Titolo della tesi: Computational Methods for Risk Management: Graph Optimization, Neural-Symbolic Integration, and Spatial Prediction
Risk management is a structured process whose operational phases—from preparedness to response and recovery—impose structurally distinct requirements on computational tools designed to support them. The form of the computational problems arising from each phase differs not only in domain but in fundamental structure, and this heterogeneity motivates taking problem formulation as the primary guide for method design. This thesis develops three computational contributions, each targeting an inherently distinct phase of the risk management process, and demonstrates that problem formulation is an effective guide for method design under heterogeneous requirements of risk management.
The first contribution addresses structural preparedness in Critical Information Infrastructures (CIIs), where heterogeneous AI-based monitoring components must be deployed across network nodes such that every critical routing path is guaranteed coverage. This requirement is formalized as the Shortest Path Labeling Problem (SPLP), a combinatorial optimization problem seeking a minimum-cost assignment of monitoring component types subject to hard path-coverage constraints. Two solution approaches are developed: an exact Integer Linear Programming formulation and a Reactive GRASP metaheuristic. Experiments on scale-free benchmark instances ranging from 30 to 300 nodes show that the metaheuristic consistently finds lower-cost solutions within the same time budget and scales to realistic network sizes, while the exact approach achieves acceptable performance only on the smallest instances.
The second contribution targets a computational bottleneck in the Probabilistic Algebraic Layer (PAL) framework for Neuro-Symbolic (NeSy) AI, which has so far prevented deployment in real-time safety-critical settings. PAL realizes probabilistic inference through exact integration over constrained regions, an operation whose cost has made continuous operational use impractical. This thesis introduces STOKED!, a GPU-accelerated PyTorch implementation based on Homogeneous Numerical Integration (HNI) method designed as drop-in replacements for GASP! within PAL. STOKED! reduces median GPU memory consumption by approximately 3 times and eliminates out-of-memory failures on complex instances, though the preparation phase remains a scalability bottleneck—exponential at higher dimensions as a consequence of the curse of dimensionality—and constitutes an open challenge.
The third contribution addresses post-event damage assessment for earthquake-induced lateral spreading, a geohazard whose damage patterns are spatially correlated and conditioned on neighborhood geological context. A synthetic spatial graph is constructed over geotechnical measurement sites by connecting each site to its k nearest neighbors, and a Graph Convolutional Network (GCN) is trained on this graph-structured input to propagate neighborhood information into node embeddings for damage prediction. The GCN consistently outperforms random forest and feedforward neural network baselines across all evaluation metrics, validating spatial structure as an effective inductive bias for post-event geohazard prediction. Explainability is provided through SHapley Additive exPlanations (SHAP) analysis.
Together, these contributions illustrate that the inherent characteristics of each risk management phase impose a precise computational structure on the problems arising within it: the scenario drives the formulation, but the phase determines its fundamental requirements.