  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.
