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This paper introduces a classical, PDE-constrained multiscale inverse framework to assess the device-level identifiability of strain-tuned valley splitting in 2D magnetic heterostructures, specifically for MoS2/CrBr3. By bridging continuum elastodynamics to valley-resolved anomalous Hall transport, it quantifies the statistical recoverability of microscopic quantum predictions in macroscopic devices. The framework establishes a precise diagnostic threshold for experimental viability, demonstrating that a predicted coupling magnitude yields a confidence interval consistent with zero, thus highlighting the need for rigorous statistical identifiability before fabrication.
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Controlling valley degrees of freedom with mechanical strain is a promising approach for solid-state information processing. Current theoretical literature routinely predicts strain-tuned valley splitting at the microscopic level but rarely evaluates whether these quantum predictions remain statistically recoverable in realistic macroscopic devices. This manuscript establishes a fully classical, partial differential equation-constrained multiscale inverse framework for quantifying the device-level identifiability of predicted strain-tunable valley effects in two-dimensional magnetic heterostructures, demonstrated here for a molybdenum disulfide and chromium tribromide heterostructure. First-principles structural relaxations confirm a chiral $C_3$ point-group symmetry which mathematically reduces the relevant exchange-strain coupling tensor to a single scalar. A partial differential equation-constrained adjoint-state architecture successfully bridges continuum elastodynamics to valley-resolved anomalous Hall transport. Density functional theory yields a coupling estimate of $\eta \approx -0.07$ meV whose 95% confidence interval is consistent with zero. Evaluating this specific coupling magnitude against established thermal noise and velocity saturation limits defines a safe operating window bounded between 262.0 and 22,337.6 V/cm. Rather than asserting a confirmed nonzero material property this bounded operational window functions as a precise diagnostic threshold. Deploying this rigorous statistical identifiability framework provides a necessary mathematical filter to determine the true experimental viability of theoretically predicted two-dimensional materials before complex physical fabrication.