锤炼熵：一种利用 PINN 学习聚合物流变本构方程的 GENERIC 引导方法
Hammering at the entropy: A GENERIC-guided approach to learning polymeric rheological constitutive equations using PINNs
AI总结：
本文提出 GENERIC 引导的 PINN 框架以学习聚合物溶液额外应力本构方程中的熵贡献，并证明基于复杂绕流数据训练的模型在复杂场景中更优且可跨几何拓扑迁移。
摘要：
我们提出了一个多功能框架，该框架采用物理信息神经网络（PINNs）来发现熵贡献，这种熵贡献会导出聚合物溶液流变模型中额外应力的本构方程。在该框架中，神经网络的训练由构象张量的演化方程引导，而该演化方程符合 GENERIC。我们比较了数据驱动 PINN 本构模型的两种训练方法：一种基于稳态测粘流动下 Oldroyd-B 模型解析解的数据进行训练（PINN-rheometric），另一种基于使用 Oldroyd-B 模型的圆柱绕流复杂流动 CFD 模拟所生成的电子计算机模拟数据进行训练（PINN-complex）。通过与以底层 Oldroyd-B 模型为参考的 CFD 模拟进行比较，评估 PINN 模型提供良好预测的能力。两种模型都能够预测瞬态和复杂条件下的流动行为；然而，在更广泛的混合流动数据范围上训练的 PINN-complex 模型在复杂流动场景中优于 PINN-rheometric 模型。我们方法的几何无关特性使我们能够将学习到的 PINN 模型应用于与训练所用拓扑不同的流动。
英文摘要：
We present a versatile framework that employs Physics-Informed Neural Networks (PINNs) to discover the entropic contribution that leads to the constitutive equation for the extra-stress in rheological models of polymer solutions. In this framework the training of the Neural Network is guided by an evolution equation for the conformation tensor which is GENERIC-compliant. We compare two training methodologies for the data-driven PINN constitutive models: one trained on data from the analytical solution of the Oldroyd-B model under steady-state rheometric flows (PINN-rheometric), and another trained on in-silico data generated from complex flow CFD simulations around a cylinder that use the Oldroyd-B model (PINN-complex). The capacity of the PINN models to provide good predictions are evaluated by comparison with CFD simulations using the underlying Oldroyd-B model as a reference. Both models are capable of predicting flow behavior in transient and complex conditions; however, the PINN-complex model, trained on a broader range of mixed flow data, outperforms the PINN-rheometric model in complex flow scenarios. The geometry agnostic character of our methodology allows us to apply the learned PINN models to flows with different topologies than the ones used for training.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
