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A Primer on Statistics, Data Analytics, and Artificial Intelligence

Two speakers collaborated to offer a primer on statistics, data analytics, and artificial intelligence (AI). Planning committee member Alyson G. Wilson, North Carolina State University, began with the basics: what a statistical sample is, what a statistical model is, and what uncertainty is and how it is expressed. She also presented two key theorems that underlie statistical analysis, the central limit theorem and the law of large numbers.

Wilson spoke briefly about how statistics can inform the design of experiments and the importance of proper sampling techniques. Then she described Bayesian methods, which can be employed if one believes one knows something about the population characteristic of interest before starting to collect data from that population. These methods offer a structured way to combine prior information with current experimentation.

Last, she discussed how statistics is used in situations where there is both observational data on and a physics-based model (i.e., a simulation) of the phenomenon of interest. She also spoke about the importance of verification, validation, and uncertainty quantification (VVUQ), where verification refers to making sure that the approximate computer model accurately represents the mathematical description, and validation looks at how well the computer model matches with reality.

This is the foundation on which digital twins are built, Wilson said, and she handed the microphone to planning committee member Wei Chen, Northwestern University, who expanded on the idea of digital twins.

Chen began with a definition of a digital twin, which she took from the 2024 National Academies of Sciences, Engineering, and Medicine

report Foundational Research Gaps and Future Directions for Digital Twins: “a set of virtual information constructs that mimics the structure, context, and behavior of a natural, engineered, or social system (or system of systems), is dynamically updated with data from its physical twin, has a predictive capability, and informs decisions that realize value” (Figure 7-1).

In additive manufacturing (AM), for example, a digital twin can be built for directed energy deposition. Data (e.g., melt pool temperature and width) from sensors monitoring the process are used to inform the digital twin about the state of the real system so that it can be used for real-time control and optimization of the process. Ideally, the digital twin combines physics-based thermal analysis and materials models with the real-time data and also considers and mitigates various sources of uncertainty.

Fulfilling the potential of digital twin control of AM requires machine learning (ML), which can extract meaningful data from the large amounts of data produced in the process, build surrogate models, make decisions in real time, and adjust the parameters of the process in response to changing conditions, changes in material properties, and so on. Chen described some ML models that are widely used in AM. In particular, she spoke about surrogate models with uncertainty qualification, which is crucial for improving the accuracy, reliability, and decision-making capabilities of digital twins.

After their presentations, Wilson and Chen answered a few questions. The first concerned how users of AM should address the fact that they are mostly dealing with small sample sizes, which are challenging to use for statistical analyses. Chen said that certain areas of AM do generate large datasets, but in the cases where large amounts of experiment data do not exist, physics-based modeling can be useful by providing computer simulations, which can provide data for analyses. Wilson offered a different perspective on the issue. First, when there are few data available, she suggests broadening the definition of “data” and finding other ways to offer insight into an issue; the use of computer modeling is one example of this approach. Second, she noted that it is important to understand the impact of uncertainty and understand how uncertainty contributes to the decision being made.

A second question concerned how to use data from the AM process to make a convincing case that an AM part can be effectively deployed. Chen spoke about extending the digital twin into the lifetime of the product to understand not only processing–structure but also structure–property–performance relations so that the end part’s performance is part of the record and can be used to demonstrate the benefits of the product. Wilson said that her strategy for using heterogeneous data to convince someone of the value of an AM part has three pieces: doing everything with methodological rigor, being able to use data about the part to make predictions

about its performance, and reducing uncertainty about the performance as much as possible.

Last, in response to a question about digital twins, Wilson said that many of the statistical ideas that she had talked about in her presentation can be applied to issues that arise with digital twins, such as how to accelerate testing in order to more quickly develop data on failures that can be fed into the model.