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.

基于随机微分方程的扩散生成多保真度（DGMF）学习方法通过连续去噪过程生成解决方案输出，同时利用条件分数模型控制解决方案的生成，可有效学习和预测多维解决方案数组，将离散和连续保真度建模统一，展示了多保真度学习的有希望的新方向。