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Implement ensemble excited state optimization from Entwistle et al #405

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willwheelera opened this issue Dec 18, 2023 · 1 comment
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@willwheelera
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Implement optimization of multiple states simultaneously as described in Entwistle et al. https://www.nature.com/articles/s41467-022-35534-5

The cost function for wave function i consists of the energy of wf i plus the overlap between wfs i and j for j<i (only overlaps with lower wave functions).

A copy of optimize_excited_states.py should be used as the starting point.

@lkwagner
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lkwagner commented Jan 4, 2024

We should think about how we want to design this, considering that we probably want to optimize only sections of parameters at a time. For example, do we want to change just one wave function, with one parameter set at a time? That way we'd only need to compute parameter derivatives for one wave function at a time, although at the cost of running a new VMC (presumably with fewer walkers) for each excited state.

We could also consider a KFAC-like approximation to the Fischer information matrix.

It might be really useful to produce some kind of convergence plot of chosen direction versus walkers, as a function of the number of parameters optimized.

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