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There's no doubt about it. Machine Learning (ML) is one of the hottest topics out there and it plays an important role in computational science.

One application I have seen is to use ML and Density Functional Theory DFT for the rational design of functional materials, for applications such as solar cells. Two examples are here and here.

I have never worked with ML myself and am curious to know, aside from being used in combination with existing methods,

How is it being used and what are some key examples of ML being used to develop new - or extend existing methodologies for modeling matter? What is the current state of the art in this sense?

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It is certainly possible to develop ML models that yield more accurate results than would be possible without ML.

One route to do this is through so-called "Δ-learning" where you use ML to learn a correction to a less expensive, often less accurate level of theory. An example can be found here for thermochemical properties of organic molecules. Somewhat related to this general idea, here is a paper discussing how ωB97X-D/def2-TZVP energies were able to be predicted from semi-empirical GFN1-xTB input features.

Naturally, another route one can take is to use ML with data from experiments, which can yield more accurate results than theory alone. For instance, it is well-established that GGA functionals yield underpredicted band gaps, and prior ML work has been carried out to predict band gaps at greater-than-DFT accuracy with this in mind. Many other studies are of this type, such as this paper on ML models that can be more accurate than TD-DFT for emission wavelengths.

Given a large dataset of inexpensive but somewhat inaccurate data and a smaller dataset of more expensive (or difficult to obtain) but accurate data, one can also use "transfer learning" to develop a ML model that has an accuracy comparable to the high-fidelity reference data. As an example, this work showed that a neural network potential could approach CCSD(T)/CBS accuracy on a dataset that is largely DFT-generated.

It is also possible to use ML models to identify likely issues or errors with a given calculation, as nicely demonstrated in this paper by Kulik and coworkers. Presumably, this could be used to make your calculations more accurate by knowing what calculation failures need to be addressed.

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Within Monte Carlo (MC) methods, there are a few areas of active research in this regard:

  1. Training ML models to identify phase transitions: In practice, it challenging to identify phase transitions in Monte Carlo methods. The simulations only measure observables that are manually programmed in, so you have to know where to look, or you may not even realize that phase transition is occurring. Some phase transitions have nonobvious order parameters (especially for topological phase transitions. E.g. Carrasquilla & Melko Nat. Phys. 13, 431 (2017)
  2. Training ML models on Monte Carlo configurations from a conventional method and then using the trained models to generate more data: The idea here is to train a model that can generalize from (for example) a small system and generate accurate sample configurations from a larger system or one at a more difficult-to-study point. E.g. Liu, Qi, Meng & Fu, Phys. Rev. B 95, 041101 (2017)
  3. Using ML to identify new types of MC update schemes: For special cases, there are often clever cluster update algorithms that can greatly improve MC sampling efficiency, but these are difficult to discover. This line of inquiry attempts to train ML models to invent new update types (or at least get inspiration that humans can then refine into an algorithm). E.g. Zhao, Kao, Wu & Kao, Phys. Rev. E 99, 062106 (2019)
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