By Dr. Brett Borghetti (with assistance from NIPRGPT)
Article contributions by Dr. Matthew Robbins, Maj. Nick Yielding, Ph.D., Lt. Col. Phillip LaCasse, Ph.D., Dr. Jonah Reeger, Dr. Christine Schubert Kabban and Dr. Scott Nykl
Air Force Institute of Technology 

AFIT Department of Electrical and Computer Engineering students attend a course on how to safely refuel autonomous vehicles in contested environments where typical approaches such as GPS-based high-precision navigation are not guaranteed and delays in the control link impact the ability for a human to precisely guide the autonomous vehicle during refueling operations. This ongoing research applies artificial intelligence and machine learning techniques as a foundational technology in the search for a solution. (U.S. Air Force photo by Jaima Fogg)

The demand for artificial intelligence expertise is growing rapidly, with applications in fields such as national security, healthcare, finance, and more. As the Department of Defense (DoD) increasingly relies on AI technologies to inform decision-making and drive innovation, the need for professionals with advanced training in AI has never been more pressing.

The Air Force Institute of Technology is uniquely positioned to address this need. AFIT is at the forefront of preparing the next generation of leaders and innovators in the field of artificial intelligence by developing a comprehensive AI curriculum and research program that equips students with the knowledge and skills necessary to succeed in this rapidly evolving field, ensuring that its students and the broader community stay abreast of the latest advancements needed to address tomorrow’s national security challenges. 

AFIT’s Graduate School of Engineering and Management (GSEM) and the School of Systems and Logistics (AFIT/LS) offer a wide range of courses, certificates, and degree programs that cater to both degree and non-degree seeking students.

GRADUATE-LEVEL COURSES & CERTIFICATES

AFIT’s Graduate School of Engineering and Management (GSEM) offers graduate level courses, certificates, and degree programs that cover a broad range of topics in AI, including data analytics, statistical machine learning (ML), deep learning and reinforcement learning, natural language processing, computer vision, unmanned and autonomous systems and human-agent teams. These multi-disciplinary offerings are designed to provide students with a deep understanding of the theoretical foundations and practical applications of AI and ML.

Although AI and ML graduate courses can be taken individually by non-degree seeking students, they are typically elements within an educational plan that fulfils part of a student’s journey toward a graduate program or certificate. Many AI courses are project-based, allowing students to work on independent research that can lead to theses and dissertations, as well as solutions to challenging national security needs. In addition to graduate degrees with AI focus at both the masters and doctoral level, AFIT also offers several AI-related certificate programs including the Autonomy Certificate (https://e.AFIT.edu/3PP97k) for in-residence students and the Data Analytics Certificate for remote learners (https://e.AFIT.edu/4XXJV1r). An article on the Data Analytics Certificate program can be found on pages 14-15.

SPECIAL CURRICULUM FOCUS AREAS

There are 34 AI-relevant graduate-level courses offered throughout most of the departments within the Graduate School. Below are some key AI areas in the curriculum: reinforcement learning, natural language processing, and math and statistics.

>> Reinforcement Learning (RL):

AFIT’s GSEM offers courses and research opportunities in reinforcement learning (RL), which is a key area of AI research. Dr. Matthew Robbins, Professor of Operations Research, and Maj. Nick Yielding, Ph.D., Assistant Professor of Electrical Engineering, provide insights into the applications and challenges of RL in the Air Force. 

RL is a subfield of machine learning focused on determining how an agent should act in a complex, uncertain environment over time while it seeks to achieve a goal. Mathematically, the agent is designed to behave in a way such that it learns how to maximize expected cumulative reward while experiencing the unknown environment. Unlike supervised machine learning wherein the model learns from a labeled dataset, RL involves an agent learning from the consequences of its actions, receiving feedback in the form of the rewards and penalties it experiences. Several mathematical and computational models, methodologies, and solution procedures exist for solving the agent’s challenging sequential decision problem – that is, determining a policy that governs its behavior or the value of being in a state or taking an action from that state. The integration of deep learning with RL has led to significant advancements. For example, neural networks can approximate value functions or policies, enabling RL to address problems with high-dimensional and continuous state and action spaces without overly relying on domain expertise. Applications of RL abound in engineering and the sciences, including the development of robotics, the control of autonomous vehicles, and the optimal allocation of resources over time to name but a few.

AFIT’s GSEM offers three graduate-level courses focusing on RL:

DSOR 646 – Reinforcement Learning introduces fundamental concepts about RL, including Markov decision processes, the underlying mathematical model formalism that provides a firm theoretical foundation for the development of RL algorithms; temporal difference learning and bootstrapping, important algorithm paradigms for rapidly and accurately estimating the value of state-actions in model-free situations; and value function approximation, an algorithmic mechanism allowing an agent to learn policies for environments with very large state spaces.

DSOR 746 – Advanced Reinforcement Learning continues to delve into important concepts in RL, examining mathematical modeling frameworks, policy design considerations, and attendant solution procedures in more detail. Advanced RL algorithms making use of neural networks (e.g., double deep Q-networks and proximal policy optimization) and mathematical programs are discussed in depth. Multi-agent reinforcement learning extensions are also discussed.

CSCE 723 – Advanced Topics in Artificial Intelligence focuses on artificial intelligence from an agent-based perspective, teaching RL with custom simulation environments and scalable computing, demonstrating how to train agents in real world applications.

RL represents a powerful artificial intelligence technique for solving sequential decision problems wherein the decision-making agent learns an optimal policy via repeated interactions with its environment. The ability of RL to handle complex, uncertain, and dynamic tasks in a wide variety of application areas makes RL a critical area of research and graduate education in the Graduate School.

>> Natural Language Processing (NLP):

Natural language processing is a crucial area of AI research, and AFIT’s Department of Operational Sciences (AFIT/ENS) offers courses and research opportunities in this field. Lt. Col. Phillip LaCasse, Ph.D., Assistant Professor of Operations Research, highlights the importance of NLP in understanding human language and creating models that can accomplish complex linguistic tasks.

NLP is a subset of artificial intelligence that mathematically expresses the nuances of human language and employs those representations to create models that accomplish a task. Text mining, a subset of NLP, is the organizing, classification, labeling, and extraction of information from text sources. Common NLP tasks include sentiment analysis, information retrieval, information extraction, word sense disambiguation, machine translation, document summarization, and question/answer response generation.

AFIT’s GSEM currently offers one graduate-level course in NLP, OPER 655 – Text Mining. The course targets students enrolled in two Department of Operations Research M.S. programs (Data Science, Operations Research) whose thesis is in the NLP domain, although any student can enroll subject to satisfying the proper prerequisites. Pedagogically, OPER 655 is a hybrid between independent study and traditional lecture. Lectures cover both foundational and cutting-edge concepts, but the primary focus of the course is independent study. The independent study element empowers students to engage in self-driven learning by applying course concepts to some relevant NLP application. Students select a single project topic during the first week of the course and are assessed on oral presentations that progressively track and direct the project to its completion. Students have wide latitude to select their projects; many can perform work that supports their M.S. thesis.

Project topics span a broad spectrum of cutting-edge NLP applications. Generative AI for word sense disambiguation (WD), transfer learning to identify sources of synthetically-generated content, influence analysis of open source news articles, and large language model (LLM)-as-judge model validation for document summarization are examples of student OPER 655 projects from fall 2023 and fall 2024. In each of two prior OPER 655 cohorts (summer 2021, fall 2023), a manuscript originating in a student’s OPER 655 final project report was successfully published in a high-quality, Scimago Journal Rank (SJR) Q1, journal. This is in addition to at least two students for whom OPER 655 provided a supporting effort to theses that also culminated in publication in SJR Q1 journals. These successful efforts are a testament to the motivation, creativity, and excellence that our students can achieve.

Future efforts will expand OPER 655 into a two-course sequence, one appropriate for inclusion in the M.S. in Data Science core program and one appropriate as a Ph.D. core or M.S. elective course. Such a maturation will broaden the exposure of AFIT students to this important discipline and position graduates to function and excel in this exciting, challenging problem space.

>> Math and Statistics:

AFIT embraces the belief that students studying AI must have a solid grasp of the core math and statistics that make AI possible. AFIT’s Department of Math and Statistics (AFIT/ENC) offers a range of courses that provide a thorough introduction to the mathematical foundations of AI and ML. Dr. Jonah Reeger, Assistant Professor of Applied Mathematics, and Dr. Christine Schubert Kabban, Professor of Statistics, explain how mathematics and statistics courses in AFIT/ENC provide a strong foundation in AI foundational topics such as linear algebra, optimization, numerical methods, statistical analysis and modeling. These underpinnings enhance the understanding of important techniques other AI and ML coursework as well as research. Listed on the next page are some key courses providing the foundational math and statistics used in the field.

• MATH 521 provides a thorough introduction to linear algebra at a level that should allow students to understand the algebraic and arithmetic processes involved in network models, in particular. 

• MATH 508 provides an understanding of methods for root finding (and satisfaction of first order necessary conditions for optimization), interpolation and approximation (typical AI/ML models are extensions of these ideas with an extreme number of parameters), and numerical differentiation (a necessary tool if you want to check if you are computing sensitivities correctly).

• MATH 509 and MATH 511 are available to assist students that are weaker in their calculus skills in understanding concepts like automatic differentiation/backpropagation. 

• MATH 621, which can provide an even deeper understanding of how to represent, for instance, layers in a neural network at the operator level and act on them appropriately to assist in processes like automatic differentiation. 

• MATH 672 provides an understanding of important tools like matrix decompositions and iterative solvers, which are useful for both preparing data for use in a model and ensuring model efficiency. 

• MATH 674 provides a much deeper understanding of the theory behind the computational tools discussed in Math 508. 

• STAT 642 is a computational statistics course which covers many AI/ML models in addition to the means to develop algorithms for providing statistical inference to such models including resampling methods such as the bootstrap, Monte Carlo and Markov Chain methods in addition to contemporary inferential methods such as conformal inference.

• STAT 643 is a nonparametric statistics course which provides a broad range of statistical tools for complex modeling (such as AI/ML network and complex modeling) in which typical distribution assumptions such as normality (or large sample inference) should not be applied. Topics include inferential methods for testing (from comparison of two samples to DOE applications), 1D and multi-dimensional distribution testing, density estimation, smoothers, wavelets, rank-based regression, and life distributions, among other topics.

• STAT 696 is a course on applied general linear regression using linear algebra, maximum likelihood and least squares to provide interpretable prediction equations and inference to support testing, factor importance identification and uncertainty quantification. Penalized methods such as ridge regression are also covered.

• STAT 644 is called Categorical Data Analysis which entails modeling discrete outcomes. Topics include common AI/ML methods for classification such as logistic regression, clustering, and classification trees/random forests in addition to iterative solvers and decent methods such as Newton-Raphson, Gauss-Newton, Levenberg-Marquardt among various penalized regression methods (lasso, elastic net) and likelihood methods (pseudo, quasi-likelihood). Log-linear models for Poisson count and negative binomial outcomes are also included.

• STAT 645 is a Bayesian inference class focused on the fundamental and computational aspects of Bayesian statistics. Topics include choice of priors, posterior analysis, prediction and computational methods.

• STAT 594 is an applied design of experiment class which is helpful when running complex, computationally intense AI/ML models for comparison and testing. Reduced and proper designs to lessen the burden of computational cost while maintaining inference for all factor level/parameter settings desired by the researcher is emphasized.

• Many introductory courses to probability and statistics, from those not requiring calculus (STAT 521, STAT 525, STAT 535), to those that do (STAT 583, STAT 586, STAT 587) provide background and method for data visualization, analysis and decision making.

• Special topics courses (STAT 899) are a common means to match department statistical expertise with research-based needs. Recent special topics courses covered statistical analysis of graphical network data, non-linear and advanced regression methodologies, cryptographic hardware applications, in addition emerging efforts in natural language processing. 

• The department is also developing a MATH course at the 600 level on numerical methods and numerical optimization that would be useful in understanding alternatives for minimizing loss functions.

ENROLLMENT & REGISTRATION AT AFIT

AFIT’s graduate and continuing education courses are available to degree and non-degree seeking students. Students can enroll in courses through the AFIT website and are encouraged to explore the course catalog and listings to learn more about the courses.

APPLY HERE: https://e.AFIT.edu/LL2TTry  
VIEW THE COURSE CATALOG: https://e.AFIT.edu/xjDXc2

Department of Computer and Electrical Engineering Professor of Computer Science, Dr. Scott Nykl, leads automated aerial refueling research at AFIT. (U.S. Air Force photo)

RESEARCH & FACULTY

One of the key strengths of AFIT’s AI curriculum is its emphasis on real-world applications and research opportunities. Students work on projects that apply AI techniques to solve real-world problems, under the guidance of experienced faculty members. This approach not only provides students with practical skills but also prepares them for the challenges of working in a rapidly evolving field. Below are highlights of two multidisciplinary research areas and an example of the GSEM’s talent growth efforts via new hiring in AI to guide future AFIT students.

>> Battlespace Management:  Students and faculty are partnering with the Air Force Research Laboratory to apply RL to defense-focused research. At AFIT, Maj. Nick Yielding, Assistant Professor of Electrical Engineering, is spearheading RL research projects which develop agents for managing satellite missions such as automated docking and assisting operators and leaders in strategic decision-making for Battlespace Management, Command, Control, and Communication (BMC3). The rapid and adaptable control and decision-making capabilities of RL-based solutions have the potential to significantly impact the complex landscape of the Great Power Competition.

>> Autonomous Aerial Refueling (AAR):  as the USAF increases its use of autonomy, a natural challenge emerges – how to safely refuel autonomous vehicles in contested environments where typical approaches such as GPS-based high-precision navigation are not guaranteed and delays in the control link impact the ability for a human to precisely guide the autonomous vehicle during refueling operations. Professor of Computer Science Dr. Scott Nykl’s AAR team has been addressing this challenge for over half a decade, with AI and ML techniques being a foundational technology in the solution. Using computer vision, his team has managed to create high-precision, fast neural-network-based solutions to AAR which can determine the relative six-degrees-of-freedom position and orientation between the tanker and receiver aircraft using a single camera on the tanker. These solutions enable other control algorithms to guide the receiver into a refueling configuration the meets the tight safety requirements of the operation. For more on this AFIT success story, view the video online https://e.AFIT.edu/DpqrbCC.

>> Growing the Pool of AFIT Talent: One of the Graduate School’s goals is to grow strong independent researchers to tackle tomorrow’s important national security challenges. With an existing robust faculty and a commitment to growing its faculty and research capabilities in AI, the GSEM ensures that its current and future students receive the best education and training possible to prepare them to solve these challenges with these powerful AI tools. 

One example of growing faculty capabilities is in the Department of Electrical and Computer Engineering (AFIT/ENG) where Dr. Brett Borghetti, Professor of Computer Science, is leading the search for the next AI-specialized faculty member for the department. The department is expecting many high-quality prospective faculty to apply. AFIT/ENG will select the best of the best from this talent pool and have its newest AI faculty member in place by the start of the fall 2025 quarter.

AFIT is committed to providing its students and the broader Air Force community with the best education and training possible in AI and ML. With its strong faculty, research capabilities, and course offerings, AFIT is well-positioned to lead the way in AI and ML education and research.