Evaluating Low-Fidelity Data in Surrogate Modeling

In recent years, the use of Surrogate Models has gained popularity in industrial design. These models are particularly useful when evaluating a design is expensive or time-consuming. Instead of directly testing every design, which can be costly, surrogate models allow for quicker evaluations by simulating the design's behavior based on previously collected data.

#What Are Surrogate Models?

Surrogate models serve as stand-ins for expensive simulations or experiments. They take known data from high-cost evaluations and use it to predict outcomes in new scenarios. This approach can significantly reduce costs and time in the design process. However, the accuracy of surrogate models heavily depends on the quality of the data used to train them.

#Types of Data Sources

When building a surrogate model, one often encounters multiple data sources. These may include:

• High-Fidelity Data: This type of data comes from accurate but expensive evaluations. It is trustworthy and typically the primary source for training models.
• Low-Fidelity Data: This data is easier and cheaper to obtain but may not be as accurate. It can be helpful when there is little high-fidelity data available.

#The Challenge with Low-Fidelity Data

Low-fidelity sources can sometimes lead to poor model performance. If the low-fidelity data does not correlate well with high-fidelity data, it may mislead the model, resulting in inaccurate predictions. This issue raises the need to identify when it is beneficial to use low-fidelity data and when it is better to avoid it.

#Goals of the Study

The main aim is to characterize harmful low-fidelity data sources when building multi-fidelity surrogate models. By understanding which low-fidelity sources are detrimental, practitioners can make informed decisions on data usage. This will ultimately lead to better model accuracy and more efficient design processes.

#Importance of Guidelines

Creating clear guidelines can aid in determining when to use low-fidelity data. These recommendations will stem from a focused analysis, aiming to provide easy-to-follow rules for practitioners in the field.

#The Role of Instance Space Analysis

Instance Space Analysis (ISA) is a valuable tool for understanding how different types of data affect algorithm performance. Instead of averaging performance across instances, ISA visualizes the relationships between various features of data and modeling approaches. This method can highlight areas where certain models excel or fail.

#Features in ISA

In ISA, features are characteristics that define how a problem looks. They can include factors like:

• Dimension of the Problem: The number of variables involved.
• Data Source Quality: How well the low-fidelity data represents the high-fidelity data.
• Data Availability: The amount of each type of data at hand.

These features allow for a deeper understanding of how different modeling approaches, like Kriging or Co-Kriging, can perform under specific conditions.

#Surrogate Modeling Techniques

Surrogate models are primarily based on Gaussian processes, a statistical method that combines various data sources into a single model. Two common techniques are:

• Kriging: A model that uses only high-fidelity data for predictions.
• Co-Kriging: An extension that incorporates both high- and low-fidelity data, aiming for improved predictions.

#The Importance of Accuracy

In the context of surrogate modeling, accuracy is crucial. Models that are trained poorly can lead to flawed design decisions. It is essential to assess the quality of both high- and low-fidelity data before combining them in a model.

#Previous Studies and Findings

Past studies have suggested that low-fidelity data can sometimes be detrimental. Researchers found that if low-fidelity data does not closely relate to high-fidelity data, it may be better to train models solely on high-fidelity information. This conclusion highlights the necessity for further exploration into how to identify harmful data sources.

#Identifying Harmful Data Sources

By creating a framework to evaluate low-fidelity data, researchers can better understand its impact on model performance. The goal is to establish criteria for deciding when to include or exclude low-fidelity data in model training.

#Methodology

To achieve the study's goals, a systematic approach is taken that includes generating diverse data instances and analyzing their properties.

#Data Generation

A wide range of function pairs are generated based on existing literature and additional methods to diversify the dataset. The diversity in data allows for more comprehensive testing of the surrogate models.

#Analysis of Data Performance

Once a robust dataset is established, various surrogate models-Kriging and Co-Kriging-are trained using different combinations of high- and low-fidelity data.

#Performance Assessment

The models are evaluated based on their ability to predict outcomes accurately. Statistical tests are used to determine if the models are performing well in particular scenarios, guiding the decision on whether to use low-fidelity data.

#Results and Observations

After training the models and evaluating their performance, distinct trends emerge.

#Key Findings

• Regions in the instance space show where Kriging models perform better than Co-Kriging, and vice-versa.
• High-fidelity data consistently yields better results than low-fidelity data, particularly in areas where accuracy is crucial.
• Low-fidelity data can provide benefits in specific contexts but can also lead to inaccuracies if not carefully assessed.

#Guidelines for Practitioners

Based on the findings, several practical guidelines can be established for practitioners working with multi-fidelity surrogate models.

#Recommendations

1. Use High-Fidelity Data: When available, always prioritize high-fidelity data for model training.
2. Assess Low-Fidelity Data: Before incorporating low-fidelity sources, evaluate their correlation with high-fidelity data.
3. Positioning in Instance Space: Understand the characteristics of the instance space to make informed decisions about data usage.

#Future Directions

The field of surrogate modeling is evolving, and new techniques continue to emerge. Further research can expand upon the findings of this study to refine and enhance the understanding of low-fidelity data sources.

#Exploring New Techniques

Future work could explore adaptive methods that dynamically choose when to use low-fidelity sources, improving overall modeling strategies.

#Conclusion

This study emphasizes the importance of characterizing low-fidelity data sources when constructing surrogate models. By identifying harmful low-fidelity sources and establishing guidelines, practitioners can improve the accuracy and efficiency of industrial design processes. The insights gained from analysis help create a more informed framework for the usage of multi-fidelity models, ultimately enhancing decision-making in engineering and design.

#Acknowledgments

This research is supported by various initiatives that aim to foster advancements in optimization technologies and methodologies. The collaboration between institutions and researchers contributes to the growth of knowledge in this field.

This study's code and methodologies are available for further exploration. By making these resources accessible, researchers can continue developing techniques that optimize the use of data in modeling practices, driving improvements in surrogate modeling for industrial applications.