Machine learning universal bosonic functionals

The one-body reduced density matrix $\gamma$ plays a fundamental role in describing and predicting quantum features of bosonic systems, such as Bose-Einstein condensation. recently proposed functional theory for ground states establishes the existence universal $\mathcal{F}[\gamma]$ that recovers correlations exactly. Based on novel decomposition $\gamma$, we have developed method to design reliable approximations functionals: our results suggest translational invariant systems constrained search approach theories can be transformed into an unconstrained problem through parametrization Euclidian space. This simplification allows us use standard machine-learning methods perform quite efficient computation both its derivative. For Bose-Hubbard model, present comparison between Quantum Monte Carlo.