[Paper Review] Fast Aquatic Swimmer Optimization with Differentiable Projective Dynamics and Neural Network Hydrodynamic Models

Elvis Nava, John H. Zhang+6 more|arXiv (Cornell University)|Mar 30, 2022

Lattice Boltzmann Simulation Studies4 citations

TL;DR

This paper presents a differentiable, hybrid fluid-structure interaction (FSI) simulator that combines differentiable projective dynamics for soft body deformation and a physics-constrained neural network for fluid dynamics, enabling fast, accurate, and gradient-based optimization of aquatic robot designs. The method achieves a 100x speedup over traditional FSI solvers like COMSOL while maintaining physical fidelity, allowing direct optimization of swimmer controller parameters via gradient descent.

ABSTRACT

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.

Motivation & Objective

• To address the high computational cost of simulating fluid-structure interaction (FSI) in soft robotic swimmers, especially for design and control optimization.
• To enable gradient-based optimization of swimmer controllers by making the FSI simulation fully differentiable.
• To develop a computationally efficient yet physically accurate FSI framework that combines differentiable solid mechanics with learned fluid dynamics.
• To demonstrate the feasibility of using the simulator for direct optimization of swimming frequency and performance.
• To validate the method against a standard FSI solver (COMSOL) in terms of both accuracy and computational efficiency.

Proposed method

• The deformable solid structure of the swimmer is simulated using Differentiable Projective Dynamics (DiffPD), a differentiable finite element method (FEM) that enables efficient gradient computation through the solid mechanics.
• The fluid dynamics are modeled using a U-Net neural network trained with a physics-based loss function derived from the incompressible Navier-Stokes equations, eliminating the need for labeled training data.
• A differentiable immersed boundary method (IBM) with Gaussian distance fields computes fluid-to-solid forces by sampling the neural network’s predicted pressure and velocity fields at the fluid-solid interface.
• The fluid boundary condition is implemented as a soft mask using differentiable rendering techniques to maintain differentiability across the fluid-solid interface.
• The full simulator is end-to-end differentiable, enabling backpropagation through time for long simulation episodes using gradient checkpointing to manage memory.
• Controller parameters (e.g., swimming frequency) are optimized using first-order gradient methods like Adam, leveraging the differentiability of the simulation.

Experimental results

Research questions

• RQ1 Can a hybrid FSI simulator combining differentiable solid mechanics and learned fluid dynamics achieve both computational efficiency and physical accuracy?
• RQ2 Can the resulting simulator support direct gradient-based optimization of robotic swimmer controllers, such as swimming frequency?
• RQ3 How does the performance of the differentiable simulator compare to a standard FSI solver like COMSOL in terms of speed and physical consistency?
• RQ4 Does the differentiable simulator preserve monotonic relationships in performance metrics (e.g., distance traveled) across controller parameters, enabling reliable optimization?
• RQ5 Can the neural network fluid model generalize to unseen fluid parameters (e.g., density, viscosity) without retraining?

Key findings

• The hybrid simulator achieves a 100x speedup over COMSOL Multiphysics, with a forward pass taking 3 min 33 s compared to COMSOL’s 5h 16m 39s for a 300-frame episode.
• The simulator produces realistic forward swimming motion in a 2D carangiform swimmer, with the fish achieving maximum forward distance at 5 Hz, consistent with COMSOL results.
• A monotonic relationship between swimming frequency and distance traveled is preserved between the hybrid simulator and COMSOL, validating the physical consistency of the method.
• Gradient-based optimization of the swimming frequency converged to 6.3 Hz in 21 iterations using Adam, while CMA-ES failed to escape its initialization and settled at 2.63 Hz.
• The backward pass of the simulator took 3 min 57 s due to gradient checkpointing, but the method remains computationally feasible for long-horizon optimization.
• The method enables direct, differentiable simulation of soft body swimming, making it suitable for co-optimization of shape, material, and control in soft robotics.