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Iterative methods such as iterative closest point (ICP) for point cloud registration often suffer from bad local optimality (e.g. saddle points), due to the nature of nonconvex optimization. To address this fundamental challenge, in this…
Stochastic gradient descent (SGD) is widely used in deep learning due to its computational efficiency, but a complete understanding of why SGD performs so well remains a major challenge. It has been observed empirically that most…
Recovering high-resolution images from limited sensory data typically leads to a serious ill-posed inverse problem, demanding inversion algorithms that effectively capture the prior information. Learning a good inverse mapping from training…
Multiphase powder X-ray diffraction (PXRD) analysis remains a fundamental bottleneck in structure identification, as real-world synthesis often produces complex mixtures whose constituent phases (components) cannot be reliably disentangled.…
A solution to the inversion problem of scattering would offer aberration-free diffraction-limited 3D images without the resolution and depth-of-field limitations of lens-based tomographic systems. Powerful algorithms are increasingly being…
High-throughput powder X-ray diffraction (XRD) simulations are a key prerequisite for generating large datasets used in the development of machine-learning models for XRD-based materials analysis. However, the widely used pymatgen powder…
Matrix sensing problems exhibit pervasive non-convexity, plaguing optimization with a proliferation of suboptimal spurious solutions. Avoiding convergence to these critical points poses a major challenge. This work provides new theoretical…
Editing High Dynamic Range (HDR) environment maps using an inverse differentiable rendering architecture is a complex inverse problem due to the sparsity of relevant pixels and the challenges in balancing light sources and background. The…
Machine learning (ML) facilitates rapid channel modeling for 5G and beyond wireless communication systems. Many existing ML techniques utilize a city map to construct the radio map; however, an updated city map may not always be available.…
As the problem of minimizing functionals on the Wasserstein space encompasses many applications in machine learning, different optimization algorithms on $\mathbb{R}^d$ have received their counterpart analog on the Wasserstein space. We…
We applied the analysis of x-ray intensity angular correlation function to dilute ensembles of identical spinel crystals. Firstly, we show that the angular correlation from measured diffraction patterns with many crystals per shot converges…
Recent 3D Gaussian Splatting (3DGS) representations have demonstrated remarkable performance in novel view synthesis; further, material-lighting disentanglement on 3DGS warrants relighting capabilities and its adaptability to broader…
This paper explores optimal methods for obtaining one-dimensional (1D) powder pattern intensities from two-dimensional (2D) planar detectors with good estimates of their standard deviations. We describe methods to estimate uncertainties…
This paper studies the problem of recovering a low-rank matrix from several noisy random linear measurements. We consider the setting where the rank of the ground-truth matrix is unknown a priori and use an objective function built from a…
Recent work has demonstrated the effectiveness of gradient descent for directly recovering the factors of low-rank matrices from random linear measurements in a globally convergent manner when initialized properly. However, the performance…
Efficiently and accurately determining the symmetry is a crucial step in the structural analysis of crystalline materials. Existing methods usually mindlessly apply deep learning models while ignoring the underlying chemical rules. More…
Many core problems in robotics can be framed as constrained optimization problems. Often on these problems, the robotic system has uncertainty, or it would be advantageous to identify multiple high quality feasible solutions. To enable…
The data consistency for the physical forward model is crucial in inverse problems, especially in MR imaging reconstruction. The standard way is to unroll an iterative algorithm into a neural network with a forward model embedded. The…
Coherent X-ray scattering techniques are critical for investigating the fundamental structural properties of materials at the nanoscale. While advancements have made these experiments more accessible, real-time analysis remains a…
Recent innovations in x-ray technology (namely phase-based and energy-resolved imaging) offer unprecedented opportunities for material discrimination, however they are often used in isolation or in limited combinations. Here we show that…