We present partial evolutionary tensor neural networks (pETNNs), a novel framework for solving time-dependent partial differential equations with both of high accuracy and remarkable extrapolation. Our proposed architecture leverages the inherent accuracy of tensor neural networks, while incorporating evolutionary parameters that enable remarkable extrapolation capabilities. By adopting innovative parameter update strategies, the pETNNs achieve a significant reduction in computational cost while maintaining precision and robustness. Notably, the pETNNs enhance the accuracy of conventional evolutional deep neural networks and empowers computational abilities to address high-dimensional problems. Numerical experiments demonstrate the superior performance of the pETNNs in solving time-dependent complex equations, including the Navier-Stokes equations, high-dimensional heat equation, high-dimensional transport equation and Korteweg-de Vries type equation.

翻译：我们提出了偏进化张量神经网络（pETNNs），这是一种兼具高精度与出色外推能力的新型框架，用于求解时间依赖型偏微分方程。所提出的架构充分利用了张量神经网络的固有精度，同时引入具有显著外推能力的进化参数。通过采用创新的参数更新策略，pETNNs在保持精度和鲁棒性的同时显著降低了计算成本。值得注意的是，pETNNs提升了传统进化深度神经网络的精度，并增强了处理高维问题的计算能力。数值实验表明，pETNNs在求解时间依赖型复杂方程（包括Navier-Stokes方程、高维热方程、高维输运方程及Korteweg-de Vries型方程）方面展现了优越性能。