Solving time-dependent partial differential equations (PDEs) is an important problem in computational science and engineering. Physics-informed neural networks (PINNs) learn PDE solutions from governing equations. However, accurately capturing temporal evolution remains challenging. Recent sequence-model-based approaches parameterize time evolution using general-purpose sequence models, which capture temporal dependencies but do not explicitly encode the structured dynamics of PDE solutions. In addition, their memory requirements can scale unfavorably with sequence length and resolution, limiting applicability in large-scale or high-dimensional settings. This work introduces a PINN approach that incorporates oscillatory state-space dynamics to represent the modal structure of PDE solutions. The proposed method leverages a linear-oscillator-based temporal evolution, together with a PDE-aware spectral basis in space. This design enables closed-form spatial differentiation and consistent enforcement of boundary conditions. The method is evaluated on forward, inverse, and high-dimensional PDE problems, including cases up to 100 spatial dimensions. The results show improved accuracy and reduced memory usage compared to recent sequence-model-based PINN approaches. Overall, this work highlights the benefits of incorporating structured dynamical priors into the temporal evolution of neural PDE solvers and suggests designing more physics-aligned and computationally efficient PINN architectures.

翻译：求解含时偏微分方程是计算科学与工程中的重要问题。物理信息神经网络通过控制方程学习偏微分方程的解，但准确捕捉时间演化仍具挑战性。现有基于序列模型的方法虽能利用通用序列模型参数化时间演化过程，却未显式编码偏微分方程解的结构化动力学特性，且其内存需求随序列长度与分辨率呈不利扩展，限制了大尺度或高维场景下的适用性。本文提出一种融入振荡状态空间动力学的物理信息神经网络方法，用以表征偏微分方程解的模态结构。该方法采用基于线性振荡器的时间演化机制，结合偏微分方程感知的空间谱基，实现解析形式的空间微分与一致边界条件约束。在前向、反演及高维偏微分方程问题（含100维空间维度算例）的评估中，该方法相较于近期基于序列模型的物理信息神经网络方法展现出更高的精度与更低的内存占用。本研究揭示了将结构化动力学先验融入神经偏微分方程求解器时间演化的优势，为设计更契合物理机制且计算高效的物理信息神经网络架构提供了思路。