@Article{CSIAM-AM-6-862,
author = {Kao , TunanZhang , HeZhang , Lei and Zhao , Jin},
title = {pETNNs: Partial Evolutionary Tensor Neural Networks for Solving Time-Dependent Partial Differential Equations},
journal = {CSIAM Transactions on Applied Mathematics},
year = {2025},
volume = {6},
number = {4},
pages = {862--891},
abstract = {<p style="text-align: justify;">We present partial evolutionary tensor neural networks (pETNNs), a novel approach for solving time-dependent partial differential equations with high accuracy and capable of handling high-dimensional problems. Our architecture incorporates tensor neural networks and evolutionary parametric approximation. A posteriori error bound is proposed to support the extrapolation capabilities. In numerical
implementations, we adopt a partial update strategy to achieve a significant reduction in computational cost while maintaining precision and robustness. Notably, as
a low-rank approximation method of complex dynamical systems, pETNNs enhance
the accuracy of evolutionary deep neural networks and empower computational abilities to address high-dimensional problems. Numerical experiments demonstrate the
superior performance of the pETNNs in solving complex time-dependent equations,
including the incompressible Navier-Stokes equations, high-dimensional heat equations, high-dimensional transport equations, and dispersive equations of higher-order
derivatives.</p>},
issn = {2708-0579},
doi = {https://doi.org/10.4208/csiam-am.SO-2024-0048},
url = {http://global-sci.org/intro/article_detail/csiam-am/24505.html}
}