Gradient-Enhanced Spline Dimensional Decomposition via Energy-Balanced Scaling and L1-Regularized Sparse Reconstruction
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A spline dimensional decomposition (SDD) surrogate is effective for representing high-dimensional, non-smooth, and locally oscillatory nonlinear responses in uncertainty quantification (UQ) of engineering systems. However, the accuracy of SDD strongly depends on reliable estimation of its expansion coefficients, which becomes challenging when training data are scarce. In this work, we present a gradient-enhanced SDD method that combines energy-balanced scaling with ℓ1-regularized sparse reconstruction. The proposed method integrates derivative information into the surrogate construction and employs an energy-based normalization strategy to balance the contributions of function and gradient data within the regression system. This method improves numerical stability and enables efficient exploitation of gradient information without The method is demonstrated on a practical engineering UQ problem characterized by limited training data. The results show that the proposed method achieves higher accuracy and improved efficiency compared with a conventional SDD method.
