A stable rank-adaptive step-and-truncate finite volume method for Vlasov transport on domains with piecewise linear boundaries

What the math gives to ML

The transferable contribution is a rank-adaptive evolution rule that alternates a stable full-space step with an explicit best low-rank truncation, rather than projecting the dynamics onto a moving tangent space. The key asset is that, under a CFL-like contractivity condition on the full update, Frobenius/L2 norm stability is inherited by the truncated update while the discarded singular-value tail gives a directly controllable approximation error. This suggests stable low-rank residual or recurrent neural layers in which hidden-state matrices are evolved by a contractive learned operator and compressed after every step. The finite-volume flux construction is domain-specific, but the contractive-step-plus-SVD-truncation mechanism is broadly testable for token-feature propagation and activation-memory reduction.