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

TL;DR

This paper introduces MFNets, a flexible, data-efficient method for constructing multifidelity surrogates using directed networks of information sources, capable of handling non-hierarchical and noisy data.

Contribution

The paper presents a novel approach for building multifidelity surrogates with flexible source connections, improving data efficiency and accommodating non-hierarchical, noisy evaluations.

Findings

Error reduction by orders of magnitude in low-data regimes

Outperforms single-fidelity and hierarchical methods

Applicable to synthetic and physics-based simulations

Abstract

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.