MFNets: Data efficient all-at-once learning of multifidelity surrogates as directed networks of information sources
This addresses the challenge of data-efficient surrogate modeling for applications like computational mechanics, where information sources may not be strictly hierarchical, offering a more flexible and efficient alternative to state-of-the-art methods.
The paper tackles the problem of constructing multifidelity surrogates from ensembles of information sources with varying cost and accuracy, proposing a method that uses directed acyclic graphs for flexible, non-hierarchical connections, resulting in errors orders-of-magnitude smaller than existing approaches in low-data regimes.
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.