# Optimization-Embedded Active Multi-Fidelity Surrogate Learning for Multi-Condition Airfoil Shape Optimization

arXiv: https://arxiv.org/abs/2603.17057 · HTML: https://mlsanity.com/paper/2603.17057/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 66 references that are in the map.
- First posted on arXiv 17 Mar 2026.

## Builds on (most cited first, 10 of 10)

- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Multi-fidelity Bayesian Neural Networks: Algorithms and Applications](https://mlsanity.com/paper/2012.13294/) (2020)
- [Multifidelity Deep Operator Networks For Data-Driven and Physics-Informed Problems](https://mlsanity.com/paper/2204.09157/) (2022)
- [Deep Gaussian Processes for Multi-fidelity Modeling](https://mlsanity.com/paper/1903.07320/) (2019)
- [Airfoil Design Parameterization and Optimization using B'ezier Generative Adversarial Networks](https://mlsanity.com/paper/2006.12496/) (2020)
- [Overview of Gaussian process based multi-fidelity techniques with variable relationship between fidelities](https://mlsanity.com/paper/2006.16728/) (2020)
- [Deep neural operators can serve as accurate surrogates for shape optimization: A case study for airfoils](https://mlsanity.com/paper/2302.00807/) (2023)
- [Gradient-enhanced kriging for high-dimensional problems](https://mlsanity.com/paper/1708.02663/) (2017)
- [Multi-fidelity reinforcement learning framework for shape optimization](https://mlsanity.com/paper/2202.11170/) (2022)
- [Fast and robust parametric and functional learning with Hybrid Genetic Optimisation (HyGO)](https://mlsanity.com/paper/2510.09391/) (2025)

## Abstract (arXiv)

Active multi-fidelity surrogate modeling is developed for multi-condition airfoil shape optimization to reduce high-fidelity CFD cost while retaining RANS-consistent aerodynamic metrics. The framework couples a low-fidelity-informed Gaussian process regression transfer model with uncertainty-triggered sampling and a synchronized elitism rule embedded in a hybrid genetic algorithm. Low-fidelity XFOIL evaluations provide inexpensive features, while sparse RANS simulations are adaptively allocated when predictive uncertainty exceeds a threshold; elite candidates are mandatorily validated at high fidelity, and the population is re-evaluated to prevent evolutionary selection based on outdated fitness values produced by earlier surrogate states. The method is demonstrated for a two-point problem at Re=6×106 with cruise at α=2^circ (maximize E=L/D) and take-off at α=10^circ (maximize CL) using a 12-parameter CST representation. Independent multi-fidelity surrogates per flight condition enable decoupled refinement. The optimized design improves cruise efficiency by 41.05% and take-off lift by 20.75% relative to the best first-generation individual. Over the full campaign, RANS evaluations were required for only 14.78% and 9.5% of the condition-specific candidate evaluations at cruise and take-off, respectively. These percentages quantify the reduction in high-fidelity usage relative to the fixed automated RANS workflow adopted as the high-fidelity reference in this study.