Bridging Machine Learning and Electron Density Theory with Adaptive Real-Space Integration.

Machine learning electron densities enabled fast quantum chemistry but suffered from a fidelity gap in downstream tasks due to integration errors and unbalance on uniform grids. We introduce MARGR, an adaptive framework that refines the grid only in the critical regions. We analyze its efficiency through theory and benchmark it on molecular property calculations, demonstrating that adaptive grid refinement achieves an accuracy comparable to high-resolution uniform grids at substantially reduced computational cost.