MAST: A Multi-fidelity Augmented Surrogate model via Spatial Trust-weighting

TL;DR

MAST is introduced, a method that blends corrected low-fidelity observations with high-fidelity predictions, trusting high-fidelity near observed samples and relying on corrected low-fidelity elsewhere, producing a single heteroscedastic Gaussian process.

Abstract

In engineering design and scientific computing, computational cost and predictive accuracy are intrinsically coupled. High-fidelity simulations provide accurate predictions but at substantial computational costs, while lower-fidelity approximations offer efficiency at the expense of accuracy. Multi-fidelity surrogate modelling addresses this trade-off by combining abundant low-fidelity data with sparse high-fidelity observations. However, existing methods suffer from expensive training cost or rely on global correlation assumptions that often fail in practice to capture how fidelity relationships vary across the input space, leading to poor performance particularly under tight budget constraints. We introduce MAST, a method that blends corrected low-fidelity observations with high-fidelity predictions, trusting high-fidelity near observed samples and relying on corrected low-fidelity elsewhere. MAST achieves this through explicit discrepancy modelling and distance-based weighting with closed-form variance propagation, producing a single heteroscedastic Gaussian process. Across multi-fidelity synthetic benchmarks, MAST shows a marked improvement over the current state-of-the-art techniques. Crucially, MAST maintains robust performance across varying total budget and fidelity gaps, conditions under which competing methods exhibit significant degradation or unstable behaviour.

Figures (15)

• Figure 1: Sensitivity of surrogate model performance to budget allocation. The HF fraction represents the proportion of total budget $\mathcal{B} = 5D$ allocated to high-fidelity evaluations, with the remainder spent on low-fidelity samples. Top row: Normalized RMSE; bottom row: Normalized Mean PDF. All values are normalized relative to the HF-only baseline (dotted line at 1.0). Square markers indicate single-fidelity baselines: LF-only (navy) and HF-only (black).
• Figure 2: Sensitivity of surrogate model performance to total computational budget. Budget scale is relative to the base budget $\mathcal{B} = 5D$, with fixed 70%/30% HF/LF cost allocation. Top row: Normalized RMSE (lower is better); bottom row: Normalized Mean PDF (higher is better). All values are normalized relative to the HF-only baseline at each budget level (dotted line at 1.0).
• Figure 3: Sensitivity of surrogate model performance to fidelity discrepancy. The cost parameter $d$ controls the deviation between low- and high-fidelity functions per Eq \ref{['eq:cost_controlled']}: low $d$ yields high inter-fidelity correlation, while high $d$ increases discrepancy. Top row: Normalized RMSE; bottom row: Normalized Mean PDF.
• Figure 4: Budget allocation sensitivity for low-dimensional functions: Branin (2D), Hartmann3 (3D), and Ackley (4D).
• Figure 5: Budget allocation sensitivity for mid-dimensional functions: Park1 (4D), Park2 (4D), and Rastrigin (5D).