# Multi fidelity models

Data-driven multi-scale sampling, multi-resolution, super-resolution

August 24, 2020 — November 20, 2023

At the collision of coarse graining and sampling theory and variational inference, we have multi-fidelity modeling, which is an 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

*Acta Numerica*.

*Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence*.

*Journal of Fourier Analysis and Applications*.

*Nature Communications*.

*Proceedings of the National Academy of Sciences*.

*arXiv:1903.07320 [Cs, Stat]*.

*Theoretical and Computational Fluid Dynamics*.

*Physics of Fluids*.

*PLOS ONE*.

*Molecular Simulation*.

*Biometrika*.

*Journal of the Royal Statistical Society: Series B (Statistical Methodology)*.

*Proceedings of the National Academy of Sciences*.

*Acta Materialia*.

*Proceedings of International Conference on Learning Representations (ICLR) 2017*.

*International Conference on Learning Representations*.

*Soft Matter*.

*IEEE Transactions on Signal Processing*.

*Journal of Computational Physics*.

*Frontiers in Chemistry*.

*Reliability Engineering & System Safety*.

*Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*.

*SIAM Journal on Scientific Computing*.

*Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*.

*arXiv:1604.07484 [Cs, Stat]*.

*Water Resources Research*.

*ACM SIGGRAPH 2022 Conference Proceedings*. SIGGRAPH ’22.

*NeurIPS*.

*Journal of Computational Dynamics*.

*The Journal of Chemical Physics*.

*ACS Central Science*.

*Living Journal of Computational Molecular Science*.

*ACS Omega*.