# Liquid Splash Modeling with Neural Networks

arXiv: https://arxiv.org/abs/1704.04456 · HTML: https://mlsanity.com/paper/1704.04456/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Apr 2017.

## Built on by (most cited first, 16 of 16)

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- [Leveraging Stochastic Predictions of Bayesian Neural Networks for Fluid Simulations](https://mlsanity.com/paper/2205.01222/) (2022)
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- [Adaptive Swarm Mesh Refinement using Deep Reinforcement Learning with Local Rewards](https://mlsanity.com/paper/2406.08440/) (2024)
- [M4GN: Mesh-based Multi-segment Hierarchical Graph Network for Dynamic Simulations](https://mlsanity.com/paper/2509.10659/) (2025)
- [Exploring Physical Latent Spaces for High-Resolution Flow Restoration](https://mlsanity.com/paper/2211.11298/) (2022)
- [End-to-End Mesh Optimization of a Hybrid Deep Learning Black-Box PDE Solver](https://mlsanity.com/paper/2404.11766/) (2024)
- [Attention-Based Learning for Fluid State Interpolation and Editing in a Time-Continuous Framework](https://mlsanity.com/paper/2406.08188/) (2024)
- [Adaptive Graph Rewiring to Mitigate Over-Squashing in Mesh-Based GNNs for Fluid Dynamics Simulations](https://mlsanity.com/paper/2511.12709/) (2025)
- [Subspace Graph Physics: Real-Time Rigid Body-Driven Granular Flow Simulation](https://mlsanity.com/paper/2111.10206/) (2021)
- [SEA: State-Exchange Attention for High-Fidelity Physics Based Transformers](https://mlsanity.com/paper/2410.15495/) (2024)

## Abstract (arXiv)

This paper proposes a new data-driven approach to model detailed splashes for liquid simulations with neural networks. Our model learns to generate small-scale splash detail for the fluid-implicit-particle method using training data acquired from physically parametrized, high resolution simulations. We use neural networks to model the regression of splash formation using a classifier together with a velocity modifier. For the velocity modification, we employ a heteroscedastic model. We evaluate our method for different spatial scales, simulation setups, and solvers. Our simulation results demonstrate that our model significantly improves visual fidelity with a large amount of realistic droplet formation and yields splash detail much more efficiently than finer discretizations.