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This dissertation presents recursive approaches to modeling, learning, and decision-making in dynamic environments using structured machine learning. We unify contributions across three domains—bio-inspired flight modeling, physics-informed neural state estimation, and online inverse reinforcement learning—under the theme of recursive and interpretable learning. Emphasis is placed on integrating domain knowledge into learning architectures to enable efficient, sample-conscious, and generalizable models that can operate under partial observability or structural uncertainty.
In the first part of the dissertation, we introduce a data-driven modeling framework for a flapping-wing robotic platform. Inspired by the biomechanics of flight, we construct reduced-order representations of the robot’s nonlinear, high-dimensional dynamics. A central contribution is the integration of the Cubature Kalman Filter (CKF), which enables online estimation of unmeasured aerodynamic forces from inertial data. The CKF leverages cubature rules to compute nonlinear expectations efficiently, and these same rules are employed to guide the update of neural network parameters during model learning. This unified use of cubature principles supports adaptive, interpretable identification of complex aerodynamic behaviors under nonstationary and uncertain flight conditions.
In the second part, we develop hybrid neural ordinary differential equation (ODE) models for dynamical systems where partial knowledge of the governing equations is available. Rather than embedding full physical constraints like energy conservation or mass balance, we leverage known structure in the ODEs governing measured states to constrain the learning process. This structural prior enhances the identifiability of latent dynamics and improves generalization in the presence of limited or noisy data. The resulting models balance physical interpretability with data-driven flexibility, and we demonstrate their effectiveness on benchmark biological and mechanical systems.
In the third contribution, we propose a recursive algorithm for deep inverse reinforcement learning (IRL), enabling the real-time inference of reward functions from streaming expert demonstrations. Departing from traditional batch IRL formulations, our method applies second-order updates inspired by the Extended Kalman Filter to optimize a derived upper bound on the maximum entropy IRL objective. We validate the method on multiple domains—ranging from cognitive radar to continuous control—and show superior sample efficiency and reward recovery performance compared to state-of-the-art approaches such as GAIL and AIRL.
Through theory and experiments, this work demonstrates the advantages of hybrid, recursive architectures for control, prediction, and behavior inference. Collectively, the methods developed in this dissertation advance the integration of structure, adaptability, and scalability in machine learning for dynamical systems.