新模型直接遵循输运方程，精准模拟高雷诺数流体演化。
Transport-Embedded Neural Architecture: Redefining the Landscape of physics aware neural models in fluid mechanics
- 模型设计上嵌入输运方程，确保物理一致性。
- 在泰勒-格林涡问题中，准确捕捉高雷诺数下的时间演化。
- 可避免虚假极小值，适合复杂多物理场问题。
本文提出一种新型神经网络模型，其设计遵循输运方程。以双周期域上的泰勒-格林涡为基准测试问题，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，仅返回整个时间跨度的初始条件；而本模型成功捕捉了物理量随时间的变化，尤其在高雷诺数流动下表现优异。此外，该模型避免虚假极小值的能力，为解决更易出现此类问题的多物理场问题提供了可能，有助于准确预测复杂物理行为。
原文摘要 · Abstract (English)
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.
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