# Fast Aquatic Swimmer Optimization with Differentiable Projective Dynamics and Neural Network Hydrodynamic Models

arXiv: https://arxiv.org/abs/2204.12584 · HTML: https://mlsanity.com/paper/2204.12584/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 52 references that are in the map.
- First posted on arXiv 30 Mar 2022.

## Builds on (most cited first, 9 of 9)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Soft Rasterizer: A Differentiable Renderer for Image-based 3D Reasoning](https://mlsanity.com/paper/1904.01786/) (2019)
- [The CMA Evolution Strategy: A Tutorial](https://mlsanity.com/paper/1604.00772/) (2016)
- [Learning Particle Dynamics for Manipulating Rigid Bodies, Deformable Objects, and Fluids](https://mlsanity.com/paper/1810.01566/) (2018)
- [ChainQueen: A Real-Time Differentiable Physical Simulator for Soft Robotics](https://mlsanity.com/paper/1810.01054/) (2018)
- [Spline-PINN: Approaching PDEs without Data using Fast, Physics-Informed Hermite-Spline CNNs](https://mlsanity.com/paper/2109.07143/) (2021)
- [Flow Navigation by Smart Microswimmers via Reinforcement Learning](https://mlsanity.com/paper/1701.08848/) (2017)
- [DiffAqua: A Differentiable Computational Design Pipeline for Soft Underwater Swimmers with Shape Interpolation](https://mlsanity.com/paper/2104.00837/) (2021)

## Built on by (most cited first, 5 of 5)

- [SoftZoo: A Soft Robot Co-design Benchmark For Locomotion In Diverse Environments](https://mlsanity.com/paper/2303.09555/) (2023)
- [Fluid Simulation on Neural Flow Maps](https://mlsanity.com/paper/2312.14635/) (2023)
- [Physics-aware Machine Learning Revolutionizes Scientific Paradigm for Machine Learning and Process-based Hydrology](https://mlsanity.com/paper/2310.05227/) (2023)
- [RAFL: Generalizable Sim-to-Real of Soft Robots with Residual Acceleration Field Learning](https://mlsanity.com/paper/2603.22039/) (2026)
- [Neural Operators for Immersed-Boundary Soft Swimmers Locomotion](https://mlsanity.com/paper/2608.07722/) (2026)

## Abstract (arXiv)

Aquatic locomotion is a classic fluid-structure interaction (FSI) problem of interest to biologists and engineers. Solving the fully coupled FSI equations for incompressible Navier-Stokes and finite elasticity is computationally expensive. Optimizing robotic swimmer design within such a system generally involves cumbersome, gradient-free procedures on top of the already costly simulation. To address this challenge we present a novel, fully differentiable hybrid approach to FSI that combines a 2D direct numerical simulation for the deformable solid structure of the swimmer and a physics-constrained neural network surrogate to capture hydrodynamic effects of the fluid. For the deformable solid simulation of the swimmer's body, we use state-of-the-art techniques from the field of computer graphics to speed up the finite-element method (FEM). For the fluid simulation, we use a U-Net architecture trained with a physics-based loss function to predict the flow field at each time step. The pressure and velocity field outputs from the neural network are sampled around the boundary of our swimmer using an immersed boundary method (IBM) to compute its swimming motion accurately and efficiently. We demonstrate the computational efficiency and differentiability of our hybrid simulator on a 2D carangiform swimmer. Due to differentiability, the simulator can be used for computational design of controls for soft bodies immersed in fluids via direct gradient-based optimization.