Transfer Learning in Bayesian Optimization for Aircraft Design

Ali Tfaily; Youssef Diouane; Nathalie Bartoli; Michael Kokkolaras

math.OCMar 30, 2026

Transfer Learning in Bayesian Optimization for Aircraft Design

Authors: Ali Tfaily, Youssef Diouane, Nathalie Bartoli, Michael Kokkolaras

Organizations: 1*Department of Mechanical Engineering, McGill University, Canada. · 2Advanced Product Development, Bombardier, Canada. · Department of Mathematical and Industrial Engineering, Polytechnique Montréal, Canada. · 6GERAD, Canada. ·

Abstract

The use of transfer learning within Bayesian optimization addresses the disadvantages of the so-called cold start problem by using source data to aid in the optimization of a target problem. We present a method that leverages an ensemble of surrogate models using transfer learning and integrates it in a constrained Bayesian optimization framework. We identify challenges particular to aircraft design optimization related to heterogeneous design variables and constraints. We propose the use of a partial-least-squares dimension reduction algorithm to address design space heterogeneity, and a meta data surrogate selection method to address constraint heterogeneity. Numerical benchmark problems and an aircraft conceptual design optimization problem are used to demonstrate the proposed methods. Results show significant improvement in convergence in early optimization iterations compared to standard Bayesian optimization, with improved prediction accuracy for both objective and constraint surrogate models.

Figures & tables

Problem	Description
Target (T)	BRAC
Source 1 (S1)	BRAC with a modified engine weight (+500 lb) and a relaxed BFL constraint (+10%)
Source 2 (S2)	BRAC with a longer fuselage (+100 inch) and longer range (+20%)
Source 3 (S3)	BRAC with higher cruise speed requirement (+ Mach 0.05)
Source 4 (S4)	BRAC with a different engine architecture and rear spar configuration
Source 5 (S5)	BRAC with slats

Table 1: Setup of source and target problems in the aircraft conceptual MDO transfer learning problem.

Panel of Figure 1 — Figure 1: Scaled top views of selected aircraft from the source problem’s DOE highlighting the differences in wing and fuselage geometries.

Input	Description	T	S1	S2	S3	S4	S5
$x_{1}$	Rubber engine scaling factor	✓	✓	✓ 1	✓ 1	✓	✓
$x_{2}$	Rubber engine bypass ratio					✓
$x_{3}$	Rubber engine overall pressure ratio					✓
$x_{4}$	Wing aspect ratio	✓	✓	✓	✓	✓	✓
$x_{5}$	Wing area	✓	✓	✓ 1	✓ 1	✓	✓ 1
$x_{6}$	Wing trailing edge sweep	✓	✓	✓	✓	✓	✓

Table 2: Design variables and their applicability (noted as a checkmark ✓) to the target (T) and each source (S1 to S5).

Constraint	Description	T	S1	S2	S3	S4	S5
$c_{1}(x)$	Balanced field length (BFL)	=	+10%	=	=	=	=
$c_{2}(x)$	Initial cruise altitude (ICA)	=	=	=	=	=	=
$c_{3}(x)$	Aircraft reference speed ( $V_{\mbox{ref}}$ )	=	=	=	=	=	=
$c_{4}(x)$	Excess fuel weight	=	=	=	=	=	=
$c_{5}(x)$	Inboard Wing flight controls actuation height clearance	∗	∗	∗	∗	∗	∗
$c_{6}(x)$	Outboard Wing flight controls actuation height clearance	∗	∗	∗	∗	∗	∗

Table 3: A list of the aircraft conceptual design problem constraints.

Figure 2: XDSM representation of the aircraft conceptual design MDA framework.

Figure 3: Heterogeneous transfer learning categories (adapted from Bao et al. (2023) ).

Panel of Figure 4 — Figure 4: Heterogeneous data-based transfer learning methods (adapted from Bao et al. (2023) ).

Figure 5: Heterogeneous design space in transfer learning using meta data.

Figure 6: Heterogeneous constraints transfer of surrogates approach showing the matching of source and target constraints using meta data.

Panel of Figure 7 — Figure 7: Target problem constraints without matching meta data in source problems.

Constraints type	Constraints description
Performance	Minimum range at different speeds and payloads
	Maximum takeoff (or balanced) field length
	Maximum landing field length
	Minimum initial cruise altitude
	Maximum approach (or reference) speed
	Maximum climb duration

Table 4: Aircraft MDO constraints.

Panel of Figure 8 — Figure 8: Results of the analytical problem showing the improved convergence using TLBO over the standard VBO over 20 optimization runs.

Panel of Figure 9 — Figure 9: Results of the 5-dimensional Rosenbrock multi-fidelity problem showing the improved convergence of TLBO over VBO over 20 optimizations runs.

Panel of Figure 10 — Figure 10: Results of 10 runs of the BRAC optimization problem showing the improved convergence and the variance of TLBO over VBO .

Panel of Figure 11 — Figure 11: Box plots comparing the prediction errors relative to the objective function and the constraints of TLBO and VBO at iteration 15 of the optimization.

Bayesian Optimization

Bayesian optimization uses probabilistic models and sequential experiments to find strong solutions when evaluating a black-box objective is costly.

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Self-driving laboratories increasingly rely on multi-fidelity Bayesian optimization (MFBO) to balance cheap, approximate evaluations against scarce, expensive ones, with a predictive surrogate at its core. Gaussian processes (GPs) are the default choice, but they scale poorly as data accumulate and assume a smooth landscape that molecular and materials search spaces routinely violate. Transfer learning offers an alternative suited to this regime: it learns a representation from abundant cheap data and adapts it to sparse expensive data. Despite its use in property prediction, transfer learning has not been tested as the engine of a closed-loop optimization. Here we benchmark eleven transfer-learning surrogates against four GP methods under an identical selection rule, fidelity budget, and model size, across nine tasks spanning synthetic functions to real chemistry and materials problems. GPs win on smooth, low-dimensional functions but perform worst on molecular and materials problems, where transfer-learning surrogates reach substantially better solutions using far less computation. Because acquisition policy is held fixed across surrogates, this advantage is attributable to the surrogate itself. Uncertainty-driven exploration is not reliably beneficial, and calibration does not predict optimization performance, so greedy exploitation of the transfer-learned mean is the more robust default. Transfer learning is therefore the surrogate of choice for molecular and materials MFBO.

Abstract

Bayesian Optimization

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