Assessing Reduced Model Performance for Chaotic Systems via Autocorrelation Analysis

Advantages: PIDMD offers several advantages over traditional non-intrusive model reduction techniques. Firstly, it improves the accuracy and robustness of the reduced model by preserving the structure of the full system. Secondly, it enables the use of complex models in situations where direct access to the code is unavailable, such as in black-box simulations or when working with opaque software. Finally, PIDMD can be used for both linear and nonlinear systems, making it a versatile tool for model reduction in various fields.
Conclusion: In conclusion, this article proposes a non-intrusive model reduction method that preserves the structure of complex systems while reducing their complexity. The proposed method, PIDMD, leverages manifold optimization to learn linear operators that capture the underlying dynamics of the full system. By ensuring structure preservation, PIDMD offers improved accuracy and robustness compared to existing methods, making it a valuable tool for various applications in engineering and science.