Probabilistic Neural Data Fusion for Learning from an Arbitrary Number of Multi-fidelity Data Sets

TL;DR

This paper introduces a neural network-based probabilistic data fusion method for multi-fidelity data sources, effectively modeling biases and uncertainties to improve predictions with scarce data.

Contribution

The paper presents a novel neural network architecture that transforms multi-fidelity modeling into a nonlinear manifold learning problem with interpretable bias encoding.

Findings

High predictive accuracy demonstrated on multiple examples.

Effective quantification of model and aleatoric uncertainties.

Robustness and improved accuracy on unseen high-fidelity data.

Abstract

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