In this talk, we will present two examples of exploiting similarity of solutions to minimize the computational effort while maintaining accuracy for the simulation of approximation to quantum mechanical systems.
In the first example we present an alternative to extended Lagrangian Born-Oppenheimer molecular dynamics simulations at the level of theory of DFT or Hartree-Fock that is based on an extrapolation of previous solutions on the tangent space of the Grassmann manifold.
The second example illustrates the performance of the reduced basis method for quantum-spin systems. We illustrate in examples that, surprisingly, while the dimension of the underlying Hilbert space increases exponentially with the number of particles, the Kolmogorov N-width for these parametrised examples only increases slightly. Further, the greedy-strategy to assemble the reduced basis only requires very few high-dimensional solutions to be computed.
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