Transition Dynamics for a bistable membrane-type acoustic metamaterial system

Transition phenomena between bistable states induced by noise fluctuations have emerged as a critical topic in ensuring the reliability of complex systems. These transitions cause abrupt jumps between states, often compromising the structural stability of metamaterials. This paper investigates the transition dynamics in an acoustic metamaterial model. The Onsager-Machlup action functional theory provides a potential way to capture the most probable transition path within a small tube, governed by the Euler-Lagrange equation. Solving this boundary-value problem efficiently presents a significant challenge. To address this, we employ the physics-informed neural networks(PINNs) method enhanced with a combined optimizer. Our results demonstrate that the AdamW+LBFGS optimization approach consistently achieves the higher accuracy and the faster convergence. Additionally, we analyze the effects of transition time and noise fluctuations on the transition path. The findings reveal that noise fluctuations can trigger transitions, altering the transition path through various manifold orientations. The minimum probable transition time is also derived numerically.