  A primary challenge of physics-informed machine learning (PIML) is its
generalization beyond the training domain, especially when dealing with complex
physical problems represented by partial differential equations (PDEs). This
paper aims to enhance the generalization capabilities of PIML, facilitating
practical, real-world applications where accurate predictions in unexplored
regions are crucial. We leverage the inherent causality and temporal sequential
characteristics of PDE solutions to fuse PIML models with recurrent neural
architectures based on systems of ordinary differential equations, referred to
as neural oscillators. Through effectively capturing long-time dependencies and
mitigating the exploding and vanishing gradient problem, neural oscillators
foster improved generalization in PIML tasks. Extensive experimentation
involving time-dependent nonlinear PDEs and biharmonic beam equations
demonstrates the efficacy of the proposed approach. Incorporating neural
oscillators outperforms existing state-of-the-art methods on benchmark problems
across various metrics. Consequently, the proposed method improves the
generalization capabilities of PIML, providing accurate solutions for
extrapolation and prediction beyond the training data.
