Conclusions and where do we stand
- Extension of the work of G. Carleo and M. Troyer, Science 355, Issue 6325, pp. 602-606 (2017) gives excellent results for two-electron systems as well as good agreement with standard VMC calculations for many electrons.
- Promising results with neural Networks as well. Next step is to use trial wave function in final Green's function Monte Carlo calculations.
- Minimization problem can be tricky.
- Anti-symmetry dealt with multiplying the trail wave function with either a simple or an optimized Slater determinant.
- Extend to more fermions. How do we deal with the antisymmetry of the multi-fermion wave function?
- Here we also used standard Hartree-Fock theory to define an optimal Slater determinant. Takes care of the antisymmetry. What about constructing an anti-symmetrized network function?
- Use thereafter ML to determine the correlated part of the wafe function (including a standard Jastrow factor).
- Can we use ML to find out which correlations are relevant and thereby diminish the dimensionality problem in say CC or SRG theories?
- And many more exciting research avenues