Abstract:Computer simulations are indispensable for analyzing complex systems, yet high-fidelity models often incur prohibitive computational costs. Multi-fidelity frameworks address this challenge by combining inexpensive low-fidelity simulations with costly high-fidelity simulations to improve both accuracy and efficiency. However, certain scientific problems demand even more accurate results than the highest-fidelity simulations available, particularly when a tuning parameter controlling simulation accuracy is available, but the exact solution corresponding to a zero-valued parameter remains out of reach. In this paper, we introduce the Diffusion Non-Additive (DNA) model, inspired by generative diffusion models, which captures nonlinear dependencies across fidelity levels using Gaussian process priors and extrapolates to the exact solution. The DNA model: (i) accommodates complex, non-additive relationships across fidelity levels; (ii) employs a nonseparable covariance kernel to model interactions between the tuning parameter and input variables, improving predictive performance; (iii) provides closed-form expressions for the posterior predictive mean and variance, allowing efficient inference and uncertainty quantification; and (iv) establishes rigorous theoretical bounds on the prediction error, leading to an optimal experimental design strategy. The methodology is validated on a suite of numerical studies and real-world case studies. An R package implementing the proposed methodology is available to support practical applications.
From: Junoh Heo [view email]
[v1]
Tue, 10 Jun 2025 01:32:04 UTC (1,579 KB)
[v2]
Sun, 26 Oct 2025 18:25:55 UTC (569 KB)
[v3]
Mon, 15 Jun 2026 02:58:34 UTC (977 KB)
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