Diffusion-Based Surrogate Modeling and Multi-Fidelity Calibration

Physics simulations have become fundamental tools to study myriad engineering systems. As physics simulations often involve simplifications, their outputs should be calibrated using real-world data. In this paper, we present a diffusion-based surrogate (DBS) that calibrates multi-fidelity physics simulations with diffusion generative processes. DBS categorizes multi-fidelity physics simulations into inexpensive and expensive simulations, depending on the computational costs. The inexpensive simulations, which can be obtained with low latency, directly inject contextual information into diffusion models. Furthermore, when results from expensive simulations are available, DBS refines the quality of generated samples via a guided diffusion process. This design circumvents the need for large amounts of expensive physics simulations to train denoising diffusion models, thus lending flexibility to practitioners. DBS builds on Bayesian probabilistic models and is equipped with a theoretical guarantee that provides upper bounds on the Wasserstein distance between the sample and underlying true distribution. The probabilistic nature of DBS also provides a convenient approach for uncertainty quantification in prediction. Our models excel in cases where physics simulations are imperfect and sometimes inaccessible. We use a numerical simulation in fluid dynamics and a case study in laser-based metal powder deposition additive manufacturing to demonstrate how DBS calibrates multi-fidelity physics simulations with observations to obtain surrogates with superior predictive performance. Note to Practitioners—In engineering applications, physics-based simulators are often employed to model complex systems. While these simulations encode our understanding of the underlying physics, they are frequently oversimplified or miscalibrated, leading to biased outputs. A natural approach to mitigating this bias is to calibrate simulation outputs using real-world data. Traditionally, Gaussian processes have been used for this purpose. In this paper, we introduce an alternative calibration framework called Diffusion-based Surrogates (DBS). DBS leverages the flexibility of diffusion generative models to calibrate high-dimensional physics simulations. We introduce two designs to explicitly or implicitly incorporate physics simulations into the generative process. Our approach effectively integrates information from multi-fidelity physics models and excels in large-scale, high-dimensional calibration tasks. Notably, DBS operates without requiring additional domain knowledge beyond simulation outputs. Further, DBS is shown to effectively quantify the uncertainty in the predictions.