pETNNs: Partial Evolutionary Tensor Neural Networks for Solving Time-dependent Partial Differential Equations

Understand

We present the partial evolutionary tensor neural networks (pETNNs), a novel framework 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 posterior error bounded is proposed to support the extrapolation capabilities.
• In the numerical implementations, we adopt a partial update strategy to achieve a significant reduction in computational cost while maintaining precision and robustness.