# SPNets: Differentiable Fluid Dynamics for Deep Neural Networks

arXiv: https://arxiv.org/abs/1806.06094 · HTML: https://mlsanity.com/paper/1806.06094/

## Key facts

- Cited by 62 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jun 2018.

## Built on by (most cited first, 30 of 62)

- [PlasticineLab: A Soft-Body Manipulation Benchmark with Differentiable Physics](https://mlsanity.com/paper/2104.03311/) (2021)
- [gradSim: Differentiable simulation for system identification and visuomotor control](https://mlsanity.com/paper/2104.02646/) (2021)
- [DiffCloth: Differentiable Cloth Simulation with Dry Frictional Contact](https://mlsanity.com/paper/2106.05306/) (2021)
- [DiffPD: Differentiable Projective Dynamics](https://mlsanity.com/paper/2101.05917/) (2021)
- [Fast and Feature-Complete Differentiable Physics for Articulated Rigid Bodies with Contact](https://mlsanity.com/paper/2103.16021/) (2021)
- [Point Cloud Matters: Rethinking the Impact of Different Observation Spaces on Robot Learning](https://mlsanity.com/paper/2402.02500/) (2024)
- [DiffSkill: Skill Abstraction from Differentiable Physics for Deformable Object Manipulations with Tools](https://mlsanity.com/paper/2203.17275/) (2022)
- [FluidLab: A Differentiable Environment for Benchmarking Complex Fluid Manipulation](https://mlsanity.com/paper/2303.02346/) (2023)
- [Efficient Differentiable Simulation of Articulated Bodies](https://mlsanity.com/paper/2109.07719/) (2021)
- [Spline-PINN: Approaching PDEs without Data using Fast, Physics-Informed Hermite-Spline CNNs](https://mlsanity.com/paper/2109.07143/) (2021)
- [Physical Design using Differentiable Learned Simulators](https://mlsanity.com/paper/2202.00728/) (2022)
- [NeuroFluid: Fluid Dynamics Grounding with Particle-Driven Neural Radiance Fields](https://mlsanity.com/paper/2203.01762/) (2022)
- [Guaranteed Conservation of Momentum for Learning Particle-based Fluid Dynamics](https://mlsanity.com/paper/2210.06036/) (2022)
- [Boundary Graph Neural Networks for 3D Simulations](https://mlsanity.com/paper/2106.11299/) (2021)
- [Dress-1-to-3: Single Image to Simulation-Ready 3D Outfit with Diffusion Prior and Differentiable Physics](https://mlsanity.com/paper/2502.03449/) (2025)
- [Global Transport for Fluid Reconstruction with Learned Self-Supervision](https://mlsanity.com/paper/2104.06031/) (2021)
- [SAGCI-System: Towards Sample-Efficient, Generalizable, Compositional, and Incremental Robot Learning](https://mlsanity.com/paper/2111.14693/) (2021)
- [Transformer with Implicit Edges for Particle-based Physics Simulation](https://mlsanity.com/paper/2207.10860/) (2022)
- [Direct Prediction of Steady-State Flow Fields in Meshed Domain with Graph Networks](https://mlsanity.com/paper/2105.02575/) (2021)
- [Physics perception in sloshing scenes with guaranteed thermodynamic consistency](https://mlsanity.com/paper/2106.13301/) (2021)
- [Thermodynamics of learning physical phenomena](https://mlsanity.com/paper/2207.12749/) (2022)
- [DiffAqua: A Differentiable Computational Design Pipeline for Soft Underwater Swimmers with Shape Interpolation](https://mlsanity.com/paper/2104.00837/) (2021)
- [Fine-grained differentiable physics: a yarn-level model for fabrics](https://mlsanity.com/paper/2202.00504/) (2022)
- [A Thermodynamics-informed Active Learning Approach to Perception and Reasoning about Fluids](https://mlsanity.com/paper/2203.05775/) (2022)
- [Latent Intuitive Physics: Learning to Transfer Hidden Physics from A 3D Video](https://mlsanity.com/paper/2406.12769/) (2024)
- [DQC: a Python program package for Differentiable Quantum Chemistry](https://mlsanity.com/paper/2110.11678/) (2021)
- [Jade: A Differentiable Physics Engine for Articulated Rigid Bodies with Intersection-Free Frictional Contact](https://mlsanity.com/paper/2309.04710/) (2023)
- [Learning to Manipulate Amorphous Materials](https://mlsanity.com/paper/2103.02533/) (2021)
- [Learning to Estimate Single-View Volumetric Flow Motions without 3D Supervision](https://mlsanity.com/paper/2302.14470/) (2023)
- [Zero Grads: Learning Local Surrogate Losses for Non-Differentiable Graphics](https://mlsanity.com/paper/2308.05739/) (2023)

## Abstract (arXiv)

In this paper we introduce Smooth Particle Networks (SPNets), a framework for integrating fluid dynamics with deep networks. SPNets adds two new layers to the neural network toolbox: ConvSP and ConvSDF, which enable computing physical interactions with unordered particle sets. We use these lay- ers in combination with standard neural network layers to directly implement fluid dynamics inside a deep network, where the parameters of the network are the fluid parameters themselves (e.g., viscosity, cohesion, etc.). Because SPNets are imple- mented as a neural network, the resulting fluid dynamics are fully differentiable. We then show how this can be successfully used to learn fluid parameters from data, perform liquid control tasks, and learn policies to manipulate liquids.