Explore nonlinear reduced basis methods and optimal transport techniques in electronic structure calculations through this 53-minute lecture. Delve into the challenges of computationally demanding large-scale electron simulations and discover innovative approaches to reduce computational costs. Learn about a novel method combining sparse representation and optimal transport to efficiently approximate solutions for eigenvalue problems parametrized by nuclei positions. Gain insights into potential extensions for larger systems and their applications in designing machine-learned interatomic potentials for materials and molecules.