About

Professor Shivkumar Chandrasekaran is a faculty member in the Department of Electrical and Computer Engineering at the University of California, Santa Barbara, with an affiliation in the Department of Computer Science. His research specialization includes numerical analysis, numerical linear algebra, structured matrix decomposition and inversion, and fast numerical algorithms. Professor Chandrasekaran's recent research activities include work on MSN interpolation of scattered derivative data, fast indefinite multi-point clustering, and minimum Sobolev-norm methods for partial differential equations. He leads a research group that explores advanced computational methods and algorithms, contributing to the development of efficient numerical techniques for scientific computing.

Research topics

• Artificial Intelligence
• Computer Science
• Machine Learning
• Data Mining
• Mathematics
• Econometrics
• Business

Selected publications

• Wrivinder: Towards Spatial Intelligence for Geo-locating Ground Images onto Satellite Imagery

  Open MIND · 2026-02-16

  preprint

  Aligning ground-level imagery with geo-registered satellite maps is crucial for mapping, navigation, and situational awareness, yet remains challenging under large viewpoint gaps or when GPS is unreliable. We introduce Wrivinder, a zero-shot, geometry-driven framework that aggregates multiple ground photographs to reconstruct a consistent 3D scene and align it with overhead satellite imagery. Wrivinder combines SfM reconstruction, 3D Gaussian Splatting, semantic grounding, and monocular depth--based metric cues to produce a stable zenith-view rendering that can be directly matched to satellite context for metrically accurate camera geo-localization. To support systematic evaluation of this task, which lacks suitable benchmarks, we also release MC-Sat, a curated dataset linking multi-view ground imagery with geo-registered satellite tiles across diverse outdoor environments. Together, Wrivinder and MC-Sat provide a first comprehensive baseline and testbed for studying geometry-centered cross-view alignment without paired supervision. In zero-shot experiments, Wrivinder achieves sub-30\,m geolocation accuracy across both dense and large-area scenes, highlighting the promise of geometry-based aggregation for robust ground-to-satellite localization.

  DOI

• Wrivinder: Towards Spatial Intelligence for Geo-locating Ground Images onto Satellite Imagery

  ArXiv.org · 2026-02-16

  articleOpen access

  Aligning ground-level imagery with geo-registered satellite maps is crucial for mapping, navigation, and situational awareness, yet remains challenging under large viewpoint gaps or when GPS is unreliable. We introduce Wrivinder, a zero-shot, geometry-driven framework that aggregates multiple ground photographs to reconstruct a consistent 3D scene and align it with overhead satellite imagery. Wrivinder combines SfM reconstruction, 3D Gaussian Splatting, semantic grounding, and monocular depth--based metric cues to produce a stable zenith-view rendering that can be directly matched to satellite context for metrically accurate camera geo-localization. To support systematic evaluation of this task, which lacks suitable benchmarks, we also release MC-Sat, a curated dataset linking multi-view ground imagery with geo-registered satellite tiles across diverse outdoor environments. Together, Wrivinder and MC-Sat provide a first comprehensive baseline and testbed for studying geometry-centered cross-view alignment without paired supervision. In zero-shot experiments, Wrivinder achieves sub-30\,m geolocation accuracy across both dense and large-area scenes, highlighting the promise of geometry-based aggregation for robust ground-to-satellite localization.

  PublisherOA PDF

• PAMDAC: Platform-Agnostic Malware Detection and Classification Based on Binary Features

  Signals and communication technology · 2026-01-01

  book-chapter
  PublisherDOI

• Tree Quasi-separable Matrices: A Simultaneous Generalization of Sequentially and Hierarchically Semiseparable Representations

  SIAM Journal on Matrix Analysis and Applications · 2025-06-09

  article
  PublisherDOI

• Flux-Preserving Adaptive Finite State Projection for Multiscale Stochastic Reaction Networks

  ArXiv.org · 2025-12-18

  articleOpen access

  The Finite State Projection (FSP) method approximates the Chemical Master Equation (CME) by restricting the dynamics to a finite subset of the (typically infinite) state space, enabling direct numerical solution with computable error bounds. Adaptive variants update this subset in time, but multiscale systems with widely separated reaction rates remain challenging, as low-probability bottleneck states can carry essential probability flux and the dynamics alternate between fast transients and slowly evolving stiff regimes. We propose a flux-based adaptive FSP method that uses probability flux to drive both state-space pruning and time-step selection. The pruning rule protects low-probability states with large outgoing flux, preserving connectivity in bottleneck systems, while the time-step rule adapts to the instantaneous total flux to handle rate constants spanning several orders of magnitude. Numerical experiments on stiff, oscillatory, and bottleneck reaction networks show that the method maintains accuracy while using substantially smaller state spaces.

  PublisherOA PDF

• MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs

  ArXiv.org · 2025-07-16

  preprintOpen accessSenior author

  We introduce a novel Multimodal Neural Operator (MNO) architecture designed to learn solution operators for multi-parameter nonlinear boundary value problems (BVPs). Traditional neural operators primarily map either the PDE coefficients or source terms independently to the solution, limiting their flexibility and applicability. In contrast, our proposed MNO architecture generalizes these approaches by mapping multiple parameters including PDE coefficients, source terms, and boundary conditions to the solution space in a unified manner. Our MNO is motivated by the hierarchical nested bases of the Fast Multipole Method (FMM) and is constructed systematically through three key components: a parameter efficient Generalized FMM (GFMM) block, a Unimodal Neural Operator (UNO) built upon GFMM blocks for single parameter mappings, and most importantly, a multimodal fusion mechanism extending these components to learn the joint map. We demonstrate the multimodal generalization capacity of our approach on both linear and nonlinear BVPs. Our experiments show that the network effectively handles simultaneous variations in PDE coefficients and source or boundary terms.

  PublisherOA PDFDOI

• METAREG: Robust Camera Parameter Estimation by Leveraging Noisy Camera Extrinsics

  2025-08-18

  article

  Novel view synthesis methods, such as Neural Radiance Fields (NeRFs) and 3D Gaussian Splatting (3DGS), rely on Structure-from-Motion (SfM) pipelines like COLMAP for camera parameter estimation. However, these pipelines are prone to errors due to factors like doppelgangers and perspective distortion. While edge devices (e.g., mobile phones) capture images with embedded GPS and IMU data, this meta-data is often noisy. We introduce MetaReg, a robust pipeline that improves camera parameter estimation by leveraging noisy GPS metadata. MetaReg enhances COLMAP with pre-and post-processing steps: the preprocessing stage estimates image overlap using metadata to reduce unnecessary image matching, while the post-processing stage aligns estimated camera coordinates with the world coordinate system using noisy GPS priors. Experiments on challenging datasets demonstrate that MetaReg significantly improves camera parameter estimation, enhancing robustness and accuracy.

  PublisherDOI

• Flux-Preserving Adaptive Finite State Projection for Multiscale Stochastic Reaction Networks

  arXiv (Cornell University) · 2025-12-18

  preprintOpen access

  The Finite State Projection (FSP) method approximates the Chemical Master Equation (CME) by restricting the dynamics to a finite subset of the (typically infinite) state space, enabling direct numerical solution with computable error bounds. Adaptive variants update this subset in time, but multiscale systems with widely separated reaction rates remain challenging, as low-probability bottleneck states can carry essential probability flux and the dynamics alternate between fast transients and slowly evolving stiff regimes. We propose a flux-based adaptive FSP method that uses probability flux to drive both state-space pruning and time-step selection. The pruning rule protects low-probability states with large outgoing flux, preserving connectivity in bottleneck systems, while the time-step rule adapts to the instantaneous total flux to handle rate constants spanning several orders of magnitude. Numerical experiments on stiff, oscillatory, and bottleneck reaction networks show that the method maintains accuracy while using substantially smaller state spaces.

  PublisherDOI

• Tree quasi-separable matrices: a simultaneous generalization of sequentially and hierarchically semi-separable representations

  arXiv (Cornell University) · 2024-02-20

  preprintOpen access

  We present a unification and generalization of what is known in the literature as sequentially and hierarchically semi-separable (SSS and HSS) representations for matrices. Describing rank-structured representations of (inverses of) sparse matrices whose adjacency graph is a tree, it is shown that these so-called tree quasi-separable (TQS) matrices inherit all the favorable algebraic properties of SSS and HSS under addition, products, and inversion. To arrive at these properties, we prove a key result that characterizes the conversion of any dense matrix into a TQS representation. Here, we specifically show through an explicit construction procedure that the generator sizes are dictated by the ranks of certain Hankel blocks of the matrix. Analogous to SSS and HSS, TQS matrices admit fast matrix-vector products and direct solvers provided the generator sizes are small. A sketch of the associated algorithms is provided.

  PublisherOA PDFDOI

• A Fast Algorithm for Computing Macaulay Null Spaces of Bivariate Polynomial Systems

  SIAM Journal on Matrix Analysis and Applications · 2024-01-24 · 1 citations

  articleOpen access

  sponsorship: This work was funded by Flemish Government: This research received funding from the Flemish Government (AI Research Program) . The first, second, and fourth authors are affiliated with Leuven.AI--KU Leuven institute for AI, B-3000, Leuven, Belgium. This work was supported by the Fonds de la Recherche Scientifique--FNRS and the Fonds Wetenschappelijk Onderzoek-Vlaanderen under EOS project G0F6718N (SeLMA) KU Leuven Internal Funds: iBOF/23/064, C14/22/096, C16/15/059, and IDN/19/014. (Flemish Government, Fonds de la Recherche Scientifique-FNRS, Fonds Wetenschappelijk Onderzoek-Vlaanderen|iBOF/23/064, Fonds Wetenschappelijk Onderzoek-Vlaanderen|C14/22/096, Fonds Wetenschappelijk Onderzoek-Vlaanderen|C16/15/059, Fonds Wetenschappelijk Onderzoek-Vlaanderen|IDN/19/014, G0F6718N)

  PublisherOA PDFDOI

Recent grants

• Collaborative Research: Super-fast Direct Sparse Solvers

  NSF · $175k · 2005–2008

• Collaborative Research: Minimum Sobolev Norm Methods

  NSF · $450k · 2008–2013

• AF EAGER: Minimum Sobolev Norm techniques for systems of elliptic PDEs

  NSF · $50k · 2014–2016

Frequent coauthors

• B.S. Manjunath

  University of California, Santa Barbara

  72 shared

• Lakshmanan Nataraj

  66 shared

• Tajuddin Manhar Mohammed

  Mayachitra (United States)

  54 shared

• Satish Chikkagoudar

  United States Naval Research Laboratory

  27 shared

• Jawadul H. Bappy

  19 shared

• Amit K. Roy–Chowdhury

  16 shared

• Michael Goebel

  16 shared

• Ming Gu

  Zhejiang University

  15 shared

Labs

• Scientific Computing GroupPI

  The lab focuses on numerical analysis, numerical linear algebra, structured matrix decomposition and inversion, fast numerical algorithms, neural network architectures, generalization of DNNs, physics based DNNs, neural operators, efficiency, computational imaging, machine learning, inverse problems, dynamical systems, infinite-dimensional operators, numerical linear algebra, fast solvers for structured matrix representations (HSS, FMM), and more.