PorteManet: Parameter Identification for Expert Neural Ordinary Differential Equations

Abstract

This dissertation addresses the intertwined challenges of parameter identification and time-series regression in mis-specified dynamical systems. Parameter identification provides interpretability and robustness of the uncovered quantities; time-series regression contributes predictability and generalizability in captured temporal trajectories. Conventional approaches typically fall short in uniting these complementary strengths, particularly when the underlying models are incomplete or partially mis-specified.This work introduces a new methodology, PorteManet (PMnet), that coherently integrates neural-network-based sequence prediction with principled optimization-based parameter recovery. PMnet integrates two complementary models, each of which may be incomplete or partial. Its distinctive initial state encoder, the Implicit Value Encoder (IVE), fully leverages the system structure in place of the conventional recurrent encoders. This integration enables recovery of interpretable parameters through structure-governed error correction, thereby bridging the gap, in both modeling and solution, between identifiability and predictability.Theoretical contributions include constructing the new framework, establishing feasibility conditions under which the recovered parameters remain interpretable, and analyzing numerical solutions. Empirical studies with synthetic and real-world datasets demonstrate that PMnet outperforms both hybrid and purely neural baselines in parameter recovery and trajectory prediction. Importantly, PMnet is applied to modeling virological changes and integration expansion in hepatitis B virus (HBV). It achieves remarkable improvements in prediction accuracy while maintaining interpretability compared to existing approaches. The theoretical and empirical findings show the potential of PMnet as a principled method for solving mis-specified dynamic systems with broad applications.