Reversible GNS for Dissipative Fluids with Consistent Bidirectional Dynamics

2025-09-26

AI Summary

In dissipative fluid systems, inverse inference of physically plausible trajectories is hindered by irreversibility, leading to poor convergence, slow optimization, and low stability in conventional methods. To address this, we propose R-GNS—the first unified reversible graph network framework supporting both forward and inverse simulation. R-GNS employs a shared-parameter residual reversible message-passing mechanism, enabling bidirectional dynamical consistency without explicit physical inversion. Fully differentiable, it tightly couples forward prediction with inverse reasoning. Experiments across multiple dissipative fluid benchmarks demonstrate that R-GNS achieves superior accuracy and trajectory consistency compared to state-of-the-art methods, with only ~25% of the parameters of GNS. Its inverse inference is up to 100× faster than iterative optimization approaches, while forward simulation performance matches that of GNS. Moreover, R-GNS efficiently generates complex target fluid shapes, highlighting its efficacy for controllable physics-based modeling.

Technology Category

• Machine Learning: Imitation Learning & Inverse Reinforcement Learning
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

Abstract

Simulating physically plausible trajectories toward user-defined goals is a fundamental yet challenging task in fluid dynamics. While particle-based simulators can efficiently reproduce forward dynamics, inverse inference remains difficult, especially in dissipative systems where dynamics are irreversible and optimization-based solvers are slow, unstable, and often fail to converge. In this work, we introduce the Reversible Graph Network Simulator (R-GNS), a unified framework that enforces bidirectional consistency within a single graph architecture. Unlike prior neural simulators that approximate inverse dynamics by fitting backward data, R-GNS does not attempt to reverse the underlying physics. Instead, we propose a mathematically invertible design based on residual reversible message passing with shared parameters, coupling forward dynamics with inverse inference to deliver accurate predictions and efficient recovery of plausible initial states. Experiments on three dissipative benchmarks (Water-3D, WaterRamps, and WaterDrop) show that R-GNS achieves higher accuracy and consistency with only one quarter of the parameters, and performs inverse inference more than 100 times faster than optimization-based baselines. For forward simulation, R-GNS matches the speed of strong GNS baselines, while in goal-conditioned tasks it eliminates iterative optimization and achieves orders-of-magnitude speedups. On goal-conditioned tasks, R-GNS further demonstrates its ability to complex target shapes (e.g., characters "L" and "N") through vivid, physically consistent trajectories. To our knowledge, this is the first reversible framework that unifies forward and inverse simulation for dissipative fluid systems.

Problem

• Simulating bidirectional fluid dynamics in dissipative systems
• Achieving efficient inverse inference without reversing physics
• Unifying forward and inverse simulation with reversible architecture

Innovation

• Reversible graph network with bidirectional consistency
• Invertible residual reversible message passing design
• Unified forward and inverse simulation framework