Improving Prediction Accuracy in Computer Experiments through Empirical Dimensional Analysis

In the field of computer experiments, researchers often face the challenge of accurately predicting output values for untested input variables. To address this issue, the article proposes a new technique called data-adaptive dimensional analysis (DA). DA builds on the basic GaSP surrogate paradigm by incorporating input and output transformations guided by dimensional analysis (DA) and physical units of measurement.
DA is related to physical units of measurement, which helps to ensure that the predictions are meaningful and accurate. By using DA, researchers can improve the prediction accuracy for untested input variables, resulting in more reliable and efficient computer experiments. The proposed method has several advantages, including its ability to handle complex systems with multiple inputs and outputs, its robustness to noise and uncertainty, and its flexibility in incorporating different types of measurements and units.
One of the key benefits of DA is its ability to adapt to the specific characteristics of each system being studied. By using a combination of dimensional analysis and input/output transformations, DA can identify the most relevant variables and scaling factors for accurate prediction. This approach can be particularly useful in situations where the experimental conditions are complex or difficult to predict, such as in the design of experiments.
Another advantage of DA is its ability to incorporate different types of measurements and units. For example, researchers may use dimensional analysis to identify the most important variables and scaling factors, while also accounting for differences in units between inputs and outputs. This can help to ensure that the predictions are consistent and meaningful across different experimental conditions.
The proposed method is demonstrated using several case studies in computer experiments, including the prediction of pressure drop in a heat exchanger and the optimization of a chemical process. In both cases, DA was shown to improve the accuracy of the predictions compared to traditional surrogate methods.
In conclusion, data-adaptive dimensional analysis offers a powerful tool for improving the accuracy of computer experiments by incorporating input and output transformations guided by dimensional analysis and physical units of measurement. By adapting to the specific characteristics of each system being studied, DA can provide more reliable and efficient predictions, resulting in better decision-making and improved outcomes.