论文标题
通过主动子空间的固有维度低的标量函数的近似值近似的多效数据融合
Multi-fidelity data fusion for the approximation of scalar functions with low intrinsic dimensionality through active subspaces
论文作者
论文摘要
在贝叶斯环境中，使用高斯工艺用于非参数回归。它们概括了线性回归，将输入嵌入了无限二维繁殖内核希尔伯特空间内的潜在歧管中。我们可以通过对低保真模型的观察来增强输入，以学习更具表现力的潜在歧管，从而提高模型的准确性。这可以通过一系列高斯过程递归地实现，并具有更高的保真度。我们想将这些多保真模型实现扩展到受高维输入空间影响但内在维度低的案例研究。在这种情况下，当查询响应时，物理支持或纯粹的低阶模型仍会受维度的诅咒的影响。当提供模型的梯度信息时，可以利用主动空间的存在来设计低保真响应表面，从而实现高斯过程的多效率回归，而无需执行新的模拟。在数据稀缺的情况下，这特别有用。在这项工作中，我们提出了一种涉及活动子空间的多保真方法，并在两个不同的高维基准测试中对其进行了测试。
Gaussian processes are employed for non-parametric regression in a Bayesian setting. They generalize linear regression, embedding the inputs in a latent manifold inside an infinite-dimensional reproducing kernel Hilbert space. We can augment the inputs with the observations of low-fidelity models in order to learn a more expressive latent manifold and thus increment the model's accuracy. This can be realized recursively with a chain of Gaussian processes with incrementally higher fidelity. We would like to extend these multi-fidelity model realizations to case studies affected by a high-dimensional input space but with low intrinsic dimensionality. In this cases physical supported or purely numerical low-order models are still affected by the curse of dimensionality when queried for responses. When the model's gradient information is provided, the presence of an active subspace can be exploited to design low-fidelity response surfaces and thus enable Gaussian process multi-fidelity regression, without the need to perform new simulations. This is particularly useful in the case of data scarcity. In this work we present a multi-fidelity approach involving active subspaces and we test it on two different high-dimensional benchmarks.
