Wei Li - Beihang University To explore the intriguing quantum states like spin liquids in the low-dimensional magnetic materials, precise inference of the microscopic spin model — the quantum magnetism genome — from experimental measurements constitutes an important yet very challenging inverse many-body problem. In this talk, I will present an unbiased and efficient approach learning the effective Hamiltonian through many-body simulations and fittings of measured thermal data. Our approach combines the strategies including the automatic gradient and Bayesian optimization with the thermodynamics solvers, with the latter including exact diagonalization for high-T properties and the large-scale thermal tensor networks down to low temperatures. We showcase the accuracy and powerfulness of the Hamiltonian learning approach on test thermal data generated from a given spin model, and then to realistic experimental data of both spin-chain (Copper Nitrate) and triangular-lattice (TmMgGaO4) magnets. The present automatic approach constitutes a unified framework of many-body thermal data analysis in the studies of quantum magnets and strongly correlated materials in general.