CAREER: Theoretical Foundations for Learning Network Dynamics

Dynamic processes on complex networks of interconnected entities abound as models of physical, biological, engineered, social, and economic systems. Learning flexible, human-interpretable statistical models of these processes from data is a vital prerequisite for their prediction and control. Designing machine learning models and algorithms, even in a non-networked setting, is not fully understood mathematically. The networked nature of the processes brings additional challenges for model accuracy, human interpretability, and efficiency. This project seeks a new mathematical framework, efficient algorithms, and theoretical guarantees for learning data-driven models of evolving processes on complex networks. It aims also to provide rigorous techniques for validation and interpretation of learned models. These advances should result in improved model validation, accuracy, efficiency, and interpretability for diverse, societally impactful application domains such as epidemiology, misinformation spread on social networks, electrical power networks, supply chain networks, and nutrient diffusion processes in agriculture. The project additionally involves mentoring of doctoral, undergraduate, and high school students; expansion of the investigator's home department's theory curriculum; collaboration with domain experts in agriculture; and a bootcamp on machine learning and statistics for network dynamics. The investigator targets a comprehensive mathematical framework for learning of dynamics on graphs, drawing from probability, random graphs, and information and learning theory. It will address statistical (sample complexity) and computational efficiency of learning algorithms and models, expressive power of existing and novel model classes, and model validation, selection, and interpretation. Throughout, the impact of graph structural parameters on performance will be studied with mathematical rigor. The limitations of classical learning rules will be elucidated, and novel learning rules with theoretical guarantees will be devised. Quantitative universal approximation guarantees for new and classical neural network-based dynamic model classes will be given. Novel cross-validation-based algorithms with provable guarantees for model validation and selection will be devised. Criteria for consistent ground-truth model parameter estimation, important for interpretability of models, will be formulated. This will enable a theoretically-backed pipeline for learning, validation, and interpretation of data-driven network dynamics models. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.