# Optimization of the Shape of a Hydrokinetic Turbine's Draft Tube and Hub Assembly Using Design-by-Morphing with Bayesian Optimization

arXiv: https://arxiv.org/abs/2207.11451 · HTML: https://mlsanity.com/paper/2207.11451/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 69 references that are in the map.
- First posted on arXiv 23 Jul 2022.

## Builds on (most cited first, 5 of 5)

- [Bayesian optimization for materials design](https://mlsanity.com/paper/1506.01349/) (2015)
- [ChemBO: Bayesian Optimization of Small Organic Molecules with Synthesizable Recommendations](https://mlsanity.com/paper/1908.01425/) (2019)
- [BOCK : Bayesian Optimization with Cylindrical Kernels](https://mlsanity.com/paper/1806.01619/) (2018)
- [Bayesian Optimization in AlphaGo](https://mlsanity.com/paper/1812.06855/) (2018)
- [Bayesian Optimization For Multi-Objective Mixed-Variable Problems](https://mlsanity.com/paper/2201.12767/) (2022)

## Built on by (most cited first, 3 of 3)

- [Computationally Efficient Optimisation of Elbow-Type Draft Tube Using Neural Network Surrogates](https://mlsanity.com/paper/2401.08700/) (2024)
- [Multi-view Bayesian optimisation in an input-output reduced space for engineering design](https://mlsanity.com/paper/2501.01552/) (2025)
- [Airfoil optimization using Design-by-Morphing with minimized design-space dimensionality](https://mlsanity.com/paper/2510.16020/) (2025)

## Abstract (arXiv)

Finding the optimal design of a hydrodynamic or aerodynamic surface is often impossible due to the expense of evaluating the cost functions (say, with computational fluid dynamics) needed to determine the performances of the flows that the surface controls. In addition, inherent limitations of the design space itself due to imposed geometric constraints, conventional parameterization methods, and user bias can restrict it all of the designs within a chosen design space regardless of whether traditional optimization methods or newer, data-driven design algorithms with machine learning are used to search the design space. We present a 2-pronged attack to address these difficulties: we propose (1) a methodology to create the design space using morphing that we call it Design-by-Morphing (DbM); and (2) an optimization algorithm to search that space that uses a novel Bayesian Optimization (BO) strategy that we call it Mixed variable, Multi-Objective Bayesian Optimization (MixMOBO). We apply this shape optimization strategy to maximize the power output of a hydrokinetic turbine. Applying these two strategies in tandem, we demonstrate that we can create a novel, geometrically-unconstrained, design space of a draft tube and hub shape and then optimize them simultaneously with a it minimum number of cost function calls. Our framework is versatile and can be applied to the shape optimization of a variety of fluid problems.