Quantum embedding theory promises the simulation of realistic materials in quantum computers. In this Perspective, challenges and opportunities of applying different embedding frameworks to calculate solid materials properties are discussed, with a focus on electronic structures of spin defects.

The determination of state variables to describe physical systems is a challenging task. A data-driven approach is proposed to automatically identify state variables for unknown systems from high-dimensional observational data.

We highlight how this year’s awardees from some of the most important prizes in mathematics have had an impact in the computational science community.

Machine learning has been used to accelerate the simulation of fluid dynamics. However, despite the recent developments in this field, there are still challenges to be addressed by the community, a fact that creates research opportunities.

The determination of state variables to describe physical systems is a challenging task. A data-driven approach is proposed to automatically identify state variables for unknown systems from high-dimensional observational data.

A machine learning method that can predict how complex molecules bind to the surfaces of transition metals and alloys is developed, which will be useful for catalyst screening, and for understanding and improving catalyst performance.

A deep learning method for protein sequence design on given backbones, ABACUS-R, is proposed in this study. ABACUS-R shows an improved performance when compared with conventional energy function-based methods in wet experiments.

ActiveSVM is introduced as a feature selection procedure for discovering minimal gene sets in large single-cell mRNA-seq datasets.

A graph neural network-based cell clustering model for spatial transcripts obtains cell embeddings from global cell interactions across tissue samples and identifies cell types and subpopulations.

A deep neural network method is developed to learn the mapping function from atomic structure to density functional theory (DFT) Hamiltonian, which helps address the accuracy–efficiency dilemma of DFT and is useful for studying large-scale materials.

We highlight how this year’s awardees from some of the most important prizes in mathematics have had an impact in the computational science community.