Random sampling-high dimensional model representation (RS-HDMR) and orthogonality of its different order component...

Area of Science:

• Computational Mathematics
• Data Analysis and Modeling

Background:

• High Dimensional Model Representation (HDMR) is a technique for analyzing complex systems.
• Existing HDMR methods face challenges with systems having dependent input variables.
• Orthogonality of component functions is crucial for accurate HDMR approximations.

Purpose of the Study:

• To extend HDMR to systems with non-independent input variables.
• To develop new orthonormal polynomial approximation formulas for HDMR component functions.
• To enhance the accuracy and applicability of HDMR.

Main Methods:

• Extended the definition of HDMR component functions for dependent inputs.
• Developed new orthonormal polynomial approximation formulas.
• Applied the new method to an integrated exposure and dose model and ionospheric electron density data.

Main Results:

• The new orthonormal polynomial approximation preserves the orthogonality property.
• The proposed method demonstrates improved accuracy compared to prior approaches.
• Successfully applied to complex real-world datasets.

Conclusions:

• The new orthonormal polynomial approximation formulas offer a more accurate HDMR approach for systems with dependent inputs.
• This advancement enhances the utility of HDMR in quantitative model assessment and analysis.
• The method shows significant potential for various scientific and engineering applications.