GPU-accelerated Differential Evolution with gradient polishing and decorrelation-based convergence control

Abstract

Differential Evolution (DE) is widely used for global optimization in simulation-based parameter estimation, but its performance degrades when objective evaluations require solving stiff or unstable dynamical systems. In such settings, numerical divergence and stagnation can waste substantial computational effort and hinder convergence. To address this, we present a fully tensorized, GPU-accelerated optimization framework that tightly integrates global exploration with fine-grained local refinement. Central to our approach is the Batched GPU Solver of Ordinary Differential Equations (BGSODE), which introduces an alive-masking strategy to dynamically identify and terminate divergent trajectories during parallel population evaluation, effectively mitigating the costs of stiff dynamics. The framework is further enhanced by an elite gradient-based polishing phase governed by a data-driven, decorrelation-based stopping criterion that monitors the statistical independence of top solutions to avoid redundant evaluations. Computational experiments on nonlinear parameter estimation problems demonstrate that the proposed framework delivers robust optimization performance and achieves substantial speedups of up to $55\times$ over conventional implementations. By accelerating both the evolutionary layer and the underlying simulation mechanics, the integrated method reduces classical differential evolution runtime by up to 98.2% without sacrificing solution accuracy.