A differentiable physics solver for pavement mechanical responses

Engineering systems increasingly rely on data-driven optimization and closed-loop decision-making. Accordingly, computational models in engineering are no longer only tools for forward analysis, but also need to support parameter updating, design optimization, and feedback decision-making. In contrast, existing pavement mechanics computation still mainly serves response prediction under given parameter conditions and lacks a dedicated differentiable physics solver that directly provides stable gradient information. To address this gap, this study develops ∂ Pave, a differentiable physics solver for pavement mechanical response computation. ∂ Pave builds on a spectral element forward solution framework for layered pavement systems under moving loads. The solver connects load, material, geometric, and evaluation parameters to explicit stages of an end-to-end differentiable spectral element method solution path. Within this unified physical framework, ∂ Pave returns selected mechanical responses at specified points in the layered pavement coordinate system together with their gradients with respect to specified input parameters. This study verifies the computed gradients through examples involving multiple response quantities. The results show that the automatic differentiation gradients from ∂ Pave are generally consistent with finite difference results. In multi-parameter joint differentiation tasks, the efficiency advantage of ∂ Pave over parameter-by-parameter finite differences increases with the number of differentiated parameters. This study further illustrates the use of the same response-gradient interface in two gradient-driven pavement engineering workflows, namely pavement structural design optimization and measurement-point layout optimization for pavement inspection. The two examples use task-specific variables, objectives, constraints, and decision procedures outside the physics solver. They demonstrate that ∂ Pave can serve as a reusable physics-based response-gradient provider for different pavement mechanics task formulations.