DiLLSUE: a differentiable GPU solver for link-based logit stochastic user equilibrium

Logit stochastic user equilibrium (SUE) captures imperfect route cost perceptions, but its practical solvers rely on route enumeration, which becomes prohibitive on large networks, or on link-based heuristics without convergence guarantees. We develop DiLLSUE, a differentiable solver for the link-based logit SUE that requires no route enumeration, no training data, and no network-specific tuning. Its inner loading algorithm batches all destinations into fixed-shape tensor operations, yielding, to our knowledge, the first GPU implementation of link-based logit SUE. Four outer solvers -- successive averages, self-regulating averaging, Anderson mixing, and implicit-function-theorem Newton -- are benchmarked under identical settings, and a family of acyclicity filters provides fast approximations with a quantified speed-accuracy trade-off. On five standard benchmark networks, GPU and CPU executions agree to within $10^{-4}$\% mean absolute percentage error, and the computed equilibrium converges monotonically to the independently computed Wardrop equilibrium, reaching 0.33\% error on Sioux Falls, where the zero-training solver is more accurate than published trained surrogates.