Diffusion-Generative Multi-Fidelity Learning for Physical Simulation
Zheng Wang Shibo Li Shikai Fang Shandian Zhe
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.