发表机构
Southern University of Science and Technology; Guangdong Provincial Key Laboratory of Geophysical High-resolution Imaging Technology, Southern University of Science and Technology（南方科技大学; 南方科技大学地球物理高分辨率成像技术广东省重点实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出ADEPTS，一个基于自动微分的地幔对流反演框架，通过比较展开与隐式微分策略，实现高维初始温度场和低维物理参数的联合反演。
AI 中文摘要
时间依赖的地幔动力学反演必须解决初始状态的高维性、非线性流变学以及通过长期热机械演化的梯度传播问题。我们开发了ADEPTS，一个基于自动微分的二维交错网格有限差分地幔动力学反演框架。正演模型求解不可压缩斯托克斯流、温度平流-扩散和成分平流，并考虑温度和应变率相关的粘度及塑性屈服。对于非线性斯托克斯系统，我们比较了两种梯度策略：通过固定次数的Picard迭代展开微分，以及对收敛的离散残差方程进行隐式微分。数值实验表明，即使非线性求解未完全收敛，展开微分仍保持稳定，而隐式微分需要足够精确的非线性解；否则梯度一致性和优化收敛性会恶化。在求解充分收敛的情况下，隐式微分能够恢复与展开微分相当的精确梯度和重建质量。联合热化学孪生实验表明，ADEPTS可以同时恢复高维初始温度场和低维物理参数，包括成分密度、参考粘度和应力指数，同时拟合最终时刻的温度、地表水平速度和地表法向应力。这些结果证明了可微分时间依赖地幔动力学反演的可行性，并阐明了展开微分和隐式微分不同的收敛要求。
英文摘要
Time-dependent mantle-dynamics inversion must address the high dimensionality of the initial state, nonlinear rheology, and gradient propagation through long-term thermo-mechanical evolution. We develop ADEPTS, a two-dimensional staggered-grid finite-difference framework for mantle-dynamics inversion based on automatic differentiation. The forward model solves incompressible Stokes flow, temperature advection-diffusion, and compositional advection with temperature- and strain-rate-dependent viscosity and plastic yielding. For the nonlinear Stokes system, we compare two gradient strategies: unrolled differentiation through a fixed number of Picard iterations and implicit differentiation of the converged discrete residual equations. Numerical experiments show that unrolled differentiation remains stable even when the nonlinear solve is not fully converged, whereas implicit differentiation requires sufficiently accurate nonlinear solutions; otherwise gradient consistency and optimization convergence deteriorate. With sufficiently converged solves, implicit differentiation recovers accurate gradients and reconstruction quality comparable to unrolled differentiation. Joint thermo-chemical twin experiments show that ADEPTS can simultaneously recover a high-dimensional initial temperature field and low-dimensional physical parameters, including compositional density, reference viscosity, and stress exponent, while fitting final-time temperature, surface horizontal velocity, and surface normal stress. These results demonstrate the feasibility of differentiable time-dependent mantle-dynamics inversion and clarify the different convergence requirements of unrolled and implicit differentiation.
Comments40 pages, 12 figures
