This work introduces a new neural model which follows the transport equation by design. A physical problem, the Taylor-Green vortex, defined on a bi-periodic domain, is used as a benchmark to evaluate the performance of both the standard physics-informed neural network and our model (transport-embedded neural network). Results exhibit that while the standard physics-informed neural network fails to predict the solution accurately and merely returns the initial condition for the entire time span, our model successfully captures the temporal changes in the physics, particularly for high Reynolds numbers of the flow. Additionally, the ability of our model to prevent false minima can pave the way for addressing multiphysics problems, which are more prone to false minima, and help them accurately predict complex physics.

翻译：本研究提出了一种新型神经模型，其设计遵循输运方程。我们以双周期域上定义的泰勒-格林涡旋这一物理问题为基准，分别评估标准物理信息神经网络与本模型（输运嵌入神经网络）的性能。结果表明：标准物理信息神经网络无法准确预测解，仅在整个时间跨度内返回初始条件；而本模型成功捕捉了物理场的时序变化，尤其在高雷诺数流动条件下表现突出。此外，本模型规避伪极小值的能力为处理更易出现伪极小值的多物理场问题开辟了新途径，有助于精确预测复杂物理现象。