Linear response across interaction regimes in two-dimensional ferromagnets

What the math gives to ML

The paper offers a concrete computational mechanism: represent a nonequilibrium bosonic distribution as a finite sum of Gaussian components so that multidimensional interaction collision integrals become tractable, then solve the linearized quantum Boltzmann equation across ballistic and hydrodynamic regimes. This representation is transferable to neural surrogates for kinetic equations, where an unconstrained pointwise MLP often produces distributions that violate positivity, conservation laws, or the correct relaxation spectrum. The strongest implementation is a Gaussian-mixture-output neural kinetic solver trained with a differentiable collision residual and tested against the predicted transition from weakly collisional modes to collective hydrodynamic modes.