arXiv subjects

Rakesh Kumar

Publications and source records attributed to Rakesh Kumar.

At least 19 recordsLinked to original sources

arXiv2026

Constraint Preserving AFD-WENO Schemes for Relativistic Hydrodynamics with General Equations of State

We develop a high-order physical-constraint-preserving (PCP) alternative finite difference weighted essentially non-oscillatory (AFD-WENO) scheme for the special relativistic hydrodynamics equations with general equations of state. The proposed scheme comprises two key limiters: a state limiter, which acts after the WENO state interpolation step, and a flux limiter, which acts on the final high-order fluxes. The state limiter ensures that the interpolated states are physically admissible, while the flux limiter ensures that the numerical fluxes are physically admissible. The resulting scheme is rigorously proved to satisfy the physical constraints. Incorporating multiple WENO interpolation techniques, including an improved adaptive-order formulation (WENO-AOI), the method is validated through extensive one- and two-dimensional numerical benchmarks with various equations of state. The numerical results demonstrate high-order accuracy, sharp resolution of discontinuities, and robust stability in extreme relativistic regimes.

math.NA↗

arXiv2026

XDG: Accelerated Visual Disambiguation

Visual aliasing, also known as the doppelganger problem, remains a key challenge for structure-from-motion (SfM): visually similar but physically distinct surfaces can produce incorrect image matches and degrade reconstruction quality. Previous work mitigates this issue with geometry-aware foundation-model features, but places a heavy transformer classifier on top of the backbone, making large-scale disambiguation expensive. We introduce XDG, an efficient visual disambiguation model designed for scalable SfM. Our key observation is that a 3D foundation model already performs the cross-view geometric reasoning necessary for visual disambiguation, so doppelganger classification should adapt the backbone representation directly rather than relearn pair reasoning in a separate heavy decoder. XDG fine-tunes Depth Anything 3 with lightweight LoRA adapters and repurposes its camera tokens as compact pair-level classification tokens. A compact MLP head predicts whether a candidate image pair observes the same 3D surface. Extensive experiments show that XDG provides a favorable accuracy-efficiency tradeoff: it remains competitive with the state-of-the-art disambiguation method across pairwise and reconstruction benchmarks and delivers more than a 3x inference speedup. On individual LaMAR scenes containing thousands of images, XDG saves more than 10 hours of visual disambiguation processing. Code is available at https://github.com/xtcpete/xdg.

cs.CV↗

arXiv2026

Efficient Hybrid WENO Schemes for Special Relativistic Hydrodynamics with Adaptive Characteristic Reconstruction

Special relativistic hydrodynamics (SRHD) equations arise in the modeling of high-speed fluid flows encountered in astrophysical phenomena such as jets, supernova explosions, and gamma-ray bursts. Owing to their highly nonlinear hyperbolic nature, solutions often develop strong discontinuities, making the design of stable and accurate numerical schemes challenging. Although Weighted Essentially Non-Oscillatory (WENO) schemes are widely used for such problems, component-wise WENO reconstruction may produce spurious oscillations near discontinuities. On the other hand, characteristic-wise WENO reconstruction provides accurate non-oscillatory solutions for systems of conservation laws, but it involves the computation of eigenvectors in each cell, which leads to high computational cost. In this work, we intend to develop hybrid schemes which maintain the non-oscillatory feature of characteristic-wise WENO while being less costly. We propose three hybrid schemes, namely the H1-WENO, H2-WENO, and H3-WENO schemes, based on a new troubled-cell indicator constructed from the smoothness indicators of the WENO scheme. The proposed troubled-cell indicator effectively distinguishes smooth and discontinuous regions, allowing the hybrid schemes to employ inexpensive reconstructions in smooth regions and the characteristic-wise WENO reconstruction only near discontinuities. Numerical experiments demonstrate that the proposed schemes retain the accuracy and robustness of characteristic-wise WENO methods while significantly reducing the computational cost. In particular, the H1-WENO scheme achieves an approximately 30--40% improvement in computational efficiency compared to the standard WENO scheme in 2D test cases.

math.NA↗

arXiv2026

Ground-to-Satellite Localization in Unconstrained Image Collections for 3D Scene Reconstruction

Ground image localization with respect to satellite imagery is a key enabler for metrically-accurate, geo-localized 3D scene reconstruction from unconstrained image collections. Existing cross-view localization methods have strict requirements such as panoramic imagery or known initial locations, limiting their applicability for in-the-wild reconstruction settings. We propose a robust hierarchical cross-view localization framework that leverages geometric constraints from Structure-from-Motion (SfM) models derived from unconstrained ground image collections. Our method generates coarse-to-fine pose hypotheses through a cross-view matching approach and aggregates noisy predictions across SfM model(s) using Kernel Density Estimation to recover consensus alignments while filtering outliers. Experiments demonstrate reliable localization performance from challenging image collections. Empirically we found satellite-referenced alignment enables accurate metric scale estimation, doppelg\"anger detection, and merging of disjoint SfM reconstructions, resulting in more complete, geo-localized site models than are possible with SfM alone.

cs.CV↗

arXiv2026

Riemann invariant-based alternative WENO scheme for a two-layer thin film model

In this article, we develop a multi-dimensional two-layer thin film model extending the thin film model proposed in \cite{barthwal2025hyperbolic}. The model considered in \cite{barthwal2025hyperbolic} considered a very specific Marangoni scale by choosing Marangoni numbers in both layers to be $1$. We relax this condition here and prove that the obtained system possesses a full set of Riemann invariants. Based on these findings, we develop a Riemann Invariant-based Local Characteristic Decomposition WENO (RI-WENO) method for the two-layer thin film model in one and two dimensions. The method is built upon a specially designed variable transformation constructed from the derived Riemann invariants of the system. This transformation partially diagonalizes the governing equations and yields a sparse structure in the transformed eigenvector matrices. As a result, the proposed RI-WENO framework significantly reduces the computational cost of the standard Local Characteristic Decomposition WENO approach while retaining its strong capability to suppress spurious oscillations. Numerical experiments, including new benchmark test cases, demonstrate that the RI-WENO method achieves an effective balance between accuracy and computational efficiency, making it a promising and practical choice for solving the two-layer thin film model.

math.NA↗

arXiv2026

Flare: Leveraging Serverless Elasticity to Absorb Microservice Load Spikes

Online services strive to maintain application responsiveness even when the traffic is unpredictable and fluctuating. Today's online services are commonly deployed as chains of microservices, each microservice packaged as one or more containers inside virtual machines (VMs). While performant and affordable when the load is steady, VM-based deployments are known to be slow to scale when the load spikes, resulting in degraded performance for end-users of the service. To avoid such performance degradations, service providers can over-provision their deployments; however, such a strategy is costly and inefficient, leaving resources under-utilized for extended periods. To address the challenge of unpredictable load spikes, we propose Flare, a hybrid microservice architecture that combines VMs with serverless computing. Flare utilizes VMs to cost-effectively handle steady workloads and leverages serverless elasticity to absorb traffic spikes. When a spike occurs, Flare detects which specific service(s) are overloaded and shifts the excess load of only those services to serverless, thus minimizing the cost overhead. Flare seamlessly integrates into existing auto-scaling and serverless infrastructure, requiring minimal changes to the control plane and no modifications to the application.

cs.DC↗

arXiv2026

Neural-Guided Domain Restriction to Accelerate Pseudospectra Computation for Structured Non-normal Banded Matrices

Computing pseudospectra of non-normal matrices is essential for understanding the stability and transient behavior of dynamical systems. Such analysis is critical in applications including fluid dynamics, control systems, and differential operators, where non-normality can lead to significant transient amplification and sensitivity to perturbations that are not captured by eigenvalue analysis alone. At large scales, commonly used numerical approaches for pseudospectra computation can become computationally demanding, as they require repeated auxiliary computations to identify spectrally sensitive regions in the complex plane. We present a neural network-based approach that predicts sensitive regions directly from matrix features, thereby avoiding exhaustive pseudospectra evaluation across the entire complex plane. We calibrate the prediction threshold on validation data to ensure reliable coverage of sensitive regions. The trained neural network guides the selection of grid points requiring full computation, enabling focused computation only where necessary. The approach provides a practical preprocessing strategy for efficient pseudospectra computation. Numerical experiments on non-normal banded matrices demonstrate substantial speedup compared to full grid-based numerical evaluation while maintaining high accuracy in identifying sensitive regions.

math.NA↗

arXiv2026

Exact columnar dimer ground state and quantum phase transitions in a frustrated coupled spin ladder model

We study a spin-half frustrated coupled ladder system, in which ladders with leg, rung, and diagonal interactions are linked via nearest-neighbor coupling. By introducing a leg-symmetric inter-ladder interaction that connects the left-to-left and right-to-right legs of adjacent ladders, the model is found to possess an exact dimer ground state, characterized by a product of two-spin singlets forming a columnar dimer phase. We analyze this model using bond-operator mean-field theory (BOMFT) and the density matrix renormalization group (DMRG) to probe the phase transitions that occur as one traverses the coupling space. The BOMFT reveals three distinct phases: a double-stripe ordered phase, a N\'eel ordered phase, and a quantum disordered dimerized phase. The critical points for the transitions are at $ J_1 = -0.81 $ (double-stripe to dimerized) and at $ J_1 = 2.81 $ (dimerized to N\'eel phase). Further, the DMRG results corroborate the exact ground state and refine the critical points to $ J_1 = -0.79 $ and $ J_1 = 2.29 $ for the respective transitions. Additionally, another transition is identified as the N\'eel order vanishes for $ J_1 \ge 4.5 $. The model can alternatively be represented as a network of orthogonal zigzag and fully frustrated spin ladders, offering a structural framework conducive to quantum materials engineering.

cond-mat.str-el↗

arXiv2026

Athena: Synergizing Data Prefetching and Off-Chip Prediction via Online Reinforcement Learning

Prefetching and off-chip prediction are two techniques proposed to hide long memory access latencies in high-performance processors. In this work, we demonstrate that: (1) prefetching and off-chip prediction often provide complementary performance benefits, yet (2) naively combining them often fails to realize their full performance potential, and (3) existing prefetcher control policies leave significant room for performance improvement behind. Our goal is to design a holistic framework that can autonomously learn to coordinate an off-chip predictor with multiple prefetchers employed at various cache levels. To this end, we propose a new technique called Athena, which models the coordination between prefetchers and off-chip predictor (OCP) as a reinforcement learning (RL) problem. Athena acts as the RL agent that observes multiple system-level features (e.g., prefetcher/OCP accuracy, bandwidth usage) over an epoch of program execution, and uses them as state information to select a coordination action (i.e., enabling the prefetcher and/or OCP, and adjusting prefetcher aggressiveness). At the end of every epoch, Athena receives a numerical reward that measures the change in multiple system-level metrics (e.g., number of cycles taken to execute an epoch). Athena uses this reward to autonomously and continuously learn a policy to coordinate prefetchers with OCP. Our extensive evaluation using a diverse set of memory-intensive workloads shows that Athena consistently outperforms prior state-of-the-art coordination policies across a wide range of system configurations with various combinations of underlying prefetchers, OCPs, and main memory bandwidths, while incurring only modest storage overhead. Athena is freely available at https://github.com/CMU-SAFARI/Athena.

cs.AR↗

arXiv2025

GeoSURGE: Geo-localization using Semantic Fusion with Hierarchy of Geographic Embeddings

Worldwide visual geo-localization aims to determine the geographic location of an image anywhere on Earth using only its visual content. Despite recent progress, learning expressive representations of geographic space remains challenging due to the inherently low-dimensional nature of geographic coordinates. We formulate global geo-localization as aligning the visual representation of a query image with a learned geographic representation. Our approach explicitly models the world as a hierarchy of learned geographic embeddings, enabling a distributed and multi-scale representation of geographic space. In addition, we introduce a semantic fusion module that efficiently integrates appearance features with semantic segmentation through latent cross-attention, producing a more robust visual representation for localization. Experiments on five widely used geo-localization benchmarks demonstrate that our method achieves new state-of-the-art results on 22 of 25 reported metrics. Ablation studies show that these improvements are primarily driven by the proposed geographic representation and semantic fusion mechanism.

cs.CV↗

arXiv2025

CoRuTiGe: A Possible Spin Gapless Semiconductor

We report experimental and theoretical investigations on the quaternary Heusler alloy CoRuTiGe, synthesized using the arc melting technique. Crystal structure analysis reveals a tetragonal structure at room temperature. Magnetization measurements as a function of temperature and magnetic field indicate ferromagnetic nature with a saturation magnetization of 0.681 mB/f.u. at 5 K. The temperature dependence of electrical resistivity shows a nearly linear decrease in the high-temperature range, indicating the spin gapless semiconductor like behavior of the material. This SGS nature is further supported by the temperature-independent carrier concentration and mobility. Hall effect analysis reveals that the anomalous Hall effect in CoRuTiGe arises from both intrinsic and extrinsic mechanisms. Additionally, a well-defined symmetric negative magnetoresistance is observed at low temperatures. These findings suggest that CoRuTiGe holds significant promise for spintronic applications.

cond-mat.mtrl-sci↗

arXiv2025

Revelator: Rapid Data Fetching via System-Software-Guided Hash-based Speculative Address Translation

Address translation is a major performance bottleneck in modern computing systems. Predicting the physical address (PA) of requested data before address translation completes can hide this latency, but accurate virtual address (VA)-to-PA prediction is difficult because conventional operating systems make VA-to-PA mappings unpredictable. Prior work improves predictability but relies on large pages or VA-to-PA contiguity, or stores speculation metadata in costly hardware structures. We introduce Revelator, a hardware-OS cooperative technique that uses hashing to enable accurate speculative address translation with small system modifications. Revelator employs a tiered hash-based memory allocation policy for both program data and last-level page table entries (PTEs), creating predictable VA-to-PA and VA-to-PTE mappings. After an L2 TLB miss, a lightweight hardware speculation engine uses the OS hash functions to predict these mappings and prefetch the corresponding cache blocks before translation completes, hiding address translation latency and accelerating page table walks (PTWs). Revelator does not rely on large pages or VA-to-PA contiguity and requires only small OS and hardware changes. Across 11 data-intensive workloads, Revelator improves performance by 15.3% on average over the state-of-the-art speculative address translation technique under high memory fragmentation. In virtualized environments, it predicts both guest and host physical addresses, providing a 13.6% average speedup over Nested Paging. In 16-core systems, Revelator achieves 1.40x (1.50x) speedup over Transparent Huge Pages across 30 server workload mixes from Google under medium (high) memory fragmentation. RTL synthesis shows only 0.02% area and 0.03% power overheads on a high-end server-grade CPU. Revelator is freely available at \href{https://github.com/CMU-SAFARI/Virtuoso}{github.com/CMU-SAFARI/Virtuoso}.

cs.AR↗

arXiv2025

Spectral Analysis of Node- and Cell-Centered Higher-Order Compact Schemes for Fully Discrete One and Two-Dimensional Convection-Dispersion Equation

In this study, we present a comprehensive global spectral analysis of the convection dispersion equation, which is also referred to in specific contexts as the Korteweg de Vries (KdV) equation, to investigate the behaviour of high order numerical schemes across a wide range of nondimensional parameters. The motivation for this analysis stems from the equation's importance in modeling wave propagation and transport phenomena, where accurate resolution of dispersive effects is critical, and traditional numerical schemes often suffer from spurious artifacts. We analyze one sixth order and two eighth order compact spatial discretization schemes, encompassing both node centered and cell centered formulations, combined with a third order strong stability preserving Runge Kutta (SSPRK3) time integrator. The analysis is performed in terms of key nondimensional parameters such as the wavenumber, Courant Friedrichs Lewy number $N_c$, and dispersion number $D_{\alpha}$ over the full spectral plane for both one and two dimensional cases. Key numerical indicators, including the amplification factor, normalized phase speed, and normalized group velocity, are evaluated to characterize stability, dispersion error, errors in energy transport, and directional anisotropy. Critical dispersion thresholds and Courant numbers are identified, beyond which numerical instability and nonphysical phenomena such as spurious q waves and reversed phase or energy transport arise. Theoretical predictions are validated through numerical experiments involving linear and nonlinear one and two dimensional test problems, including cases with exact solutions and established benchmark results. This comprehensive analysis uncovers subtle numerical errors and offers practical guidance for selecting reliable discretization parameters, ensuring accurate and stable simulations of convection dispersion systems.

math.NA↗

arXiv2025

On Construction of Approximate Real Mutually Unbiased Bases for an infinite class of dimensions $d \not\equiv 0 \bmod 4$

It is known that real Mutually Unbiased Bases (MUBs) do not exist for any dimension $d > 2$ which is not divisible by 4. Thus, the next combinatorial question is how one can construct Approximate Real MUBs (ARMUBs) in this direction with encouraging parameters. In this paper, for the first time, we show that it is possible to construct $> \lceil \sqrt{d} \rceil$ many ARMUBs for certain odd dimensions $d$ of the form $d = (4n-t)s$, $t = 1, 2, 3$, where $n$ is a natural number and $s$ is an odd prime power. Our method exploits any available $4n \times 4n$ real Hadamard matrix $H_{4n}$ (conjectured to be true) and uses this to construct an orthogonal matrix ${Y}_{4n-t}$ of size $(4n - t) \times (4n - t)$, such that the absolute value of each entry varies a little from $\frac{1}{\sqrt{4n-t}}$. In our construction, the absolute value of the inner product between any pair of basis vectors from two different ARMUBs will be $\leq \frac{1}{\sqrt{d}}(1 + O(d^{-\frac{1}{4}})) < 2$, for proper choices of parameters, the class of dimensions $d$ being infinitely large.

cs.DM↗

arXiv2025

On Obtaining New MUBs by Finding Points on Complete Intersection Varieties over $\mathbb{R}$

Mutually Unbiased Bases (MUBs) are closely connected with quantum physics, and the structure has a rich mathematical background. We provide equivalent criteria for extending a set of MUBs for $C^n$ by studying real points of a certain affine algebraic variety. This variety comes from the relations that determine the extendability of a system of MUBs. Finally, we show that some part of this variety gives rise to complete intersection domains. Further, we show that there is a one-to-one correspondence between MUBs and the maximal commuting classes (bases) of orthogonal normal matrices in $\mathcal M_n({\mathbb{C}})$. It means that for $m$ MUBs in $C^n$, there are $m$ commuting classes, each consisting of $n$ commuting orthogonal normal matrices and the existence of maximal commuting basis for $\mathcal M_n({\mathbb{C}})$ ensures the complete set of MUBs in $\mathcal M_n({\mathbb{C}})$.

cs.DM↗

arXiv2025

Diffusion-Guided Gaussian Splatting for Large-Scale Unconstrained 3D Reconstruction and Novel View Synthesis

Recent advancements in 3D Gaussian Splatting (3DGS) and Neural Radiance Fields (NeRF) have achieved impressive results in real-time 3D reconstruction and novel view synthesis. However, these methods struggle in large-scale, unconstrained environments where sparse and uneven input coverage, transient occlusions, appearance variability, and inconsistent camera settings lead to degraded quality. We propose GS-Diff, a novel 3DGS framework guided by a multi-view diffusion model to address these limitations. By generating pseudo-observations conditioned on multi-view inputs, our method transforms under-constrained 3D reconstruction problems into well-posed ones, enabling robust optimization even with sparse data. GS-Diff further integrates several enhancements, including appearance embedding, monocular depth priors, dynamic object modeling, anisotropy regularization, and advanced rasterization techniques, to tackle geometric and photometric challenges in real-world settings. Experiments on four benchmarks demonstrate that GS-Diff consistently outperforms state-of-the-art baselines by significant margins.

cs.CV↗

arXiv2025

Filling systems of maximum size

Let $S_g$ be a closed orientable surface of genus $g\geq 2$. A collection $\Omega = \{ \gamma_1, \dots, \gamma_s\}$ of pairwise non-homotopic simple closed curves on $S_g$ such that $\gamma_i$ and $\gamma_j$ are in minimal position, is called a \emph{filling system} or a \emph{filling} of $S_g$ if the complement $S_g\setminus \Omega$ is a disjoint union of $b$ topological discs for some $b\geq 1$. The \emph{size} of a filling system is defined as the number of its elements. We prove that the maximum size of a filling system on $S_g$ with $ 1 \leq b \leq 2g-2$ boundary components is $2g+b-1$. Furthermore, we give a lower bound on mapping class group orbits of filling systems of maximum size with $ 1 \leq b \leq g-2$ boundary components.

math.GT↗

arXiv2024

Coupled Flow-Thermal Analysis of a Rocket Nozzle with Charring Ablative Thermal Protection System

This paper presents a conjugate flow-thermal analysis of a rocket nozzle protected by a charring ablative thermal protection system (TPS). The study employs a coupled approach, integrating a CFD solver with an in-house transient material response code through the exchange of boundary conditions at the fluid-solid interface. The nozzle incorporates an AVCOAT TPS and is subjected to high-temperature compressible flow. Results identify the nozzle throat as the critical location, exhibiting the highest convective loading, early attainment of the material ablation temperature, and progressive surface recession. Temporal analysis of the coupled simulations reveals an initial peak in wall heat flux followed by a transient reduction and a subsequent resurgence as viscous dissipation and evolving surface conditions modify the near-wall thermal field. At 120 s of simulated operation, the maximum surface recession at the throat is approximately 2.5 mm. This research provides a methodology for predicting the thermal and ablative response of rocket nozzles equipped with charring TPS materials. The proposed framework offers valuable insights into the design and optimization of high-performance nozzles for extreme environments.

physics.flu-dyn↗