Hemant Sharma

Ahsan Ali, Hemant Sharma, Rajkumar Kettimuthu et al.

Extracting actionable information rapidly from data produced by instruments such as the Linac Coherent Light Source (LCLS-II) and Advanced Photon Source Upgrade (APS-U) is becoming ever more challenging due to high (up to TB/s) data rates. Conventional physics-based information retrieval methods are hard-pressed to detect interesting events fast enough to enable timely focusing on a rare event or correction of an error. Machine learning~(ML) methods that learn cheap surrogate classifiers present a promising alternative, but can fail catastrophically when changes in instrument or sample result in degradation in ML performance. To overcome such difficulties, we present a new data storage and ML model training architecture designed to organize large volumes of data and models so that when model degradation is detected, prior models and/or data can be queried rapidly and a more suitable model retrieved and fine-tuned for new conditions. We show that our approach can achieve up to 100x data labelling speedup compared to the current state-of-the-art, 200x improvement in training speed, and 92x speedup in-terms of end-to-end model updating time.

Hemant Sharma

In this paper, Cimmino's classical reflection algorithm for solving the $n\times n$ nonsingular linear system $A\bx=\bb$ is analysed through the lens of spectral theory. Reformulating the weighted iteration as $\e^{(ν+1)}=M_w\,\e^{(ν)}$, where $M_w = I - A^\top D_w A$, the error is shown to contract by the spectral radius $\sprad(M_w)$ at every step, with a sharp, asymptotically tight bound. For $n=2$, a closed-form expression for the contraction factor is derived, \[ \sprad(M_w) \;=\; |1-μ| + \tfrac{1}{2}\sqrt{(w_1-w_2)^2 + 4w_1w_2\cos^2\!θ}, \] where $μ=(w_1+w_2)/2$ and $θ$ denotes the angle between the hyperplane normals. A central result of this paper is that the standard unit weights $w_1^*=w_2^*=1$ are \emph{globally optimal} over all positive weight pairs, uniquely achieving the minimum contraction factor $\sprad^*=|\cosθ|$ -- a quantity determined solely by the geometry of the hyperplane normals. The inter-normal angle $θ$ thus emerges as the single diagnostic parameter governing both convergence speed and weight selection. Extensions to a single-step convergence criterion at $θ=π/2$ and to an exact spectral rate for general~$n$ are also established.

Hemant Sharma, Nachiketa Mishra

This article introduces a trace-based metric on the space of positive semi-definite (PSD) tensors, offering a geometric perspective that connects their algebraic structure to their intrinsic geometric properties. It defines the Bures-Wasserstein distance on tensor spaces, establishing clear measurements between tensors. Moreover, the study derives trace-based eigenvalue bounds for PSD tensors and analyzes how these bounds depend on the PSD condition. The behavior of these bounds is further explored when the PSD requirement is relaxed, with illustrative examples provided to support the theoretical findings. In addition, a detailed complexity analysis is carried out for the methods proposed in this study.

Snigdhashree Nayak, Hemant Sharma, Nachiketa Mishra

This article introduces an algebraic framework for establishing eigenvalue bounds for symmetric positive definite tensors by leveraging intrinsic invariants, specifically the trace and determinant (resultant). We derive a hierarchy of inequalities via the Arithmetic Mean-Geometric Mean (AM-GM) inequality that yields progressively tighter upper and lower bounds for the tensor spectral radius and smallest eigenvalue. A comprehensive comparative analysis demonstrates that our invariant-based approach significantly outperforms classical coordinate-dependent methods such as the Gershgorin circle theorem. We explicitly show that our bounds remain robust and informative in scenarios where Gershgorin bounds fail, particularly for tensors with negative off-diagonal entries, where algebraic cancellations occur, and higher-order tensors, where combinatorial growth leads to loose estimates. Furthermore, we validate the practical utility of these bounds by applying them to certify the positive definiteness of Lyapunov functions in the stability analysis of nonlinear autonomous systems.

Hemant Sharma, Nachiketa Mishra

We develop and analyze iterative methods for computing the principal square root of third-order tensors under the T-product framework. Tensor extensions of the Newton iteration (quadratic convergence) and the Denman--Beavers iteration (geometric convergence with simultaneous computation of the inverse square root) are proposed, with rigorous convergence guarantees established via the Fourier-domain block-diagonalization of the T-product. We apply these methods to image processing, introducing Tensor Decorrelated Grayscale conversion, T-Whitening, and optimal color transfer under the T-product geometry. We also formulate the Tensor Bures--Wasserstein distance and prove it defines a valid metric on the space of T-positive definite tensors. Numerical experiments confirm rapid convergence and demonstrate that the proposed tensor-based techniques offer improved structural preservation and cross-channel decorrelation compared to classical methods.

Ming Du, Xiangyu Yin, Yanqi Luo et al.

Scientific data processing often requires task-specific algorithms or AI models, creating a barrier for domain scientists who need to analyze their data but may not have extensive computing or image-processing expertise. This barrier is especially pronounced when data are noisy, have a high dynamic range, are sparsely labeled, or are only loosely specified. We introduce CVEvolve, an autonomous agentic harness with a zero-code interface for scientific data-processing algorithm discovery. CVEvolve combines a multi-round search strategy with tools for code execution, evaluation implementation, history management, holdout testing, and optional inspection of scientific data and visual outputs. The search alternates between discovery and improvement actions, and uses lineage-aware stochastic candidate sampling to balance exploration and exploitation. We demonstrate CVEvolve on x-ray fluorescence microscopy image registration, Bragg peak detection, and high-energy diffraction microscopy image segmentation. Across these tasks, CVEvolve discovers algorithms that improve over baseline methods, while holdout test tracking helps identify candidates that generalize better than later over-optimized alternatives. These results show that zero-code, autonomous LLM-powered algorithm development can help domain scientists turn unstructured scientific image data into practical algorithms and downstream scientific discoveries.

Weijian Zheng, Jun-Sang Park, Peter Kenesei et al.

High-energy X-ray diffraction methods can non-destructively map the 3D microstructure and associated attributes of metallic polycrystalline engineering materials in their bulk form. These methods are often combined with external stimuli such as thermo-mechanical loading to take snapshots over time of the evolving microstructure and attributes. However, the extreme data volumes and the high costs of traditional data acquisition and reduction approaches pose a barrier to quickly extracting actionable insights and improving the temporal resolution of these snapshots. Here we present a fully automated technique capable of rapidly detecting the onset of plasticity in high-energy X-ray microscopy data. Our technique is computationally faster by at least 50 times than the traditional approaches and works for data sets that are up to 9 times sparser than a full data set. This new technique leverages self-supervised image representation learning and clustering to transform massive data into compact, semantic-rich representations of visually salient characteristics (e.g., peak shapes). These characteristics can be a rapid indicator of anomalous events such as changes in diffraction peak shapes. We anticipate that this technique will provide just-in-time actionable information to drive smarter experiments that effectively deploy multi-modal X-ray diffraction methods that span many decades of length scales.

Zhengchun Liu, Ahsan Ali, Peter Kenesei et al.

Extremely high data rates at modern synchrotron and X-ray free-electron laser light source beamlines motivate the use of machine learning methods for data reduction, feature detection, and other purposes. Regardless of the application, the basic concept is the same: data collected in early stages of an experiment, data from past similar experiments, and/or data simulated for the upcoming experiment are used to train machine learning models that, in effect, learn specific characteristics of those data; these models are then used to process subsequent data more efficiently than would general-purpose models that lack knowledge of the specific dataset or data class. Thus, a key challenge is to be able to train models with sufficient rapidity that they can be deployed and used within useful timescales. We describe here how specialized data center AI (DCAI) systems can be used for this purpose through a geographically distributed workflow. Experiments show that although there are data movement cost and service overhead to use remote DCAI systems for DNN training, the turnaround time is still less than 1/30 of using a locally deploy-able GPU.

Zhengchun Liu, Hemant Sharma, Jun-Sang Park et al.

X-ray diffraction based microscopy techniques such as High Energy Diffraction Microscopy rely on knowledge of the position of diffraction peaks with high precision. These positions are typically computed by fitting the observed intensities in area detector data to a theoretical peak shape such as pseudo-Voigt. As experiments become more complex and detector technologies evolve, the computational cost of such peak detection and shape fitting becomes the biggest hurdle to the rapid analysis required for real-time feedback during in-situ experiments. To this end, we propose BraggNN, a deep learning-based method that can determine peak positions much more rapidly than conventional pseudo-Voigt peak fitting. When applied to a test dataset, BraggNN gives errors of less than 0.29 and 0.57 pixels, relative to the conventional method, for 75% and 95% of the peaks, respectively. When applied to a real experimental dataset, a 3D reconstruction that used peak positions computed by BraggNN yields 15% better results on average as compared to a reconstruction obtained using peak positions determined using conventional 2D pseudo-Voigt fitting. Recent advances in deep learning method implementations and special-purpose model inference accelerators allow BraggNN to deliver enormous performance improvements relative to the conventional method, running, for example, more than 200 times faster than a conventional method on a consumer-class GPU card with out-of-the-box software.