Deep-learning-driven diagnosis of ill-posed inversion of elastic constants in orthotropic solids

The inverse identification of orthotropic elastic constants is a fundamental problem in solid mechanics, yet it is frequently compromised by ill-posedness, leading to non-unique solutions. To elucidate the fundamental causes of this ambiguity, this study proposes a deep learning diagnostic framework (DLDF). Utilizing a multi-head residual network (MHRN) as an ultra-fast surrogate for the exact semi-analytical solution, we explore the topology of the objective function with unprecedented resolution. Guided by global sensitivity analysis, we isolate the parameters responsible for the instability. Crucially, our analysis reveals that the ill-posedness stems not from stochastic optimization errors, but from a deterministic solution manifold—a continuous valley of admissible solutions inherent to the underlying mechanics. This geometric structure explains the fundamental inability to recover specific stiffness couplings using conventional displacement-based measurements. Furthermore, we demonstrate that the topological degeneracy of this manifold can be effectively collapsed into a unique solution by introducing a targeted physical constraint, specifically the surface shear stress. These results clarify the geometric origin of ill-posedness and provide a physics-informed pathway for designing well-posed inverse experiments for orthotropic material characterization.