Diffusion Non-Additive Model for Multi-Fidelity Simulations with Tunable Precision

TL;DR

This paper introduces the Diffusion Non-Additive (DNA) model, a novel multi-fidelity simulation framework inspired by diffusion models, capable of extrapolating to highly accurate solutions using Gaussian process priors and complex fidelity relationships.

Contribution

The DNA model uniquely captures nonlinear, non-additive fidelity relationships with a nonseparable kernel, enabling extrapolation to exact solutions and providing efficient inference with closed-form predictive expressions.

Findings

Accurately extrapolates to the exact solution beyond highest fidelity.

Demonstrates improved predictive performance over existing models.

Validated on numerical and real-world case studies.

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 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.