Additional data from Multi-fidelity non-intrusive reduced-order modelling based on manifold alignment

This work presents the development of a multi-fidelity, parametric and non-intrusive reduced-order modelling method to tackle the problem of achieving an acceptable predictive accuracy under a limited computational budget, i.e. with expensive simulations and sparse training data. Traditional multi-fidelity surrogate models that predict scalar quantities address this issue by leveraging auxiliary data generated by a computationally cheaper lower fidelity code. However, for the prediction of field quantities, simulations of different fidelities may produce responses with inconsistent representations, rendering the direct application of common multi-fidelity techniques challenging. The proposed approach uses manifold alignment to fuse inconsistent fields from high- and low-fidelity simulations by individually projecting their solution onto a common latent space. Hence, simulations using incompatible grids or geometries can be combined into a single multi-fidelity reduced-order model without additional manipulation of the data. This method is applied to a variety of multi-fidelity scenarios using a transonic airfoil problem. In most cases, the new multi-fidelity reduced-order model achieves comparable predictive accuracy at a lower computational cost. Furthermore, it is demonstrated that the proposed method can combine disparate fields without any adverse effect on predictive performance.

本研究提出了一种多保真度、参数化且非侵入式的降阶建模方法，旨在解决有限计算预算下（即仿真计算成本高昂且训练数据稀疏）难以获得可接受预测精度的问题。传统多保真度代理模型多针对标量预测任务，通过利用计算成本更低的低保真度代码生成的辅助数据来解决上述问题。然而，针对场量预测任务时，不同保真度的仿真所生成的响应可能存在表征不一致的问题，这使得常见多保真度技术难以直接应用。本研究提出的方法采用流形对齐（manifold alignment）技术，通过将高低保真度仿真的解分别投影至公共隐空间，以融合二者表征不一致的场量。因此，无需对数据进行额外预处理，即可将采用不兼容网格或几何结构的仿真整合至同一多保真度降阶模型中。本方法通过跨音速翼型（transonic airfoil）测试问题，被应用于多种多保真度场景中。在多数场景下，该新型多保真度降阶模型均可在更低计算成本下达到相当的预测精度。此外，实验验证表明，所提方法能够融合异质场量，且不会对预测性能造成任何负面影响。