# DiffAqua: A Differentiable Computational Design Pipeline for Soft Underwater Swimmers with Shape Interpolation

arXiv: https://arxiv.org/abs/2104.00837 · HTML: https://mlsanity.com/paper/2104.00837/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 75 references that are in the map.
- First posted on arXiv 2 Apr 2021.

## Builds on (most cited first, 20 of 20)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flows](https://mlsanity.com/paper/1906.12320/) (2019)
- [DiffTaichi: Differentiable Programming for Physical Simulation](https://mlsanity.com/paper/1910.00935/) (2019)
- [Learning Particle Dynamics for Manipulating Rigid Bodies, Deformable Objects, and Fluids](https://mlsanity.com/paper/1810.01566/) (2018)
- [Learning to Control PDEs with Differentiable Physics](https://mlsanity.com/paper/2001.07457/) (2020)
- [A Differentiable Physics Engine for Deep Learning in Robotics](https://mlsanity.com/paper/1611.01652/) (2016)
- [ChainQueen: A Real-Time Differentiable Physical Simulator for Soft Robotics](https://mlsanity.com/paper/1810.01054/) (2018)
- [Scalable Differentiable Physics for Learning and Control](https://mlsanity.com/paper/2007.02168/) (2020)
- [Learning to Control Self-Assembling Morphologies: A Study of Generalization via Modularity](https://mlsanity.com/paper/1902.05546/) (2019)
- [SPNets: Differentiable Fluid Dynamics for Deep Neural Networks](https://mlsanity.com/paper/1806.06094/) (2018)
- [Reinforcement Learning for Improving Agent Design](https://mlsanity.com/paper/1810.03779/) (2018)
- [Jointly Learning to Construct and Control Agents using Deep Reinforcement Learning](https://mlsanity.com/paper/1801.01432/) (2018)
- [Neural Graph Evolution: Towards Efficient Automatic Robot Design](https://mlsanity.com/paper/1906.05370/) (2019)
- [Functional Co-Optimization of Articulated Robots](https://mlsanity.com/paper/1707.06617/) (2017)
- [Automatic Differentiation of Rigid Body Dynamics for Optimal Control and Estimation](https://mlsanity.com/paper/1709.03799/) (2017)

## Built on by (most cited first, 9 of 9)

- [Differentiable Simulation of Soft Multi-body Systems](https://mlsanity.com/paper/2205.01758/) (2022)
- [Efficient automatic design of robots](https://mlsanity.com/paper/2306.03263/) (2023)
- [UniPhy: Learning a Unified Constitutive Model for Inverse Physics Simulation](https://mlsanity.com/paper/2505.16971/) (2025)
- [Differentiable Hybrid Traffic Simulation](https://mlsanity.com/paper/2210.08046/) (2022)
- [Differentiable Visual Computing for Inverse Problems and Machine Learning](https://mlsanity.com/paper/2312.04574/) (2023)
- [Fast Aquatic Swimmer Optimization with Differentiable Projective Dynamics and Neural Network Hydrodynamic Models](https://mlsanity.com/paper/2204.12584/) (2022)
- [Differentiable Analog Quantum Computing for Optimization and Control](https://mlsanity.com/paper/2210.15812/) (2022)
- [Biological Robots: Perspectives on an Emerging Interdisciplinary Field](https://mlsanity.com/paper/2207.00880/) (2022)
- [What Robot do I Need? Fast Co-Adaptation of Morphology and Control using Graph Neural Networks](https://mlsanity.com/paper/2111.02371/) (2021)

## Abstract (arXiv)

The computational design of soft underwater swimmers is challenging because of the high degrees of freedom in soft-body modeling. In this paper, we present a differentiable pipeline for co-designing a soft swimmer's geometry and controller. Our pipeline unlocks gradient-based algorithms for discovering novel swimmer designs more efficiently than traditional gradient-free solutions. We propose Wasserstein barycenters as a basis for the geometric design of soft underwater swimmers since it is differentiable and can naturally interpolate between bio-inspired base shapes via optimal transport. By combining this design space with differentiable simulation and control, we can efficiently optimize a soft underwater swimmer's performance with fewer simulations than baseline methods. We demonstrate the efficacy of our method on various design problems such as fast, stable, and energy-efficient swimming and demonstrate applicability to multi-objective design.