MFNets：作为信息源有向网络的多保真度代理的数据高效一次性学习
MFNets: Data efficient all-at-once learning of multifidelity surrogates as directed networks of information sources
摘要：
我们提出了一种方法来构建一个代理从不同的成本和精度的信息源的合奏。多保真度代理编码信息源之间的连接作为一个有向无环图，并通过基于梯度的非线性最小二乘目标的最小化训练。虽然绝大多数最先进的假设之间的层次结构的连接信息源，我们的方法与灵活的结构信息源，可能不承认一个严格的层次结构。该公式有两个优点：（1）由于可以根据应用定制的简约多保真度网络，提高了数据效率;（2）对训练数据没有约束-我们可以组合信息源的噪声，非嵌套评估。从合成到基于物理的计算力学模拟的数值示例表明，我们的方法中的误差可以比单保真度和分层多保真度方法小几个数量级，特别是在低数据状态下。
英文摘要：
We present an approach for constructing a surrogate from ensembles of information sources of varying cost and accuracy. The multifidelity surrogate encodes connections between information sources as a directed acyclic graph, and is trained via gradient-based minimization of a nonlinear least squares objective. While the vast majority of state-of-the-art assumes hierarchical connections between information sources, our approach works with flexibly structured information sources that may not admit a strict hierarchy. The formulation has two advantages: (1) increased data efficiency due to parsimonious multifidelity networks that can be tailored to the application; and (2) no constraints on the training data -- we can combine noisy, non-nested evaluations of the information sources. Numerical examples ranging from synthetic to physics-based computational mechanics simulations indicate the error in our approach can be orders-of-magnitude smaller, particularly in the low-data regime, than single-fidelity and hierarchical multifidelity approaches.
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