Multi-fidelity surrogate learning is important for physical simulation related applications in that it avoids running numerical solvers from scratch, which is known to be costly, and it uses multi-fidelity examples for training and greatly reduces the cost of data collection. Despite the variety of existing methods, they all build a model to map the input parameters outright to the solution output. Inspired by the recent breakthrough in generative models, we take an alternative view and consider the solution output as generated from random noises. We develop a diffusion-generative multi-fidelity (DGMF) learning method based on stochastic differential equations (SDE), where the generation is a continuous denoising process. We propose a conditional score model to control the solution generation by the input parameters and the fidelity. By conditioning on additional inputs (temporal or spacial variables), our model can efficiently learn and predict multi-dimensional solution arrays. Our method naturally unifies discrete and continuous fidelity modeling. The advantage of our method in several typical applications shows a promising new direction for multi-fidelity learning.

翻译：多保真度代理学习在物理仿真相关应用中至关重要，因为它无需从头运行计算代价高昂的数值求解器，同时利用多保真度样本进行训练，大幅降低数据采集成本。尽管现有方法种类繁多，但它们均构建模型将输入参数直接映射为解输出。受生成式模型最新突破的启发，我们提出另一种视角：将解输出视为由随机噪声生成的过程。基于随机微分方程，我们开发了一种扩散生成式多保真度学习方法，其中生成过程为连续去噪过程。我们提出条件评分模型，通过输入参数和保真度控制解的生成。通过附加时空变量等额外输入，该模型能高效学习并预测多维解数组。该方法自然地统一了离散与连续保真度建模。在多个典型应用中的优势表明，这为多保真度学习开辟了富有前景的新方向。