MAST：一种通过空间信任加权的多保真度增强代理模型
MAST: A Multi-fidelity Augmented Surrogate model via Spatial Trust-weighting
AI总结：
MAST通过空间信任加权结合修正的低保真度观测和高保真度预测，提升多保真度代理模型的鲁棒性和精度，尤其在预算受限条件下表现优异。
摘要：
在工程设计和科学计算中，计算成本和预测精度是内在耦合的。高保真度模拟提供准确预测但计算成本高，而低保真度近似在效率上牺牲了精度。多保真度代理建模通过结合大量低保真度数据和稀疏高保真度观测来解决这一权衡问题。然而，现有方法依赖于全局相关性假设，这在实践中往往无法捕捉保真度关系在输入空间中的变化，导致性能不佳，特别是在预算紧张的情况下。我们引入MAST，一种将修正的低保真度观测与高保真度预测结合的方法，信任高保真度附近的观测样本，而在其他地方依赖修正的低保真度。MAST通过显式偏差建模和基于距离的加权，结合闭式方差传播，生成一个单个的异方差高斯过程。在多保真度合成基准测试中，MAST显著优于当前最先进的技术。关键的是，MAST在总预算和保真度差距变化时保持稳健性能，而竞争方法在这些条件下表现出显著退化或不稳定行为。更广泛地说，MAST提供了一个空间自适应的多保真度高斯过程建模框架，在其中低保真度信息的贡献由其接近高保真度校准数据的 proximity 决定，为在稀疏和预算受限条件下构建更可靠的代理模型开辟了新方向。
英文摘要：
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.
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