Efficient Inverse Design Optimization through Multi-fidelity Simulations, Machine Learning, and Search Space Reduction Strategies

TL;DR

This work tackles inverse design under tight computational budgets by integrating multi-fidelity evaluations with ML surrogates and boundary refinement to guide population-based optimizers. It introduces an ML-enhanced inverse design framework that trains LF surrogates to estimate target-related scalars, decides HF evaluations via a discrepancy threshold, and compresses the search space before optimization. Applied to airfoil inverse design and scalar field reconstruction, the approach shows improved convergence for DE and PSO and demonstrates substantial HF-simulation savings while preserving target fidelity. The framework is adaptable to other inverse-design problems and population-based optimizers, offering a practical pathway to efficient, high-fidelity design under budget constraints.

Abstract

This paper introduces a methodology designed to augment the inverse design optimization process in scenarios constrained by limited compute, through the strategic synergy of multi-fidelity evaluations, machine learning models, and optimization algorithms. The proposed methodology is analyzed on two distinct engineering inverse design problems: airfoil inverse design and the scalar field reconstruction problem. It leverages a machine learning model trained with low-fidelity simulation data, in each optimization cycle, thereby proficiently predicting a target variable and discerning whether a high-fidelity simulation is necessitated, which notably conserves computational resources. Additionally, the machine learning model is strategically deployed prior to optimization to compress the design space boundaries, thereby further accelerating convergence toward the optimal solution. The methodology has been employed to enhance two optimization algorithms, namely Differential Evolution and Particle Swarm Optimization. Comparative analyses illustrate performance improvements across both algorithms. Notably, this method is adaptable across any inverse design application, facilitating a synergy between a representative low-fidelity ML model, and high-fidelity simulation, and can be seamlessly applied across any variety of population-based optimization algorithms.}

Figures (22)

• Figure 1: The creation of the ML model commences with the generation of LF data (1) used for training the ML model (2). Once the model is trained and its accuracy is determined, it enables the boundary refinement (4) and the ML-enhanced optimization methodology (5). The inverse design procedure requires the specification of a target performance or vector (3). Blocks highlighted in light green (4) and (5) denote stages involving an optimization process.
• Figure 2: Optimization boundaries generated by multiplying the $NACA0012$ baseline B-Spline coefficients by a factor of 3. The $\zeta_x$ and $\zeta_y$ axis are the chord-length normalized $x$ and $y$ coordinates.
• Figure 3: The mathematical domain $\Omega$ of the scalar reconstruction problem. The top boundary condition is the Dirichlet boundary condition where the optimization design vector $\mathbf{x_s}$ is set, while the bottom, left, and right parts are defined as the Neumann boundary condition. The height and width are presented in meters.
• Figure 4: SFR boundary refinement example. The grey lines are the $N$ solutions within the matrix $\mathbf{S}_s$, the black line is the average value of the solutions in matrix $\mathbf{S}_s$, the green line is the true boundary condition that corresponds to the $\mathbf{T}$ field measurements, and the blue line is the new upper boundary $\mathbf{ub}_R$ obtained with the boundary refinement procedure described in this section.
• Figure 5: The mean (solid lines) and standard deviation (shaded areas) K-Fold $RMSE$ for the three investigated ML algorithms for the AID problem. Lower $RMSE$ values are better.