Image-based simulation, the use of 3D images to calculate physical quantities, relies on image segmentation for geometry creation. However, this process introduces image segmentation uncertainty because different segmentation tools (both manual and machine-learning-based) will each produce a unique and valid segmentation. First, we demonstrate that these variations propagate into the physics simulations, compromising the resulting physics quantities. Second, we propose a general framework for rapidly quantifying segmentation uncertainty. Through the creation and sampling of segmentation uncertainty probability maps, we systematically and objectively create uncertainty distributions of the physics quantities. We show that physics quantity uncertainty distributions can follow a Normal distribution, but, in more complicated physics simulations, the resulting uncertainty distribution can be surprisingly nontrivial. We establish that bounding segmentation uncertainty can fail in these nontrivial situations. While our work does not eliminate segmentation uncertainty, it improves simulation credibility by making visible the previously unrecognized segmentation uncertainty plaguing image-based simulation.
Deep learning segmentation models are known to be sensitive to the scale, contrast, and distribution of pixel values when applied to Computed Tomography (CT) images. For material samples, scans are often obtained from a variety of scanning equipment and resolutions resulting in domain shift. The ability of segmentation models to generalize to examples from these shifted domains relies on how well the distribution of the training data represents the overall distribution of the target data. We present a method to overcome the challenges presented by domain shifts. Our results indicate that we can leverage a deep learning model trained on one domain to accurately segment similar materials at different resolutions by refining binary predictions using uncertainty quantification (UQ). We apply this technique to a set of unlabeled CT scans of woven composite materials with clear qualitative improvement of binary segmentations over the original deep learning predictions. In contrast to prior work, our technique enables refined segmentations without the expense of the additional training time and parameters associated with deep learning models used to address domain shift.
Fuel cells, batteries, and thermochemical and other energy conversion devices involve the transport of a number of (electro-) chemical species through distinct materials so that they can meet and react at specified multi-material interfaces. Therefore, morphology or arrangement of these different materials can be critical in the performance of an energy conversion device. In this paper, we study a model problem motivated by a solar-driven thermochemical conversion device that splits water into hydrogen and oxygen. We formulate the problem as a system of coupled multi-material reaction-diffusion equations where each species diffuses selectively through a given material and where the reaction occurs at multi-material interfaces. We introduce a phase-field formulation of the optimal design problem and numerically study selected examples.