<p>The complexity arising from the interplay of multiple factors makes it exceptionally difficult to characterize the dynamic behavior of nonlinear systems through parametric modeling approaches. To address this challenge, this study introduces a nonparametric dynamical modeling framework that replaces conventional parametric models for describing the dynamics of non-autonomous nonlinear systems. The approach builds on a key property of autonomous dynamics: the phase-space flow is uniquely determined by the current state. To restore this “state-dependent uniqueness’’ in non-autonomous settings, the excitation amplitude is treated as an additional coordinate to construct an augmented phase space in which the vector field remains single-valued and identifiable. This leads to a complete state-space learning framework independent of any prescribed parametric coupling. Time histories collected under multiple operating conditions are used to train a neural network(NN) that reconstructs the underlying dynamical model. Coupling this learned model with an ordinary differential equation solver enables prediction of time-domain responses over a wide range of excitation levels, as well as computation of amplitude–frequency characteristics, bifurcation diagrams, and response distributions. Numerical experiments show that the proposed method can reconstruct accurate models directly from measured data, correctly recover static equilibria, and faithfully capture hysteresis, jump phenomena, chaotic motions, and critical bifurcation points near primary resonance. The model automatically identifies how external excitation enters and couples with the intrinsic dynamics, thereby recovering the underlying parametric coupling structure. The framework further enables accurate prediction of forced-vibration responses even when trained solely on free or parametrically excited data, and it faithfully captures multivalued response regions.</p>