# Reversible GNS for Dissipative Fluids with Consistent Bidirectional Dynamics

arXiv: https://arxiv.org/abs/2509.22207 · HTML: https://mlsanity.com/paper/2509.22207/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 31 references that are in the map.
- First posted on arXiv 26 Sep 2025.

## Builds on (most cited first, 18 of 18)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Invertible Residual Networks](https://mlsanity.com/paper/1811.00995/) (2018)
- [DiffTaichi: Differentiable Programming for Physical Simulation](https://mlsanity.com/paper/1910.00935/) (2019)
- [Analyzing Inverse Problems with Invertible Neural Networks](https://mlsanity.com/paper/1808.04730/) (2018)
- [The Reversible Residual Network: Backpropagation Without Storing Activations](https://mlsanity.com/paper/1707.04585/) (2017)
- [PhysDreamer: Physics-Based Interaction with 3D Objects via Video Generation](https://mlsanity.com/paper/2404.13026/) (2024)
- [Learning to Control PDEs with Differentiable Physics](https://mlsanity.com/paper/2001.07457/) (2020)
- [NIKI: Neural Inverse Kinematics with Invertible Neural Networks for 3D Human Pose and Shape Estimation](https://mlsanity.com/paper/2305.08590/) (2023)
- [Guaranteed Conservation of Momentum for Learning Particle-based Fluid Dynamics](https://mlsanity.com/paper/2210.06036/) (2022)
- [Transformer with Implicit Edges for Particle-based Physics Simulation](https://mlsanity.com/paper/2207.10860/) (2022)
- [Learning Lagrangian Fluid Mechanics with E(3)-Equivariant Graph Neural Networks](https://mlsanity.com/paper/2305.15603/) (2023)
- [Neural SPH: Improved Neural Modeling of Lagrangian Fluid Dynamics](https://mlsanity.com/paper/2402.06275/) (2024)
- [InvGAN: Invertible GANs](https://mlsanity.com/paper/2112.04598/) (2021)

## Built on by (most cited first, 1 of 1)

- [CORGI: GNNs with Convolutional Residual Global Interactions for Lagrangian Simulation](https://mlsanity.com/paper/2511.22938/) (2025)

## Abstract (arXiv)

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.