标题： 通过通用微分方程和可微物理寻找基础的粘弹性本构方程 显示英文标题

标题： Finding the Underlying Viscoelastic Constitutive Equation via Universal Differential Equations and Differentiable Physics

摘要： 本研究采用通用微分方程（UDEs）与可微物理相结合来建模粘弹性流体，融合常规微分方程、神经网络和数值方法以重构本构模型中缺失的项。 本研究专注于通过使用合成数据集分析四种粘弹性模型：上对流麦克斯韦（UCM）、约翰逊-塞加尔曼、吉泽库斯和指数phan-廷顿-坦纳（ePTT）模型。 该方法在不同的实验条件下进行了测试，包括振荡流和启动流。 虽然UDE框架对大多数模型有效地预测了剪切应力和法向应力，但在应用于ePTT模型时表现出一些局限性。 研究结果强调了UDEs在流体力学中的潜力，并确定了方法改进的关键领域。 此外，采用了模型蒸馏方法从复杂模型中提取简化模型，强调了UDEs在流变学建模中的多样性和鲁棒性。 显示英文摘要

摘要： This research employs Universal Differential Equations (UDEs) alongside differentiable physics to model viscoelastic fluids, merging conventional differential equations, neural networks and numerical methods to reconstruct missing terms in constitutive models. This study focuses on analyzing four viscoelastic models: Upper Convected Maxwell (UCM), Johnson-Segalman, Giesekus, and Exponential Phan-Thien-Tanner (ePTT), through the use of synthetic datasets. The methodology was tested across different experimental conditions, including oscillatory and startup flows. While the UDE framework effectively predicts shear and normal stresses for most models, it demonstrates some limitations when applied to the ePTT model. The findings underscore the potential of UDEs in fluid mechanics while identifying critical areas for methodological improvement. Also, a model distillation approach was employed to extract simplified models from complex ones, emphasizing the versatility and robustness of UDEs in rheological modeling.