What are the most suitable metrics and criteria for evaluating the performance and robustness of ROMs in FEA?

1 Accuracy and fidelity

One of the most important aspects of ROMs is how well they capture the essential features and behaviors of the original system. Accuracy and fidelity can be measured by comparing the ROM outputs with the high-fidelity FEA results or experimental data. Some common metrics for accuracy and fidelity are the relative error, the coefficient of determination, the root mean square error, and the mean absolute error. These metrics can quantify the global or local deviations between the ROM and the FEA solutions.

2 Stability and convergence

Another aspect of ROMs is how stable and convergent they are when applied to different scenarios and parameters. Stability and convergence can be measured by analyzing the sensitivity and variability of the ROM outputs with respect to the input variations. Some common metrics for stability and convergence are the condition number, the eigenvalue spectrum, the error bounds, and the residual norms. These metrics can indicate the numerical robustness and reliability of the ROMs.

3 Efficiency and scalability

A third aspect of ROMs is how efficient and scalable they are in terms of computational resources and time. Efficiency and scalability can be measured by comparing the ROMs with the FEA in terms of the number of degrees of freedom, the memory usage, the CPU time, and the parallelization potential. Some common metrics for efficiency and scalability are the speedup factor, the compression ratio, the memory footprint, and the parallel efficiency. These metrics can demonstrate the advantages and limitations of the ROMs.

4 Generalization and adaptability

A fourth aspect of ROMs is how well they can generalize and adapt to new situations and data. Generalization and adaptability can be measured by testing the ROMs on unseen or noisy data, or on different domains or boundary conditions. Some common metrics for generalization and adaptability are the cross-validation score, the learning curve, the transferability index, and the error distribution. These metrics can evaluate the predictive power and the robustness of the ROMs.

5 Interpretability and explainability

A fifth aspect of ROMs is how interpretable and explainable they are in terms of physical meaning and insights. Interpretability and explainability can be measured by examining the ROM structure, parameters, and features, and by relating them to the underlying physics and phenomena. Some common metrics for interpretability and explainability are the sparsity, the coherence, the correlation, and the importance. These metrics can reveal the significance and the relevance of the ROM components.

6 Validation and verification

A final aspect of ROMs is how valid and verified they are in terms of scientific rigor and credibility. Validation and verification can be measured by performing rigorous and systematic tests and checks on the ROMs, and by comparing them with other methods and models. Some common metrics for validation and verification are the uncertainty quantification, the error estimation, the sensitivity analysis, and the benchmarking. These metrics can assess the confidence and the quality of the ROMs.

7 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?