  In this paper, we propose a novel conservative formulation for solving
kinetic equations via neural networks. More precisely, we formulate the
learning problem as a constrained optimization problem with constraints that
represent the physical conservation laws. The constraints are relaxed toward
the residual loss function by the Lagrangian duality. By imposing physical
conservation properties of the solution as constraints of the learning problem,
we demonstrate far more accurate approximations of the solutions in terms of
errors and the conservation laws, for the kinetic Fokker-Planck equation and
the homogeneous Boltzmann equation.
