Interpretable Modeling Frameworks for Dynamical Systems: From First Principles to Explainable AI in Smart and Industrial Applications

This dissertation develops and applies a unified methodological framework for modeling dynamical systems that places interpretability, transparency, and explainability at the center of model selection and design. The framework replaces a purely source-of-knowledge view with a dual-axis taxonomy that distinguishes four classes, white-, knowledge-driven grey-, data-driven grey-, and black-box, and operationalizes movement between them via calibration, physics-guided approximation of hard submodels, and surrogate modeling. It couples taxonomy-aware pipelines with practical indicators of model complexity, transparency, and explanatory adequacy, and it is validated across three application domains. In smart sensing, the thesis introduces a first-principle, dual-carrier partial differential equations model implemented via finite element method for bacterial-cellulose ionic transducers, preserving mechanistic clarity while enabling a hybrid 2D–1D simulation. The model is experimentally validated and used to explain the roles of curvature, advection, and interfacial phenomena. Transparent data-driven models are then benchmarked: Auto-Regressive with eXogenous Inputs and Finite Input Response (FIR) excel in one-step prediction, whereas Nonlinear FIR provides superior long-horizon simulation. In industrial soft-sensing, classical linear regressors and their nonlinear counterparts are compared with Koopman-operator-based state-space representations on processes such as Sulfur Recovery Units and distillation. Results show that knowledge-driven grey-box formulations can reconcile accuracy with structural insight, while data-driven-grey models retain auditability at higher flexibility; symbolic regression supports verifiable feature–response laws. In energy systems, the framework is applied to vehicle-to-grid (V2G) forecasting. Koopman-based state-space models and machine-learning pipelines are complemented by SHapley Additive exPlanation (SHAP) to expose feature attributions and decision logic, delivering accurate predictions of aggregated available capacity together with actionable explanations. In summary, the thesis proposes and applies a unified methodological framework that re-anchors model selection and design around interpretability, transparency, and explainability, and shows, through cross-domain studies, how hybrid paradigms can satisfy modern scientific, industrial, and financial requirements for trustworthy prediction and decision-making.