标题： 基于非线性投影的机器学习回归在潜在空间中闭合误差建模的降阶模型方法 显示英文标题

标题： Nonlinear projection-based model order reduction with machine learning regression for closure error modeling in the latent space

摘要： 在非线性投影基础上的模型降阶（PMOR）取得了重大进展，这是通过一种高效的方法实现的。该方法在潜在空间中使用高斯过程回归（GPR）和径向基函数（RBF）插值进行闭合误差建模，显著提高了效率，并扩展了PMOR的应用范围。超越了之前用于此任务的深度人工神经网络（ANNs）的局限性，这种方法在可解释性和对大量训练数据的需求方面提供了关键优势。GPR和RBF的能力在两个具有挑战性的应用中得到展示：一个二维参数化无粘性Burgers问题，特征是整个计算域中的传播冲击波，以及一个复杂三维湍流流场模拟，围绕Ahmed车身。结果表明，与传统PMOR和基于ANN的闭合建模相比，这种创新方法在保持准确性的同时，在效率和可解释性方面实现了显著改进。 显示英文摘要

摘要： A significant advancement in nonlinear projection-based model order reduction (PMOR) is presented through a highly effective methodology. This methodology employs Gaussian process regression (GPR) and radial basis function (RBF) interpolation for closure error modeling in the latent space, offering notable gains in efficiency and expanding the scope of PMOR. Moving beyond the limitations of deep artificial neural networks (ANNs), previously used for this task, this approach provides crucial advantages in terms of interpretability and a reduced demand for extensive training data. The capabilities of GPR and RBFs are showcased in two demanding applications: a two-dimensional parametric inviscid Burgers problem, featuring propagating shocks across the entire computational domain, and a complex three-dimensional turbulent flow simulation around an Ahmed body. The results demonstrate that this innovative approach preserves accuracy and achieves substantial improvements in efficiency and interpretability when contrasted with traditional PMOR and ANN-based closure modeling.