Weak gravitational lensing is the slight distortion of galaxy shapes caused primarily by the gravitational effects of dark matter in the universe. In our work, we seek to invert the weak lensing signal from 2D telescope images to reconstruct a 3D map of the universe's dark matter field. While inversion typically yields a 2D projection of the dark matter field, accurate 3D maps of the dark matter distribution are essential for localizing structures of interest and testing theories of our universe. However, 3D inversion poses significant challenges. First, unlike standard 3D reconstruction that relies on multiple viewpoints, in this case, images are only observed from a single viewpoint. This challenge can be partially addressed by observing how galaxy emitters throughout the volume are lensed. However, this leads to the second challenge: the shapes and exact locations of unlensed galaxies are unknown, and can only be estimated with a very large degree of uncertainty. This introduces an overwhelming amount of noise which nearly drowns out the lensing signal completely. Previous approaches tackle this by imposing strong assumptions about the structures in the volume. We instead propose a methodology using a gravitationally-constrained neural field to flexibly model the continuous matter distribution. We take an analysis-by-synthesis approach, optimizing the weights of the neural network through a fully differentiable physical forward model to reproduce the lensing signal present in image measurements. We showcase our method on simulations, including realistic simulated measurements of dark matter distributions that mimic data from upcoming telescope surveys. Our results show that our method can not only outperform previous methods, but importantly is also able to recover potentially surprising dark matter structures.

Refractive Index Tomography is the inverse problem of reconstructing the continuously-varying 3D refractive in-dex in a scene using 2D projected image measurements. Although a purely refractive field is not directly visible, it bends light rays as they travel through space, thus providing a signal for reconstruction. The effects of such fields appear in many scientific computer vision settings, ranging from refraction due to transparent cells in microscopy to the lensing of distant galaxies caused by dark matter in astro-physics. Reconstructing these fields is particularly difficult due to the complex nonlinear effects of the refractive field on observed images. Furthermore, while standard 3D reconstruction and tomography settings typically have access to observations of the scene from many viewpoints, many refractive index tomography problem settings only have access to images observed from a single viewpoint. We in-troduce a method that leverages prior knowledge of light sources scattered throughout the refractive medium to help disambiguate the single-view refractive index tomography problem. We differentiably trace curved rays through a neural field representation of the refractive field, and optimize its parameters to best reproduce the observed image. We demonstrate the efficacy of our approach by reconstructing simulated refractive fields, analyze the effects of light source distribution on the recovered field, and test our method on a simulated dark matter mapping problem where we successfully recover the 3D refractive field caused by a realistic dark matter distribution.

We present ProtoConcepts, a method for interpretable image classification combining deep learning and case-based reasoning using prototypical parts. Existing work in prototype-based image classification uses a "this looks like that'' reasoning process, which dissects a test image by finding prototypical parts and combining evidence from these prototypes to make a final classification. However, all of the existing prototypical part-based image classifiers provide only one-to-one comparisons, where a single training image patch serves as a prototype to compare with a part of our test image. With these single-image comparisons, it can often be difficult to identify the underlying concept being compared (e.g., "is it comparing the color or the shape?''). Our proposed method modifies the architecture of prototype-based networks to instead learn prototypical concepts which are visualized using multiple image patches. Having multiple visualizations of the same prototype allows us to more easily identify the concept captured by that prototype (e.g., "the test image and the related training patches are all the same shade of blue''), and allows our model to create richer, more interpretable visual explanations. Our experiments show that our ``this looks like those'' reasoning process can be applied as a modification to a wide range of existing prototypical image classification networks while achieving comparable accuracy on benchmark datasets.

The NASA Planetary Data System hosts millions of images acquired from the planet Mars. To help users quickly find images of interest, we have developed and deployed content-based classification and search capabilities for Mars orbital and surface images. The deployed systems are publicly accessible using the PDS Image Atlas. We describe the process of training, evaluating, calibrating, and deploying updates to two CNN classifiers for images collected by Mars missions. We also report on three years of deployment including usage statistics, lessons learned, and plans for the future.