Jonathan Tammer Eweis-Labolle

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, Chuanning Zhao, Yoonjin Won et al.

As modern electronic devices are increasingly miniaturized and integrated, their performance relies more heavily on effective thermal management. Two-phase cooling methods enhanced by porous surfaces, which capitalize on thin-film evaporation atop structured porous surfaces, are emerging as potential solutions. In such porous structures, the optimum heat dissipation capacity relies on two competing objectives that depend on mass and heat transfer. The computational costs of evaluating these objectives, the high dimensionality of the design space which a voxelated microstructure representation, and the manufacturability constraints hinder the optimization process for thermal management. We address these challenges by developing a data-driven framework for designing optimal porous microstructures for cooling applications. In our framework we leverage spectral density functions (SDFs) to encode the design space via a handful of interpretable variables and, in turn, efficiently search it. We develop physics-based formulas to quantify the thermofluidic properties and feasibility of candidate designs via offline simulations. To decrease the reliance on expensive simulations, we generate multi-fidelity data and build emulators to find Pareto-optimal designs. We apply our approach to a canonical problem on evaporator wick design and obtain fin-like topologies in the optimal microstructures which are also characteristics often observed in industrial applications.

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.

Nicholas Oune, Jonathan Tammer Eweis-Labolle, Ramin Bostanabad

Multi-fidelity modeling and calibration are data fusion tasks that ubiquitously arise in engineering design. In this paper, we introduce a novel approach based on latent-map Gaussian processes (LMGPs) that enables efficient and accurate data fusion. In our approach, we convert data fusion into a latent space learning problem where the relations among different data sources are automatically learned. This conversion endows our approach with attractive advantages such as increased accuracy, reduced costs, flexibility to jointly fuse any number of data sources, and ability to visualize correlations between data sources. This visualization allows the user to detect model form errors or determine the optimum strategy for high-fidelity emulation by fitting LMGP only to the subset of the data sources that are well-correlated. We also develop a new kernel function that enables LMGPs to not only build a probabilistic multi-fidelity surrogate but also estimate calibration parameters with high accuracy and consistency. The implementation and use of our approach are considerably simpler and less prone to numerical issues compared to existing technologies. We demonstrate the benefits of LMGP-based data fusion by comparing its performance against competing methods on a wide range of examples.