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| Natura: | Preprint |
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2025
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| Accesso online: | https://arxiv.org/abs/2506.08328 |
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| _version_ | 1866912671435063296 |
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| author | Heo, Junoh Boutelet, Romain Sung, Chih-Li |
| author_facet | Heo, Junoh Boutelet, Romain Sung, Chih-Li |
| contents | 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 both predictive performance and physical interpretability; and (iii) provides closed-form expressions for the posterior predictive mean and variance, allowing efficient inference and uncertainty quantification. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_08328 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Diffusion Non-Additive Model for Multi-Fidelity Simulations with Tunable Precision Heo, Junoh Boutelet, Romain Sung, Chih-Li Methodology 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 both predictive performance and physical interpretability; and (iii) provides closed-form expressions for the posterior predictive mean and variance, allowing efficient inference and uncertainty quantification. 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. |
| title | Diffusion Non-Additive Model for Multi-Fidelity Simulations with Tunable Precision |
| topic | Methodology |
| url | https://arxiv.org/abs/2506.08328 |