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Physics-informed neural networks (PINNs) provide a promising mesh-free paradigm for solving partial differential equations (PDEs). However, when applied to high-frequency vibration and long-time evolution problems, they often suffer from spectral bias, insufficient boundary fitting, and training imbalance among multiple loss terms. Building upon the physics-informed radial basis network (PIRBN) framework, this paper introduces a boundary-extended center initialization strategy that places auxiliary basis function centers outside the spatial boundaries to enhance local support near the domain boundaries, together with a gradient-magnitude-based adaptive weighting mechanism to mitigate training imbalance across different loss terms. For time-dependent problems such as two-dimensional membrane vibration, a curriculum learning strategy is further incorporated, whereby the full time interval is partitioned into progressively longer sub-intervals to alleviate error accumulation in long-time evolution. Three benchmark examples, a one-dimensional linear elastic rod under high-order vibration, a two-dimensional high-frequency Poisson equation, and a two-dimensional membrane vibration equation in (x, y, t) spatiotemporal input form, are employed to validate the method in terms of high-frequency representation, boundary fitting, and time-dependent dynamics prediction, respectively. Numerical results demonstrate that the improved PIRBN can accurately capture high-frequency oscillatory structures and maintain stable spatiotemporal prediction capability for the membrane vibration problem, offering a viable improvement for applying PIRBN to high-frequency vibration and coupled spatiotemporal PDEs in solid mechanics.

Physics-informed radial basis network; curriculum learning; boundary-extended centers; spatiotemporal partial differential equations; high-frequency problems