What is the current status of ongoing research on machine learning based ab intio calculation for solid state physics? Useful references of important works or reviews will be very helpful.
I highly recommend you to check out work from Michele Ceriotti's group. He's from EPFL and quite productive in the field of ML in atomistic simulations.
Here are a few example publications to check out:
Article Unsupervised machine learning in atomistic simulations, betw...
Article Machine Learning Unifies the Modelling of Materials and Molecules
Article Transferable Machine-Learning Model of the Electron Density
Article Machine Learning for the Structure-Energy-Property Landscape...
For understanding the context and methods of data-driven approaches in materials science, I recommend our recent review article Article From DFT to Machine Learning: recent approaches to Materials...
which as the title says, presents a comprehensive discussion of the current status of the computational materials science area leading to machine learning.
The discussion presents:
A general introduction presenting why machine learning and data-driven approaches are being increasingly used
The fundamentals (how) of both density functional theory (DFT) –including the recent trend of high-throughput calculations for databases creation– and machine learning methods
Examples (what) of machine learning applications in materials science
From there you will be able to further explore the literature for specific topics of your interest, such as atomistic machine learning potentials (force fields), property predictions, deep learning of Hamiltonians, and others.