Multiscale memory and nonlinear dynamics in beam-granular systems

Embedding deformable structures within granular media induces rich nonlinear dynamics characterized by strong memory effects, path dependence, and emergent collective behavior—central themes in complex systems and nonequilibrium science. These phenomena arise from nonlinear interactions spanning micro to macro scales and remain difficult to interpret and predict. Here, we present an integrated framework combining experiments, discrete element simulations, machine learning, and fractional-order modeling to unravel the mechanisms governing these phenomena in beam-driven granular systems. Power spectral density analysis reveals distinct frequency-dependent signatures linked to frictional dissipation and structural anisotropy. Crucially, interpretable neural networks enable us to disentangle the relative contributions of short-time (frictional) and long-time (structural) memory. A fractional-order model is further constructed using a memory kernel that evolves with excitation frequency, successfully reproducing amplitude jumps, hysteresis, and multistable regimes. This approach bridges granular-scale physics with macroscopic system response and demonstrates a path toward data-driven, interpretable modeling of complex nonlinear systems, but also significantly enhances predictive capabilities, providing novel strategies for intelligent granular materials, and robotic control in complex granular environments.