Probabilistic neural data fusion for learning from an arbitrary number of multi-fidelity data sets

In many applications in engineering and sciences analysts have simultaneous access to multiple data sources. such cases, the overall cost of acquiring information can be reduced via fusion or multi-fidelity (MF) modeling where one leverages inexpensive low-fidelity (LF) sources reduce reliance on expensive high-fidelity (HF) data. this paper, we employ neural networks (NNs) for scenarios is very scarce obtained from an arbitrary number with varying levels fidelity cost. We introduce a unique NN architecture that converts MF into nonlinear manifold learning problem. Our inversely learns non-trivial (e.g., non-additive non-hierarchical) biases LF interpretable visualizable each source encoded low-dimensional distribution. This probabilistic quantifies model form uncertainties small bias are close HF source. Additionally, endow output our parametric distribution not only quantify aleatoric uncertainties, but also reformulate network’s loss function based strictly proper scoring rules which improve robustness accuracy unseen Through set analytic examples, demonstrate approach provides high predictive power while quantifying various uncertainty. codes examples accessed GitLab.