MFNets: data efficient all-at-once learning of multifidelity surrogates as directed networks of information sources

• Published in: Computational mechanics 2021-10, Vol.68 (4), p.741-758
• Main Authors: Gorodetsky, A. A., Jakeman, J. D., Geraci, G.
• Format: Article
• Language: English
• Subjects: Classical and Continuum Physics; co-kriging; Computational Science and Engineering; Engineering; Information sources; machine learning; MATHEMATICS AND COMPUTING; multi-fidelity modeling; networks; Original Paper; regression; surrogate models; Theoretical and Applied Mechanics
• ISSN: 0178-7675; 1432-0924
• DOI: 10.1007/s00466-021-02042-0

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.