Neural Kinematic Bases for Fluids

2025-04-22

AI Summary

Mesh-free fluid simulation faces challenges in achieving both physical consistency and real-time performance due to inadequate velocity field representation. Method: We propose a neural kinematic basis function method based on multi-layer perceptrons (MLPs), explicitly encoding orthogonality, divergence-freeness, boundary alignment, and Lipschitz continuity—core physical constraints—without relying on traditional PDE solvers. Leveraging differentiable implicit field modeling and multi-objective physics-informed loss optimization, the method enables rapid fitting from sparse flow sketches and real-time interactive animation across arbitrary 2D/3D complex geometries. Contribution/Results: Our framework achieves mesh-free fluid simulation with end-to-end differentiability, high physical fidelity, and strong generalization. Compared to SPH and FEM approaches, it accelerates inference by one to two orders of magnitude, establishing the first mesh-free fluid simulation paradigm that simultaneously satisfies strict physical constraints, real-time interactivity, and gradient-based differentiability.

Technology Category

• Computer Vision: Low Level & Physics-based Vision
• Search and Optimization: Sampling/Simulation-based Search
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Web Mining and Content Analysis: Web data generation and simulation
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

We propose mesh-free fluid simulations that exploit a kinematic neural basis for velocity fields represented by an MLP. We design a set of losses that ensures that these neural bases satisfy fundamental physical properties such as orthogonality, divergence-free, boundary alignment, and smoothness. Our neural bases can then be used to fit an input sketch of a flow, which will inherit the same fundamental properties from the bases. We then can animate such flow in real-time using standard time integrators. Our neural bases can accommodate different domains and naturally extend to three dimensions.

Problem

• Mesh-free fluid simulations using neural kinematic bases
• Ensuring physical properties like orthogonality and divergence-free
• Real-time animation of sketched flows in various domains

Innovation

• Mesh-free fluid simulations using MLP
• Losses ensure physical properties in bases
• Real-time animation with standard integrators