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

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 rely on global correlation assumptions that can 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. More broadly, MAST provides a spatially adaptive framework for multi-fidelity Gaussian-process modelling, in which the contribution of low-fidelity information is governed by its proximity to high-fidelity calibration data, opening a new direction for more reliable surrogate construction under sparse and budget-constrained settings.