MarineHydro.jl: A Fully Differentiable Boundary Element Solver for Hydrodynamic Sensitivity Analysis

A Julia Package for Wave-Structure Interactions

software
research
Julia
hydrodynamics
optimization
Author

Kapil Khanal

Published

June 22, 2025

Research Overview

MarineHydro.jl: A Fully Differentiable Boundary Element Solver for Hydrodynamic Sensitivity Analysis of Wave-Structure Interactions

This work presents a novel implementation of a fully differentiable boundary element solver for marine hydrodynamics, enabling efficient gradient-based optimization of offshore structures and wave energy converters.

Authors

  • Kapil Khanal (Cornell University & (partly developed while interning at) Sandia National Laboratories)
  • Carlos A. Michelén Ströfer (Sandia National Laboratories)
  • Matthieu Ancellin (Eurobios Mews Labs)
  • Maha Haji (Cornell University)

🌟 Research Highlights

  • 📚 Derivation and discussion of the discrete adjoint method for the boundary integral equations
  • 💻 Review and implementation of a differentiable boundary element solver for marine hydrodynamics in Julia
  • 🌊 Exact gradient calculation for a pair of floating hemispheres with respect to their dimensions, separation distance, and wave environment
  • ⚡ Mechanical power optimization for a pair of wave energy converters using exact gradients

About MarineHydro.jl

MarineHydro.jl is a fully-differentiable boundary element solver for marine hydrodynamics. This new solver implements both direct and indirect boundary element formulations and uses two Green’s function expressions: Wu et al., and Delhommeau’s, varying in their accuracy and speed.

Key Features

  • Dual Formulation Support: Implements both direct and indirect boundary element formulations
  • Multiple Green’s Functions: Supports Wu et al. and Delhommeau’s Green’s function expressions
  • Automatic Differentiation: Fully differentiable with respect to geometry and wave parameters
  • Julia Implementation: High-performance implementation in Julia for computational efficiency
  • Open Source: MIT licensed and available on GitHub

Technical Implementation

Boundary Element Method

The boundary element method (BEM) is particularly well-suited for wave-structure interaction problems because it:

  • Reduces the problem dimensionality by one (surface instead of volume discretization)
  • Naturally handles infinite domains without artificial boundary conditions

Differentiability Framework

The key innovation in this work is the implementation of automatic differentiation throughout the boundary element solver:

using MarineHydro
using Zygote

# Calculate radiation forces with automatic differentiation
A_w_grad, = Zygote.gradient(w -> calculate_radiation_forces(mesh, ζ, w)[1], ω)

This enables: - Exact gradients without finite difference approximations for the hydrodynamic forces - Efficient optimization of complex geometries - Sensitivity analysis for design parameters

Adjoint Method Implementation

The discrete adjoint method is derived and implemented for the boundary integral equations, providing:

  • Computational efficiency for gradient calculations
  • Scalability to large-scale problems
  • Integration with modern optimization frameworks

Applications

Wave Energy Converters

The package demonstrates mechanical power optimization for wave energy converters:

  • Multi-body interactions: Analysis of arrays of floating bodies
  • Power optimization: Maximizing energy extraction efficiency
  • Geometric sensitivity: Understanding how shape affects performance

Offshore Structures

Applications extend to various offshore structures:

  • Floating platforms: Oil and gas platforms, wind turbines
  • Marine vessels: Ships, submarines, underwater vehicles
  • Coastal structures: Breakwaters, harbors, piers

Code Repository

The complete implementation is available at: https://github.com/symbiotic-engineering/MarineHydro.jl

Repository Structure

  • 📁 .github/workflows: Continuous integration and automated testing
  • 📊 paper: Plots and data generated for the research paper
  • 📜 src: Source code for the MarineHydro.jl package
  • 🧪 test: Comprehensive test suite and validation cases

Getting Started

# Clone the repository
git clone https://github.com/symbiotic-engineering/MarineHydro.jl.git
cd MarineHydro.jl

# Install dependencies
using Pkg
Pkg.activate(".")
Pkg.instantiate()

Basic Usage Example

using MarineHydro
using PyCall

# Import Capytaine mesh
cpt = pyimport("capytaine")
radius = 1.0
resolution = (10, 10)
cptmesh = cpt.mesh_sphere(name="sphere", radius=radius, center=(0, 0, 0), resolution=resolution)
cptmesh.keep_immersed_part(inplace=true)

# Convert to Julia mesh
mesh = Mesh(cptmesh)

# Calculate diffraction forces
ω = 1.03
ζ = [0, 0, 1]  # HEAVE motion
F = DiffractionForce(mesh, ω, ζ)

# Calculate radiation forces
A, B = calculate_radiation_forces(mesh, ζ, ω)

Research Impact

This work addresses several critical challenges in marine hydrodynamics:

  1. Computational Efficiency: Automatic differentiation eliminates the need for expensive finite difference calculations
  2. Design Optimization: Enables gradient-based optimization of complex marine structures
  3. Multi-physics Integration: Provides a foundation for coupling with structural and control systems
  4. Open Source Accessibility: Makes advanced hydrodynamic analysis tools available to the research community

Future Developments

The package is actively developed with plans for:

  • Enhanced API: More user-friendly interface for complex problems
  • Performance Optimization: Further improvements in computational efficiency
  • Extended Functionality: Support for additional wave theories and boundary conditions
  • Documentation: Comprehensive tutorials and examples