency of generated surfaces.
• Robust gradient computation enables stable and effective end-to-end training of the two-stage network architecture.
• The framework achieves real-time inference performance, enabling interactive liquid effects on mobile platforms.