At the collision of coarse graining, sampling theory, and variational inference, we have multi-fidelity modeling, which attempts to harness the efficiency of lower-precision and higher-precision models together. This name is a Machine Learning name; I presume that this concept has been invented many times under other names, which I will add when I learn them. Possibly one of those names is learnable coarse graining.
1 GP methods
Much to say. For now, see the fascinatingly extended version in Xing, Wang, and Xing (2023).
2 Super resolution
An interesting and charismatic special case. Resolution is a special case of multi-fidelity modeling, where the lower-fidelity model is a low-resolution version of the higher-fidelity model; typically, when we talk about resolution, we are concerned specifically with a discrete lattice approximation, which is a fancy person’s way of saying pixels. This is a one-way process, going from a coarse model to a fine model, although often learning downsampling can be instrumentally helpful.
3 Physics constraints
TBC
4 From data alone
TBC
5 With transformers
Just heard about this. TBD.
6 As coarse-graining
See coarse graining
7 References
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