Conclusions and where do we stand
- A simple 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 by 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
- Extend to more fermions. How do we deal with the antisymmetry of the multi-fermion wave function?
- 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 other popular many-body methods? Fully possible with for example Recurrent Neural Networks.