In this paper, we present a generic physics-informed generative model called MPDM that integrates multi-fidelity physics simulations with diffusion models. MPDM categorizes multi-fidelity physics simulations into inexpensive and expensive simulations, depending on computational costs. The inexpensive simulations, which can be obtained with low latency, directly inject contextual information into DDMs. Furthermore, when results from expensive simulations are available, MPDM refines the quality of generated samples via a guided diffusion process. This design separates the training of a denoising diffusion model from physics-informed conditional probability models, thus lending flexibility to practitioners. MPDM 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 MPDM 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 heat dynamics within laser-based metal powder deposition additive manufacturing to demonstrate how MPDM seamlessly integrates multi-idelity physics simulations and observations to obtain surrogates with superior predictive performance.

翻译：本文提出了一种通用的物理信息生成模型MPDM，该模型将多保真度物理仿真与扩散模型相结合。MPDM根据计算成本将多保真度物理仿真划分为廉价仿真与昂贵仿真两类。能够低延迟获取的廉价仿真直接将上下文信息注入去噪扩散模型（DDMs）。此外，当可获得昂贵仿真的结果时，MPDM通过引导扩散过程优化生成样本的质量。该设计将去噪扩散模型的训练与物理信息条件概率模型相分离，从而为实践者提供了灵活性。MPDM基于贝叶斯概率模型构建，并具备理论保证，为样本与底层真实分布之间的Wasserstein距离提供了上界。MPDM的概率特性也为预测中的不确定性量化提供了便捷途径。我们的模型在物理仿真不完美甚至有时不可获取的场景中表现卓越。我们通过流体动力学中的数值仿真以及激光金属粉末沉积增材制造中热动力学的案例研究，展示了MPDM如何无缝集成多保真度物理仿真与观测数据，从而获得具有卓越预测性能的代理模型。