Machine Learning-Based Prediction Framework for Complex Neuromorphic Dynamics of Third-Order Memristive Neurons at the Edge of Chaos

As conventional computing architectures face fundamental physical limitations and the von Neumann bottleneck constrains computational efficiency, neuromorphic systems have emerged as a promising paradigm for next-generation information processing. Memristive neurons, particularly third-order circuits operating near the edge of chaos, exhibit rich neuromorphic dynamics that closely mimic biological neural activities but present significant prediction challenges due to their complex nonlinear behavior. Current approaches typically require complete system state measurements, which is often impractical in real-world neuromorphic hardware implementations where only partial state information is accessible. This paper addresses this critical limitation by proposing an innovative hybrid machine learning framework that integrates a Modified Next-Generation Reservoir Computing (MNGRC) with XGBoost regression. The core novelty lies in its dual-path prediction architecture designed specifically for partial state observability scenarios. The primary path employs NGRC to capture and forecast the system's temporal dynamics using available state variables and input stimuli, while the secondary path leverages XGBoost as an efficient state estimator to infer unobserved state variables from minimal measurements. This strategic combination enables accurate prediction of diverse neuromorphic patterns with significantly reduced sensor requirements. Experimentally, the framework demonstrates its capability to identify and predict the complex spectrum of neuromorphic behaviors exhibited by the third-order memristive neuron. This includes accurately capturing all 18 distinct neuronal patterns, which are theoretically grounded in Hopf bifurcation analysis near the edge of chaos. Additionally, the framework successfully addresses the inverse problem of input stimulus reconstruction. By achieving accurate prediction of complex dynamics from limited states, our approach represents a key breakthrough, where full state access is often impossible, thereby addressing a critical challenge in edge AI and brain-inspired computing.