Diffusion Non-Additive Emulator for Multi-Fidelity Computer Experiments with Tuning Parameters

Music City Center 

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. In this paper, we introduce the Diffusion Non‑Additive (DNA) emulator that (1) captures Markovian dependencies among tuning parameters and extrapolates to the exact solution corresponding to a zero-valued tuning parameter, which cannot be simulated directly. The DNA emulator further (2) models complex, non-additive relationships across fidelity levels, (3) employs nonseparable covariance kernels to capture interactions between tuning parameters and input variables, and (4) supports fully nonnested experimental designs for enhanced flexibility. We (5) derive closed‑form expressions for the posterior predictive mean and variance under the nonseparable kernel, enabling efficient inference and rigorous uncertainty quantification. Lastly, We demonstrate the efficacy of our approach on a suite of numerical studies and real-world case studies.

surrogate model

finite-element simulation

multi-fidelity