arXiv subjects

Boian S. Alexandrov

Publications and source records attributed to Boian S. Alexandrov.

At least 19 recordsLinked to original sources

arXiv2026

A Tensor-Train Discontinuous Galerkin Method for the Vlasov-Maxwell System

We present a tensor-train discontinuous Galerkin (TT-DG) formulation for the Vlasov--Maxwell system that combines a modal DG discretization with low-rank tensor representations of the phase-space solution and discrete operators. The formulation exploits the tensor-product structure of the DG discretization to perform quadrature, differentiation, nonlinear upwind flux evaluation, and time integration directly in compressed form. The method is evaluated on several standard 1D2V Vlasov--Maxwell benchmark problems, including the streaming Weibel instability, weak Landau damping, and two-stream instability problems. Across these problems, the TT formulation reproduces the accuracy and conservation behavior of the underlying full-grid DG discretization while substantially reducing memory usage and runtime. For weakly nonlinear problems, compression ratios exceeding $10^4$ are obtained together with significant speedups relative to the full-grid solver. For the strongly nonlinear two-stream instability problem, the TT formulation remains effective despite reduced compressibility caused by fine-scale phase-space filamentation. These results demonstrate that tensor-train representations provide an effective approach for reducing the computational cost of deterministic DG-based kinetic plasma simulations while retaining the favorable numerical properties of the underlying discretization.

math.NA↗

arXiv2026

Detecting Satellites in Radio-Frequency Data via Semi-Supervised Learning

Radio-frequency (RF) monitoring is essential for space domain awareness, but it often generates large, variable, and sparsely populated datasets with few labels. These observations can capture satellites, space debris, and the ionospheric background, yet interpreting them typically requires specialized subject-matter expertise. Supervised deep learning methods can perform well on labeled RF data, but they require many annotated examples and may need careful retraining as RF conditions change. Semi-supervised approaches offer a practical alternative for limited-data settings by using unlabeled observations to reveal latent patterns that experts can interpret. In this paper, we present a semi-supervised RF detection and classification workflow for satellite monitoring that combines Non-negative Matrix Factorization with automatic model determination (NMFk), expert-guided cluster interpretation, and classifier-based prediction. We first represent RF observations as a non-negative feature matrix and apply NMFk to estimate the number of clusters that best captures patterns in the unlabeled data. Subject-matter experts then assign physical meaning to the resulting clusters, including satellite detections, ionospheric environmental conditions, and other RF event categories. Finally, we train a classifier on these interpreted clusters to evaluate performance on a test set and categorize future observations. This pipeline reduces reliance on large pre-labeled datasets by pairing unsupervised factorization with expert interpretation, enabling an interpretable and transferable methodology for detecting, observing, and classifying behavior in RF data.

cs.LG↗

arXiv2025

Space-Time Spectral Collocation Tensor-Network Approach for Maxwell's Equations

In this work, we develop a space--time Chebyshev spectral collocation method for three-dimensional Maxwell's equations and combine it with tensor-network techniques in Tensor-Train (TT) format. Under constant material parameters, the Maxwell system is reduced to a vector wave equation for the electric field, which we discretize globally in space and time using a staggered spectral collocation scheme. The staggered polynomial spaces are designed so that the discrete curl and divergence operators preserve the divergence-free constraint on the magnetic field. The magnetic field is then recovered in a space--time post-processing step via a discrete version of Faraday's law. The global space--time formulation yields a large but highly structured linear system, which we approximate in low-rank TT-format directly from the operator and data, without assuming that the forcing is separable in space and time. We derive condition-number bounds for the resulting operator and prove spectral convergence estimates for both the electric and magnetic fields. Numerical experiments for three-dimensional electromagnetic test problems confirm the theoretical convergence rates and show that the TT-based solver maintains accuracy with approximately linear complexity in the number of grid points in space and time.

math.NA↗

arXiv2025

Tensor-Train Operator Inference

In this study, we present a tensor--train framework for nonintrusive operator inference aimed at learning discrete operators and using them to predict solutions of physical governing equations. Our framework comprises three approaches: full--order tensor--train operator inference, full--order quantized tensor--train operator inference, and reduced--order tensor--train operator inference. In each case, snapshot data is represented in tensor--train format--either through compression or cross interpolation--enabling the efficient handling of extremely large datasets with significantly reduced computational effort compared to standard methods. The effectiveness of each approach is demonstrated through numerical experiments related to Computational Fluid Dynamics and benchmarked against the standard reduced--order operator inference method, highlighting the advantages of the tensor--train representations in both accuracy and scalability.

math.NA↗

arXiv2025

Topic Modeling and Link-Prediction for Material Property Discovery

Link prediction infers missing or future relations between graph nodes, based on connection patterns. Scientific literature networks and knowledge graphs are typically large, sparse, and noisy, and often contain missing links between entities. We present an AI-driven hierarchical link prediction framework that integrates matrix factorization to infer hidden associations and steer discovery in complex material domains. Our method combines Hierarchical Nonnegative Matrix Factorization (HNMFk) and Boolean matrix factorization (BNMFk) with automatic model selection, as well as Logistic matrix factorization (LMF), we use to construct a three-level topic tree from a 46,862-document corpus focused on 73 transition-metal dichalcogenides (TMDs). These materials are studied in a variety of physics fields with many current and potential applications. An ensemble BNMFk + LMF approach fuses discrete interpretability with probabilistic scoring. The resulting HNMFk clusters map each material onto coherent topics like superconductivity, energy storage, and tribology. Also, missing or weakly connected links are highlight between topics and materials, suggesting novel hypotheses for cross-disciplinary exploration. We validate our method by removing publications about superconductivity in well-known superconductors, and show the model predicts associations with the superconducting TMD clusters. This shows the method finds hidden connections in a graph of material to latent topic associations built from scientific literature, especially useful when examining a diverse corpus of scientific documents covering the same class of phenomena or materials but originating from distinct communities and perspectives. The inferred links generating new hypotheses, produced by our method, are exposed through an interactive Streamlit dashboard, designed for human-in-the-loop scientific discovery.

cs.LG↗

arXiv2025

Breaking the Curse of Dimensionality: Solving Configurational Integrals for Crystalline Solids by Tensor Networks

Accurately evaluating configurational integrals for dense solids remains a central and difficult challenge in the statistical mechanics of condensed systems. Here, we present a novel tensor network approach that reformulates the high-dimensional configurational integral for identical-particle crystals into a sequence of computationally efficient summations. We represent the integrand as a high-dimensional tensor and apply tensor-train (TT) decomposition together with a custom TT-cross interpolation scheme. This approach avoids the need to explicitly construct the full tensor, which would otherwise be computationally intractable. We introduce tailored rank-1 and rank-2 schemes optimized for sharply peaked Boltzmann probability densities, typical in crystalline solids. When applied to the calculation of internal energy and pressure-temperature curves for crystalline copper (Cu) and argon (Ar), as well as the alpha-to-beta phase transition in tin (Sn), our method accurately reproduces molecular dynamics simulation results using tight-binding, machine learning (HIP-NN), and MEAM potentials, all within seconds of computation time.

cond-mat.stat-mech↗

arXiv2025

Bridging Legal Knowledge and AI: Retrieval-Augmented Generation with Vector Stores, Knowledge Graphs, and Hierarchical Non-negative Matrix Factorization

Agentic Generative AI, powered by Large Language Models (LLMs) with Retrieval-Augmented Generation (RAG), Knowledge Graphs (KGs), and Vector Stores (VSs), represents a transformative technology applicable to specialized domains such as legal systems, research, recommender systems, cybersecurity, and global security, including proliferation research. This technology excels at inferring relationships within vast unstructured or semi-structured datasets. The legal domain here comprises complex data characterized by extensive, interrelated, and semi-structured knowledge systems with complex relations. It comprises constitutions, statutes, regulations, and case law. Extracting insights and navigating the intricate networks of legal documents and their relations is crucial for effective legal research. Here, we introduce a generative AI system that integrates RAG, VS, and KG, constructed via Non-Negative Matrix Factorization (NMF), to enhance legal information retrieval and AI reasoning and minimize hallucinations. In the legal system, these technologies empower AI agents to identify and analyze complex connections among cases, statutes, and legal precedents, uncovering hidden relationships and predicting legal trends-challenging tasks that are essential for ensuring justice and improving operational efficiency. Our system employs web scraping techniques to systematically collect legal texts, such as statutes, constitutional provisions, and case law, from publicly accessible platforms like Justia. It bridges the gap between traditional keyword-based searches and contextual understanding by leveraging advanced semantic representations, hierarchical relationships, and latent topic discovery. This framework supports legal document clustering, summarization, and cross-referencing, for scalable, interpretable, and accurate retrieval for semi-structured data while advancing computational law and AI.

cs.CL↗

arXiv2024

Space-Time Spectral Element Tensor Network Approach for Time Dependent Convection Diffusion Reaction Equation with Variable Coefficients

In this paper, we present a new space-time Petrov-Galerkin-like method. This method utilizes a mixed formulation of Tensor Train (TT) and Quantized Tensor Train (QTT), designed for the spectral element discretization (Q1-SEM) of the time-dependent convection-diffusion-reaction (CDR) equation. We reformulate the assembly process of the spectral element discretized CDR to enhance its compatibility with tensor operations and introduce a low-rank tensor structure for the spectral element operators. Recognizing the banded structure inherent in the spectral element framework's discrete operators, we further exploit the QTT format of the CDR to achieve greater speed and compression. Additionally, we present a comprehensive approach for integrating variable coefficients of CDR into the global discrete operators within the TT/QTT framework. The effectiveness of the proposed method, in terms of memory efficiency and computational complexity, is demonstrated through a series of numerical experiments, including a semi-linear example.

math.NA↗

arXiv2024

Domain-Specific Retrieval-Augmented Generation Using Vector Stores, Knowledge Graphs, and Tensor Factorization

Large Language Models (LLMs) are pre-trained on large-scale corpora and excel in numerous general natural language processing (NLP) tasks, such as question answering (QA). Despite their advanced language capabilities, when it comes to domain-specific and knowledge-intensive tasks, LLMs suffer from hallucinations, knowledge cut-offs, and lack of knowledge attributions. Additionally, fine tuning LLMs' intrinsic knowledge to highly specific domains is an expensive and time consuming process. The retrieval-augmented generation (RAG) process has recently emerged as a method capable of optimization of LLM responses, by referencing them to a predetermined ontology. It was shown that using a Knowledge Graph (KG) ontology for RAG improves the QA accuracy, by taking into account relevant sub-graphs that preserve the information in a structured manner. In this paper, we introduce SMART-SLIC, a highly domain-specific LLM framework, that integrates RAG with KG and a vector store (VS) that store factual domain specific information. Importantly, to avoid hallucinations in the KG, we build these highly domain-specific KGs and VSs without the use of LLMs, but via NLP, data mining, and nonnegative tensor factorization with automatic model selection. Pairing our RAG with a domain-specific: (i) KG (containing structured information), and (ii) VS (containing unstructured information) enables the development of domain-specific chat-bots that attribute the source of information, mitigate hallucinations, lessen the need for fine-tuning, and excel in highly domain-specific question answering tasks. We pair SMART-SLIC with chain-of-thought prompting agents. The framework is designed to be generalizable to adapt to any specific or specialized domain. In this paper, we demonstrate the question answering capabilities of our framework on a corpus of scientific publications on malware analysis and anomaly detection.

cs.CL↗

arXiv2024

High-order Tensor-Train Finite Volume Method for Shallow Water Equations

In this paper, we introduce a high-order tensor-train (TT) finite volume method for the Shallow Water Equations (SWEs). We present the implementation of the $3^{rd}$ order Upwind and the $5^{th}$ order Upwind and WENO reconstruction schemes in the TT format. It is shown in detail that the linear upwind schemes can be implemented by directly manipulating the TT cores while the WENO scheme requires the use of TT cross interpolation for the nonlinear reconstruction. In the development of numerical fluxes, we directly compute the flux for the linear SWEs without using TT rounding or cross interpolation. For the nonlinear SWEs where the TT reciprocal of the shallow water layer thickness is needed for fluxes, we develop an approximation algorithm using Taylor series to compute the TT reciprocal. The performance of the TT finite volume solver with linear and nonlinear reconstruction options is investigated under a physically relevant set of validation problems. In all test cases, the TT finite volume method maintains the formal high-order accuracy of the corresponding traditional finite volume method. In terms of speed, the TT solver achieves up to 124x acceleration of the traditional full-tensor scheme.

math.NA↗

arXiv2024

TopicTag: Automatic Annotation of NMF Topic Models Using Chain of Thought and Prompt Tuning with LLMs

Topic modeling is a technique for organizing and extracting themes from large collections of unstructured text. Non-negative matrix factorization (NMF) is a common unsupervised approach that decomposes a term frequency-inverse document frequency (TF-IDF) matrix to uncover latent topics and segment the dataset accordingly. While useful for highlighting patterns and clustering documents, NMF does not provide explicit topic labels, necessitating subject matter experts (SMEs) to assign labels manually. We present a methodology for automating topic labeling in documents clustered via NMF with automatic model determination (NMFk). By leveraging the output of NMFk and employing prompt engineering, we utilize large language models (LLMs) to generate accurate topic labels. Our case study on over 34,000 scientific abstracts on Knowledge Graphs demonstrates the effectiveness of our method in enhancing knowledge management and document organization.

cs.LG↗

arXiv2024

Binary Bleed: Fast Distributed and Parallel Method for Automatic Model Selection

In several Machine Learning (ML) clustering and dimensionality reduction approaches, such as non-negative matrix factorization (NMF), RESCAL, and K-Means clustering, users must select a hyper-parameter k to define the number of clusters or components that yield an ideal separation of samples or clean clusters. This selection, while difficult, is crucial to avoid overfitting or underfitting the data. Several ML applications use scoring methods (e.g., Silhouette and Davies Boulding scores) to evaluate the cluster pattern stability for a specific k. The score is calculated for different trials over a range of k, and the ideal k is heuristically selected as the value before the model starts overfitting, indicated by a drop or increase in the score resembling an elbow curve plot. While the grid-search method can be used to accurately find a good k value, visiting a range of k can become time-consuming and computationally resource-intensive. In this paper, we introduce the Binary Bleed method based on binary search, which significantly reduces the k search space for these grid-search ML algorithms by truncating the target k values from the search space using a heuristic with thresholding over the scores. Binary Bleed is designed to work with single-node serial, single-node multi-processing, and distributed computing resources. In our experiments, we demonstrate the reduced search space gain over a naive sequential search of the ideal k and the accuracy of the Binary Bleed in identifying the correct k for NMFk, K-Means pyDNMFk, and pyDRESCALk with Silhouette and Davies Boulding scores. We make our implementation of Binary Bleed for the NMF algorithm available on GitHub.

cs.DC↗

arXiv2024

Tensor Network Space-Time Spectral Collocation Method for Solving the Nonlinear Convection Diffusion Equation

Spectral methods provide highly accurate numerical solutions for partial differential equations, exhibiting exponential convergence with the number of spectral nodes. Traditionally, in addressing time-dependent nonlinear problems, attention has been on low-order finite difference schemes for time discretization and spectral element schemes for spatial variables. However, our recent developments have resulted in the application of spectral methods to both space and time variables, preserving spectral convergence in both domains. Leveraging Tensor Train techniques, our approach tackles the curse of dimensionality inherent in space-time methods. Here, we extend this methodology to the nonlinear time-dependent convection-diffusion equation. Our discretization scheme exhibits a low-rank structure, facilitating translation to tensor-train (TT) format. Nevertheless, controlling the TT-rank across Newton's iterations, needed to deal with the nonlinearity, poses a challenge, leading us to devise the "Step Truncation TT-Newton" method. We demonstrate the exponential convergence of our methods through various benchmark examples. Importantly, our scheme offers significantly reduced memory requirement compared to the full-grid scheme.

math.NA↗

arXiv2024

Cyber-Security Knowledge Graph Generation by Hierarchical Nonnegative Matrix Factorization

Much of human knowledge in cybersecurity is encapsulated within the ever-growing volume of scientific papers. As this textual data continues to expand, the importance of document organization methods becomes increasingly crucial for extracting actionable insights hidden within large text datasets. Knowledge Graphs (KGs) serve as a means to store factual information in a structured manner, providing explicit, interpretable knowledge that includes domain-specific information from the cybersecurity scientific literature. One of the challenges in constructing a KG from scientific literature is the extraction of ontology from unstructured text. In this paper, we address this topic and introduce a method for building a multi-modal KG by extracting structured ontology from scientific papers. We demonstrate this concept in the cybersecurity domain. One modality of the KG represents observable information from the papers, such as the categories in which they were published or the authors. The second modality uncovers latent (hidden) patterns of text extracted through hierarchical and semantic non-negative matrix factorization (NMF), such as named entities, topics or clusters, and keywords. We illustrate this concept by consolidating more than two million scientific papers uploaded to arXiv into the cyber-domain, using hierarchical and semantic NMF, and by building a cyber-domain-specific KG.

cs.AI↗

arXiv2024

Catch'em all: Classification of Rare, Prominent, and Novel Malware Families

National security is threatened by malware, which remains one of the most dangerous and costly cyber threats. As of last year, researchers reported 1.3 billion known malware specimens, motivating the use of data-driven machine learning (ML) methods for analysis. However, shortcomings in existing ML approaches hinder their mass adoption. These challenges include detection of novel malware and the ability to perform malware classification in the face of class imbalance: a situation where malware families are not equally represented in the data. Our work addresses these shortcomings with MalwareDNA: an advanced dimensionality reduction and feature extraction framework. We demonstrate stable task performance under class imbalance for the following tasks: malware family classification and novel malware detection with a trade-off in increased abstention or reject-option rate.

cs.CR↗

arXiv2024

Tensor Network Space-Time Spectral Collocation Method for Time Dependent Convection-Diffusion-Reaction Equations

Emerging tensor network techniques for solutions of Partial Differential Equations (PDEs), known for their ability to break the curse of dimensionality, deliver new mathematical methods for ultrafast numerical solutions of high-dimensional problems. Here, we introduce a Tensor Train (TT) Chebyshev spectral collocation method, in both space and time, for solution of the time dependent convection-diffusion-reaction (CDR) equation with inhomogeneous boundary conditions, in Cartesian geometry. Previous methods for numerical solution of time dependent PDEs often use finite difference for time, and a spectral scheme for the spatial dimensions, which leads to slow linear convergence. Spectral collocation space-time methods show exponential convergence, however, for realistic problems they need to solve large four-dimensional systems. We overcome this difficulty by using a TT approach as its complexity only grows linearly with the number of dimensions. We show that our TT space-time Chebyshev spectral collocation method converges exponentially, when the solution of the CDR is smooth, and demonstrate that it leads to very high compression of linear operators from terabytes to kilobytes in TT-format, and tens of thousands times speedup when compared to full grid space-time spectral method. These advantages allow us to obtain the solutions at much higher resolutions.

math.NA↗

arXiv2023

Interactive Distillation of Large Single-Topic Corpora of Scientific Papers

Highly specific datasets of scientific literature are important for both research and education. However, it is difficult to build such datasets at scale. A common approach is to build these datasets reductively by applying topic modeling on an established corpus and selecting specific topics. A more robust but time-consuming approach is to build the dataset constructively in which a subject matter expert (SME) handpicks documents. This method does not scale and is prone to error as the dataset grows. Here we showcase a new tool, based on machine learning, for constructively generating targeted datasets of scientific literature. Given a small initial "core" corpus of papers, we build a citation network of documents. At each step of the citation network, we generate text embeddings and visualize the embeddings through dimensionality reduction. Papers are kept in the dataset if they are "similar" to the core or are otherwise pruned through human-in-the-loop selection. Additional insight into the papers is gained through sub-topic modeling using SeNMFk. We demonstrate our new tool for literature review by applying it to two different fields in machine learning.

cs.IR↗

arXiv2023

Tensor Networks for Solving Realistic Time-independent Boltzmann Neutron Transport Equation

Tensor network techniques, known for their low-rank approximation ability that breaks the curse of dimensionality, are emerging as a foundation of new mathematical methods for ultra-fast numerical solutions of high-dimensional Partial Differential Equations (PDEs). Here, we present a mixed Tensor Train (TT)/Quantized Tensor Train (QTT) approach for the numerical solution of time-independent Boltzmann Neutron Transport equations (BNTEs) in Cartesian geometry. Discretizing a realistic three-dimensional (3D) BNTE by (i) diamond differencing, (ii) multigroup-in-energy, and (iii) discrete ordinate collocation leads to huge generalized eigenvalue problems that generally require a matrix-free approach and large computer clusters. Starting from this discretization, we construct a TT representation of the PDE fields and discrete operators, followed by a QTT representation of the TT cores and solving the tensorized generalized eigenvalue problem in a fixed-point scheme with tensor network optimization techniques. We validate our approach by applying it to two realistic examples of 3D neutron transport problems, currently solved by the PARallel TIme-dependent SN (PARTISN) solver. We demonstrate that our TT/QTT method, executed on a standard desktop computer, leads to a yottabyte compression of the memory storage, and more than 7500 times speedup with a discrepancy of less than 1e-5 when compared to the PARTISN solution.

math.NA↗