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 \( N=6 \) and \( N=12 \) electrons.
- Minimization problem can be tricky.
- Anti-symmetry dealt with multiplying the trail wave function with either a simple or an optimized Slater determinant.
- To come: Analysis of wave function from ML and compare with diffusion and Variational Monte Carlo calculations as well as comparison with Shadow wave functions approach.
- 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?
- Compare with calculations done with Shadow wave functions.
- Use thereafter ML to determine the correlated part of the wafe function (including a standard Jastrow factor).
- Test this for multi-fermion systems and compare with other many-body methods.
- Can we use ML to find out which correlations are relevant and thereby diminish the dimensionality problem in say CC or SRG theories? Fully possible with for example Recurrent Neural Networks.