PolarGrad (Polar Gradient methods; Lau et al., 2025) is a class of matrix-gradient optimizers based on the concept of gradient-anisotropy preconditioning in optimization. It has close relation to Muon ...

Abstract: The dynamics of many systems are most naturally expressed in terms of a state-dependent mass matrix, the most prominent example being rigid body dynamics. However, model predictive control ...

Let S(A) denote the orbit of a complex or real matrix A under a certain equivalence relation such as unitary similarity, unitary equivalence, unitary congruences etc. Efficient gradient-flow ...

This repository contains Python scripts and mathematical notes for performing orbital optimization on a simple H2 molecule. The main idea is to start from Hartree-Fock orbitals and iteratively ...

Fibroblast-collagen matrix culture has facilitated the analysis of cell physiology under conditions that more closely resemble an in vivo-like environment compared to conventional 2-dimensional (2D) ...