Model Validation for Multivariate Functional Responses via Autoencoder-Based Dual-Layer Feature Extraction

Model validation for complex simulation models with multivariate functional responses poses significant challenges, as it involves the dual coupling of physical correlations among variables and field correlations in time-series data. A novel Autoencoder-based Dual-Layer Feature Extraction (AE-DLFE) method is proposed. The first layer uses joint principal component analysis to decouple physical correlations, while the second layer develops an Autoencoder-improved Feature Selective Validation (AE-FSV) method that adaptively extracts features of time-series data and measures feature discrepancies via deep representation learning. On this basis, a new validation metric named U-PCDM (Uncertainty Principal Component Difference Measure) is developed to quantify the discrepancies between simulation and experiment under uncertainty. Theoretical analysis confirms the boundedness and unique temporal permutation sensitivity of the proposed metric. Case study results demonstrate that the proposed AE-FSV enhances the evaluation accuracy of traditional FSV on transient data. Furthermore, compared to benchmark methods such as MD-pooling, the U-PCDM metric significantly improves computational efficiency—especially in high-dimensional scenarios—while maintaining consistent model rankings. This work effectively addresses the heterogeneous correlation coupling issue, offering a robust quantitative tool for model validation.