A Projected Semiexplicit Integrator for Dissipative Systems with Configuration-Dependent Kinetic Energy: Contact-Herglotz Formulation and Benchmarks

What the math gives to ML

The paper provides a practical second-order integrator for dissipative Hamiltonian systems whose kinetic energy has configuration-dependent cross terms and therefore cannot be handled by ordinary explicit separable splittings. Its transferable asset is the combination of duplicated phase variables, symmetric projection back to the physical diagonal, and exact friction half-steps, which avoids a binding parameter while restricting nonlinear work to a small projection solve. This suggests a momentum optimizer or learned dynamical-system integrator with a dense configuration-dependent preconditioner, retaining stable second-order behavior even when the metric couples coordinates.