Machine learning: an alternative or aid to quantum calculations? Insights from effective Hamiltonians

Traditional atomistic machine learning (ML) models act as surrogates for quantum mechanical (QM) properties, predicting quantities such as structural energies and dipole moments directly from the geometric information of input structures. Recent approaches, however, have shifted toward modeling intermediate components of electronic structure, such as the single-particle Hamiltonian expressed in an atom-centered basis. This shift has led to the development of integrated models capable of simultaneously predicting multiple properties derived from their analytical relationship to the ML Hamiltonian.

Given the diversity of approaches, we face a crucial question -- should ML be applied directly to predict target properties, bypassing the need for electronic structure calculations, or is its potential better realized by integrating it within a workflow that emulates an electronic structure calculation?

In this talk, I will discuss how symmetry-aware ML models for atomic properties can be extended to predict self-consistent electronic Hamiltonians from QM calculations. Moreover, I will present physics-based strategies for modeling effective Hamiltonians that can replicate subsets of electronic spectra from QM calculations performed with larger basis sets or higher levels of theory. This approach improves model accuracy across diverse input structures and output properties including electronic excitations. I will present a framework that integrates ML within differentiable electronic structure workflows allowing the optimization of the intermediate Hamiltonian based on QM targets more complex than its spectrum.