Tyler Johnson

Carlos Mora, Jonathan Tammer Eweis-Labolle, Tyler Johnson et al.

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.

Jonathan Tammer Eweis-Labolle, Tyler Johnson, Xiangyu Sun et al.

In an increasing number of applications designers have access to multiple computer models which typically have different levels of fidelity and cost. Traditionally, designers calibrate these models one at a time against some high-fidelity data (e.g., experiments). In this paper, we question this tradition and assess the potential of calibrating multiple computer models at the same time. To this end, we develop a probabilistic framework that is founded on customized neural networks (NNs) that are designed to calibrate an arbitrary number of computer models. In our approach, we (1) consider the fact that most computer models are multi-response and that the number and nature of calibration parameters may change across the models, and (2) learn a unique probability distribution for each calibration parameter of each computer model, (3) develop a loss function that enables our NN to emulate all data sources while calibrating the computer models, and (4) aim to learn a visualizable latent space where model-form errors can be identified. We test the performance of our approach on analytic and engineering problems to understand the potential advantages and pitfalls in simultaneous calibration of multiple computer models. Our method can improve predictive accuracy, however, it is prone to non-identifiability issues in higher-dimensional input spaces that are normally constrained by underlying physics.