arXiv subjects

Hemant Sharma

Publications and source records attributed to Hemant Sharma.

At least 19 recordsLinked to original sources

arXiv2026

An End-to-End Differentiable Forward Model for High-Energy Diffraction Microscopy

High-Energy Diffraction Microscopy (HEDM) recovers crystallographic orientation, strain, and grain position from rotating-crystal X-ray diffraction patterns. Existing forward models in far-field (FF), near-field (NF), and point-focused (pf) HEDM are not differentiable, which forecloses gradient-based joint parameter refinement, physics-informed regularisation, and Bayesian uncertainty quantification. We present the first end-to-end differentiable HEDM forward model covering all three geometries, implemented in PyTorch with pixel-exact agreement against the established MIDAS reference simulators (162/162 FF, 2304/2304 NF including a non-zero detector-tilt sweep, and 1088/1096 pf-HEDM spots matched). Three demonstrations validate the framework: joint orientation-strain-position recovery in NF-HEDM at ~6 nm precision; round-trip refinement on a real 214-grain alpha-Ti FF-HEDM dataset reaching 100% grain recovery from a 1.5 degree initial perturbation with residuals matching the production fit to 0.3%; and joint refinement of all per-detector geometry parameters and per-grain state on a synthetic four-panel FF-HEDM setup, recovering panel rotations about the beam axis to ~10 mu-rad and a global rotation-axis wedge to ~26 mu-rad. The framework is released as the open-source midas-diffract package (pip install midas-diffract).

cond-mat.mtrl-sci↗

arXiv2026

Sharp Spectral Bounds for Symmetric Positive Definite Tensors via Multiple Algebraic Invariants

We extend the trace--determinant framework of Nayak, Sharma, and Mishra~\cite{nayak2026} for bounding the H-eigenvalues of symmetric positive definite tensors. First, we replace the Arithmetic--Geometric Mean (AM--GM) relaxation underlying previous bounds by the exact solution of the associated constrained optimization problem, yielding sharp upper and lower bounds that are attained on the admissible spectral variety. Second, we incorporate higher-order power sums as additional spectral invariants and prove a structural theorem showing that any extremizer over a $K$-invariant feasibility region has at most $K$ distinct spectral values. This reduces the problem to a finite collection of low-dimensional polynomial systems and yields a hierarchy of increasingly tight bounds. For the four-invariant case $(T,S,p_3,D)$, we develop a complete theory including solution-count estimates, a multistart Newton algorithm, and sharpness conditions. We also derive closed-form bounds in small dimensions, establish perturbation estimates, and obtain refined Lyapunov region-of-attraction bounds. Numerical experiments for dimensions up to $d=100$ show that the sharp three-invariant bound reduces the median relative overestimation gap from $53\%$ to $6\%$ while maintaining low computational cost. The framework is validated on tensors with real H-spectrum.

math.OC↗

arXiv2026

Randomized Estimation of T-Eigenvalues of T-SPD Tensors: A Two-Sided Bracket

In earlier work \cite{sharma2025} we developed deterministic analytical bounds on the T-eigenvalues of symmetric positive definite (SPD) third-order tensors under the Kilmer--Martin T-product: the trace--determinant (TDet) bounds via the AM--GM inequality, and the trace-dependent (TDep) bounds generalizing Samuelson's inequality. While these bounds are cheap and guaranteed-valid, their relative gap grows as $\sqrt{d-1}$ in the tensor dimension $d = np$, limiting their usefulness for large tensors. This paper develops randomized estimators for the extreme T-eigenvalues of T-SPD tensors that complement the deterministic bounds. We adapt the Halko--Martinsson--Tropp framework \cite{halko2011} to the T-product setting and introduce four methods: (i) a randomized power method that produces a lower bound on $\lambda_1$ with exponential convergence; (ii) a randomized subspace iteration with a tensor-analogue HMT error bound; (iii) a two-sided rigorous bracket combining the randomized lower bound with the deterministic TDep upper bound; and (iv) a Hutchinson-based fully randomized TDep bound for matvec-only settings.

math.NA↗

arXiv2026

Sharp Convergence Rates and Optimal Weights for Cimmino's Reflection Algorithm

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 $\e^{(\nu+1)}=M_w\,\e^{(\nu)}$, 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, \[ \sprad(M_w) \;=\; |1-\mu| + \tfrac{1}{2}\sqrt{(w_1-w_2)^2 + 4w_1w_2\cos^2\!\theta}, \] where $\mu=(w_1+w_2)/2$ and $\theta$ 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 $\sprad^*=|\cos\theta|$ -- a quantity determined solely by the geometry of the hyperplane normals. The inter-normal angle $\theta$ thus emerges as the single diagnostic parameter governing both convergence speed and weight selection. Extensions to a single-step convergence criterion at $\theta=\pi/2$ and to an exact spectral rate for general~$n$ are also established.

math.NA↗

arXiv2026

Spectral Bounds for Tensors Derived from Trace Functionals and Wasserstein Distance in Tensor Spaces

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.

math.NA↗

arXiv2026

Iterative Methods for Computing the T-Square Root of Third-Order Tensors

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.

math.NA↗

arXiv2026

Eigenbounds of symmetric positive definite tensors

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.

math.NA↗

arXiv2026

CVEvolve: Autonomous Algorithm Discovery for Unstructured Scientific Data Processing

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, high-energy diffraction microscopy image segmentation, and hybrid analytical-learning-based affine registration. 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.

cs.AI↗

arXiv2026

AlphaDiffract: Automated Crystallographic Analysis of Powder X-ray Diffraction Data

Materials identification and structural understanding from powder X-ray diffraction (PXRD) data is a long-standing challenge in materials science, fundamental to discovering and characterizing novel materials. A prerequisite for full structure solution is the accurate determination of the crystal lattice, including lattice parameters and crystallographic symmetries. Traditional methods for this are iterative and typically require expert input, and while existing deep learning approaches have shown promise, a robust, single-shot method for comprehensive lattice determination from experimental data remains a key goal. Here, we introduce AlphaDiffract, a deep learning framework that achieves state-of-the-art performance in predicting the crystal system, space group, and lattice parameters directly from PXRD patterns. AlphaDiffract utilizes a 1D adaptation of the ConvNeXt architecture, a modern convolutional neural network that integrates key design principles from transformers, coupled with dedicated prediction heads for each crystallographic property. The model is trained on the largest-to-date physics-based dataset of over 31 million simulated diffraction patterns, generated by augmenting 312,267 curated structures from the ICSD and Materials Project databases. Crucially, it demonstrates strong generalization to experimental data, achieving 81.7% crystal system accuracy and 66.2% space group accuracy on the RRUFF dataset while additionally predicting all six lattice parameters. By providing a unified model for rapid and accurate lattice determination from PXRD data, AlphaDiffract represents a significant step forward in leveraging deep learning for high-throughput materials discovery.

cond-mat.mtrl-sci↗

arXiv2026

Unsupervised Semantic Segmentation in Synchrotron Computed Tomography with Self-Correcting Pseudo Labels

X-ray computed tomography (CT) is a widely used imaging technique that provides detailed examinations into the internal structure of an object with synchrotron CT (SR-CT) enabling improved data quality by using higher energy, monochromatic X-rays. While SR-CT allows for improved resolution, time-resolved experimentation, and reduced imaging artifacts, it also produces significantly larger datasets than conventional CT. Accurate and efficient evaluation of these datasets is a critical component of these workflows; yet is often done manually representing a major bottleneck in the analysis phase. While deep learning has emerged as a powerful tool capable of providing a wide range of purely data-driven solutions, it requires a substantial amount of labeled data for training and manual annotation of SR-CT datasets is impractical in practice. In this paper, we introduce a novel framework that enables automatic segmentation of large, high-resolution SR-CT datasets by eliminating the need to hand label images for deep learning training. First, we generate pseudo labels by clustering on the voxel values identifying regions in the volume with similar attenuation coefficients producing an initial semantic map. Afterwards, we train a segmentation model on the pseudo labels before utilizing the Unbiased Teacher approach to self-correct them ensuring accurate final segmentations. We find our approach improves pixel-wise accuracy and mIoU by 13.31% and 15.94%, respectively, over the baseline pseudo labels when using a magnesium crystal SR-CT sample. Additionally, we extensively evaluate the different components of our workflow including segmentation model, loss function, pseudo labeling strategy, and input type. Finally, we evaluate our approach on to two additional samples highlighting our frameworks ability to produce segmentations that are considerably better than the original pseudo labels.

cs.CV↗

arXiv2026

pMSz: A Distributed Parallel Algorithm for Correcting Extrema and Morse Smale Segmentations in Lossy Compression

Lossy compression, widely used by scientists to reduce data from simulations, experiments, and observations, can distort features of interest even under bounded error. Such distortions may compromise downstream analyses and lead to incorrect scientific conclusions in applications such as combustion and cosmology. This paper presents a distributed and parallel algorithm for correcting topological features, specifically, piecewise linear Morse Smale segmentations (PLMSS), which decompose the domain into monotone regions labeled by their corresponding local minima and maxima. While a single GPU algorithm (MSz) exists for PLMSS correction after compression, no methodology has been developed that scales beyond a single GPU for extreme scale data. We identify the key bottleneck in scaling PLMSS correction as the parallel computation of integral paths, a communication-intensive computation that is notoriously difficult to scale. Instead of explicitly computing and correcting integral paths, our algorithm simplifies MSz by preserving steepest ascending and descending directions across all locations, thereby minimizing interprocess communication while introducing negligible additional storage overhead. With this simplified algorithm and relaxed synchronization, our method achieves over 90% parallel efficiency on 128 GPUs on the Perlmutter supercomputer for real world datasets.

cs.DC↗

arXiv2025

Passive Vibration Isolation Characteristics of Negative Extensibility Metamaterials

Negative extensibility refers to the category of mechanical metamaterials having an unusual phenomenon where the system contracts upon expansion. The dynamic analysis of such systems is crucial for exploring the vibration isolation characteristics, forming the prime focus of the present study. Inspired by the Braess paradox, the mechanical model incorporates coupled tunable nonlinear spring stiffness properties (strain hardening and softening), which alternate when a certain displacement threshold is exceeded. This stiffness switching mechanism facilitates low frequency passive vibration isolation using the phenomenon of countersnapping instability. The vibration isolation characteristics resulting from the stiffness switching mechanism are investigated using time and frequency domain plots. Furthermore, the relationship between the stiffness switching mechanism and various system parameters is visualized using a three dimensional parametric space. The efficacy of the proposed system is evaluated by comparing it with the existing bistable systems, revealing superior performance in isolating high-amplitude vibrations. The proposed mechanism enhances the understanding of dynamic behaviors in critical structural elements for multistable mechanical metamaterials, providing insights and opportunities for innovative adaptive designs.

nlin.AO↗

arXiv2025

Minimising the number of edges in LC-equivalent graph states

Graph states are a powerful class of entangled states with numerous applications in quantum communication and quantum computation. Local Clifford (LC) operations that map one graph state to another can alter the structure of the corresponding graphs, including changing the number of edges. Here, we tackle the associated edge-minimisation problem: finding graphs with the minimum number of edges in the LC-equivalence class of a given graph. Such graphs are called minimum edge representatives (MER) and are crucial for minimising the resources required to create a graph state. We leverage Bouchet's algebraic formulation of LC-equivalence to encode the edge-minimisation problem as an integer linear program (EDM-ILP). We further propose a simulated annealing (EDM-SA) approach guided by the local clustering coefficient for edge minimisation. We identify new MERs for graph states with up to 16 qubits by combining EDM-SA and EDM-ILP. We extend the ILP to weighted-edge minimisation, where each edge has an associated weight, and prove that this problem is NP-complete. Finally, we employ our tools to minimise the resources required to create all-photonic generalised repeater graph states using fusion operations.

quant-ph↗

arXiv2025

Catalytic entanglement transformations with noisy hardware

The availability of certain entangled resource states (catalyst states) can enhance the rate of converting several less entangled states into fewer highly entangled states in a process known as catalytic entanglement concentration (EC). Here, we extend catalytic EC from pure states to mixed states and numerically benchmark it against non-catalytic EC and distillation in the presence of state-preparation errors and operational errors. Furthermore, we analyse the re-usability of catalysts in the presence of such errors. To do this, we introduce a novel recipe for determining the positive-operator valued measurements (POVM) required for EC transformations, which allows for making tradeoffs between the number of communication rounds and the number of auxiliary qubits required. We find that in the presence of low operational errors and depolarising noise, catalytic EC can provide better rates than distillation and non-catalytic EC.

quant-ph↗

arXiv2023

Rapid detection of rare events from in situ X-ray diffraction data using machine learning

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.

cs.LG↗

arXiv2022

Entanglement distribution with minimal memory requirements using time-bin photonic qudits

Generating multiple entangled qubit pairs between distributed nodes is a prerequisite for a future quantum internet. To achieve a practicable generation rate, standard protocols based on photonic qubits require multiple long-term quantum memories, which remains a significant experimental challenge. In this paper, we propose a novel protocol based on $2^m$-dimensional time-bin photonic qudits that allow for the simultaneous generation of multiple ($m$) entangled pairs between two distributed qubit registers and outline a specific implementation of the protocol based on cavity-mediated spin-photon interactions. By adopting the qudit protocol, the required qubit memory time is independent of the transmission loss between the nodes in contrast to standard qubit approaches. As such, our protocol can significantly boost the performance of near-term quantum networks.

quant-ph↗

arXiv2022

fairDMS: Rapid Model Training by Data and Model Reuse

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.

cs.LG↗

arXiv2022

Bridging Data Center AI Systems with Edge Computing for Actionable Information Retrieval

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.

cs.LG↗