arXiv subjects

Yan Tan

Publications and source records attributed to Yan Tan.

13 recordsLinked to original sources

arXiv2026

ChipVerilog: A Large-Scale OpenCores-Derived Benchmark for LLM-Based Verilog RTL Generation

Large language models have shown strong potential for Verilog RTL generation. However, many existing benchmarks are built from short, self-contained module-level tasks. These tasks are useful for controlled evaluation, but they do not fully capture the code scale, hierarchy, and module interactions found in practical IP and processor-core RTL. We present ChipVerilog, a description-to-Verilog generation benchmark built from OpenCores IP/core designs. The benchmark contains 64 generation targets from five design families: OR1200, double-precision FPU, MIPS-16, I2C, and CORDIC. It includes both single-module targets and cross-module targets that instantiate or interact with other RTL modules. Several targets exceed 1,000 lines of Verilog, making ChipVerilog substantially larger and structurally more complex than typical module-level suites. Each benchmark instance is constructed from a pair of specification documents and reference RTL. We extract the target functionality, write a detailed natural-language description, and manually review the description for correctness and clarity. Generated RTL is checked by compilation and validated through equivalence checking for local modules, or by simulation for integrated IP/core targets. Results show that large-scale RTL remains challenging, especially for hierarchical and cross-module designs.

cs.AR↗

arXiv2026

A Uniformly High-Accuracy PML-BIE Method for Scattering by Periodic Arrays of Obstacles: The 2D Case

This paper presents a novel frequency-robust perfectly matched layer (PML) boundary integral equation (BIE) method for solving two-dimensional electromagnetic scattering problems involving periodic arrays of obstacles. In periodic scattering problems, standard BIE formulations based on the quasi-periodic Green's function require the evaluation of lattice sums or challenging Sommerfeld-type integrals, which diverge at Rayleigh--Wood (RW) anomalies. An alternative is to use BIE formulations based on the Helmholtz free-space Green's function, but these are defined on unbounded unit-cell boundaries and therefore require suitable truncation strategies, such as the Windowed Green Function (WGF) method. Although such approaches avoid the use of expensive quasi-periodic Green's functions, they also suffer from breakdowns at RW anomalies unless an appropriate mode correction is incorporated. Similarly, the direct application of PML-BIE techniques to periodic structures experiences comparable difficulties near RW anomalies due to the destruction of exponential convergence near RW anomalies for fixed PML parameters. To overcome this challenge, we propose a modified PML-BIE method that combines the PML technique with a finite-mode correction, ensuring both high accuracy and robustness at and around RW-anomalies. Convergence of the PML-truncated boundary integral operators is proved and several numerical examples are presented to validate the efficiency and performance of the proposed method.

math.NA↗

arXiv2026

TRIP-Evaluate: An Open Multimodal Benchmark for Evaluating Large Models in Transportation

Large language models (LLMs) and multimodal large models (MLLMs) are increasingly used for transportation tasks such as regulation question answering, traffic management support, engineering review, and autonomous-driving scene reasoning. Yet transportation workflows are rule-intensive, computation-intensive, safety-critical, and inherently multimodal. Existing general benchmarks provide limited evidence of whether a model can apply regulations correctly, perform verifiable engineering calculations, or interpret traffic scenes reliably, while the small number of public transportation benchmarks remain narrow in scope and rarely support fine-grained diagnosis across text, images, and point-cloud data. To address this gap, we present TRIP-Evaluate, an open multimodal benchmark for large models in transportation. The benchmark organizes 837 items using a role-task-knowledge taxonomy that covers vehicle, traffic-management, traveler, and planning-and-design functions. Each item is annotated with capability, modality, and difficulty labels, enabling diagnosis from overall accuracy down to specific failure modes. The current release includes 596 text items, 198 image items, and 43 point-cloud items. TRIP-Evaluate also standardizes item construction, quality control, prompting, decoding, and scoring to improve cross-model comparability. Results on a diverse panel of models show that text-based performance is improving, but substantial weaknesses remain in multi-step engineering calculation, rule-constrained reasoning, multimodal scene understanding, and point-cloud understanding. Overall, TRIP-Evaluate provides a reproducible, diagnosable, and engineering-aligned evaluation baseline for model selection, regression testing, and safer deployment in transportation applications.

cs.CV↗

arXiv2026

VerilogCL: A Contrastive Learning Framework for Robust LLM-Based Verilog Generation

Large Language Models (LLMs) have recently achieved strong performance in software code generation. However, applying them to hardware description languages (HDLs), such as Verilog, remains challenging because high-quality training data are relatively scarce. In practice, LLM-generated Verilog often contains syntactic or structural errors that either cause compilation failures or produce functionally incorrect designs, which limit its reliability in hardware design workflows. In this work, we propose VerilogCL, an integrated framework that enhances Verilog code generation by explicitly learning the boundary between correct and erroneous RTL through contrastive learning and proactive error screening. Our approach introduces minimal-error data augmentation, generating paired training samples of correct RTL and minimally perturbed erroneous RTL to teach the model to recognize fine-grained distinctions between correct and erroneous code. We then apply contrastive learning to learn a clearer validity boundary in the representation space, improving the separation between correct and erroneous RTL code. In addition, we introduce a proactive screening module that combines semantic embeddings with token-level uncertainty features to filter low-confidence candidates during generation. Experiments on public benchmarks, including VerilogEval and RTLLM, show that our 7B-parameter model outperforms the evaluated open-source, Verilog-specialized, and commercial baselines in both compilation success rate and functional correctness.

cs.AR↗

arXiv2026

AutoVeriFix+: High-Correctness RTL Generation via Trace-Aware Causal Fix and Semantic Redundancy Pruning

Large language models (LLMs) have demonstrated impressive capabilities in generating software code for high-level programming languages such as Python and C++. However, their application to hardware description languages, such as Verilog, is challenging due to the scarcity of high-quality training data. Current approaches to Verilog code generation using LLMs often focus on syntactic correctness, resulting in code with functional errors. To address these challenges, we propose AutoVeriFix+, a novel three-stage framework that integrates high-level semantic reasoning with state-space exploration to enhance functional correctness and design efficiency. In the first stage, an LLM is employed to generate high-level Python reference models that define the intended circuit behavior. In the second stage, another LLM generates initial Verilog RTL candidates and iteratively fixes syntactic errors. In the third stage, we introduce a Concolic testing engine to exercise deep sequential logic and identify corner-case vulnerabilities. With cycle-accurate execution traces and internal register snapshots, AutoVeriFix+ provides the LLM with the causal context necessary to resolve complex state-transition errors. Furthermore, it will generate a coverage report to identify functionally redundant branches, enabling the LLM to perform semantic pruning for area optimization. Experimental results demonstrate that AutoVeriFix+ achieves over 80% functional correctness on rigorous benchmarks, reaching a pass@10 score of 90.2% on the VerilogEval-machine dataset. In addition, it eliminates an average of 25% redundant logic across benchmarks through trace-aware optimization.

cs.PL↗

arXiv2025

On Topology of Three-dimensional Continua with Singular Points

We propose to model the topology of three-dimensional (3D) continua by Yin sets, regular open semianalytic sets with bounded boundary. Our model differs from manifold-based models in that singular points of a 3D continuum, i.e., boundary points where the tangent plane is not uniquely defined, are treated not as anomalies but as a central subject of our theoretical investigation. We characterize the local and global topology of Yin sets. Then we give a unique boundary representation of Yin sets based on the notion of a glued surface, a quotient space of an orientable compact 2-manifold along a one-dimensional CW complex. Our results apply to 3D continua with arbitrarily complex topology and may be useful in a number of scientific and engineering applications such as solid modeling, computer-aided design, and numerical simulations of multiphase flows with topological changes.

math.GT↗

arXiv2025

On Convergence of the Secant Method

The secant method, as an important approach for solving nonlinear equations, is introduced in nearly all numerical analysis textbooks. However, most textbooks only briefly address the Q-order of convergence of this method, with few providing rigorous mathematical proofs. This paper establishes a rigorous proof for the Q-order of convergence of the secant method and theoretically compares its computational efficiency with that of Newton's method.

math.NA↗

arXiv2025

AutoVeriFix: Automatically Correcting Errors and Enhancing Functional Correctness in LLM-Generated Verilog Code

Large language models (LLMs) have demonstrated impressive capabilities in generating software code for high-level programming languages such as Python and C++. However, their application to hardware description languages, such as Verilog, is challenging due to the scarcity of high-quality training data. Current approaches to Verilog code generation using LLMs often focus on syntactic correctness, resulting in code with functional errors. To address these challenges, we present AutoVeriFix, a novel Python-assisted two-stage framework designed to enhance the functional correctness of LLM-generated Verilog code. In the first stage, LLMs are employed to generate high-level Python reference models that define the intended circuit behavior. In the second stage, these Python models facilitate the creation of automated tests that guide the generation of Verilog RTL implementations. Simulation discrepancies between the reference model and the Verilog code are iteratively used to identify and correct errors, thereby improving the functional accuracy and reliability of the LLM-generated Verilog code. Experimental results demonstrate that our approach significantly outperforms existing state-of-the-art methods in improving the functional correctness of generated Verilog code.

cs.AR↗

arXiv2025

A multiphase cubic MARS method for fourth- and higher-order interface tracking of two or more materials with arbitrary topology and geometry

For interface tracking of an arbitrary number of materials in two dimensions, we propose a multiphase cubic MARS method that (a) represents the topology and geometry of the interface via graphs, cycles, and cubic splines, (b) applies to any number of materials with arbitrarily complex topology and geometry, (c) maintains an $(r,h)$-regularity of the interface so that the distance between any pair of adjacent markers is within a user-specified range, (d) distributes the markers adaptively along the interface so that arcs with high curvature are resolved by densely populated markers, and (e) achieves fourth-, sixth-, and eighth-order accuracy both in time and in space.} In particular, all possible types of junctions, which pose challenges to VOF methods and level-set methods, are handled with ease. Results of a variety of benchmark tests confirm the analysis and demonstrate the superior accuracy, efficiency, and versatility of the proposed method.

math.NA↗

arXiv2024

A fourth-order, multigrid cut-cell method for solving Poisson's equation in three-dimensional irregular domains

We propose a fourth-order cut-cell method for solving Poisson's equations in three-dimensional irregular domains. Major distinguishing features of our method include (a) applicable to arbitrarily complex geometries, (b) high order discretization, (c) optimal complexity. Feature (a) is achieved by Yin space, which is a mathematical model for three-dimensional continua. Feature (b) is accomplished by poised lattice generation (PLG) algorithm, which finds stencils near the irregular boundary for polynomial fitting. Besides, for feature (c), we design a modified multigrid solver whose complexity is theoretically optimal by applying nested dissection (ND) ordering method.

math.NA↗

arXiv2023

Adaptive Event-triggered Control For Strict-feedback Systems With Time-varying Parameters

In this article, we develop a new adaptive event-triggered asymptotic control scheme for strict-feedback systems with fast time-varying parameters. To deal with time-varying parameters with unknown variation boundaries in the feedback path and the input path, we construct three adaptive laws for parameter estimation, two for the uncertain parameters in the feedback path and one for the uncertain parameters in the input path. In particular, two sets of tuning functions are introduced to avoid over-parametrization. Additionally, an event-triggering mechanism is embedded in this adaptive control framework to reduce the data transmission from the controller to the actuator. We also introduce a soft sign function to handle the perturbations caused by sampling errors to achieve asymptotic stability and avoid the so-called parameter drift. The stability analysis shows that the closed-loop system is globally uniformly asymptotically stable and the Zeno behavior can be excluded. Simulation results verify the effectiveness and performance of the proposed adaptive scheme.

eess.SY↗

arXiv2019

Introduction of water-vapor broadening coefficients and their temperature dependence exponents into the HITRAN database, Part I: CO2, N2O, CO, CH4, O2, NH3, and H2S

The amount of water vapor in the terrestrial atmosphere is highly variable both spatially and temporally. In the tropics it sometimes constitutes 4-5% of the atmosphere. At the same time collisional broadening of spectral lines by water vapor is much larger than that by nitrogen and oxygen. Therefore, in order to accurately characterize and model spectra of the atmospheres with significant amounts of water vapor, the line-shape parameters for spectral lines broadened by water vapor are required. In this work, the line-broadening coefficients (and their temperature dependence exponents) due to the pressure of water vapor for lines of CO2, N2O, CO, CH4, O2, NH3, and H2S from both experimental and theoretical studies were collected and carefully reviewed. A set of semi-empirical models based on these collected data was created and then used to estimate water broadening and its temperature dependence for all transitions of selected molecules in the HITRAN2016 database.

physics.ao-ph↗

arXiv2019

Some Hopf Algebras related to $\mathfrak{sl}_2$

We define a series of Artin-Schelter Gorenstein Hopf algebras $H_\beta$ with injective dimensions 3. Radford's Hopf algebra and Gelaki's Hopf algebra are homomorphic images of $H_\beta$. We determine its Grothendieck ring $G_0(H_\beta)$. Meanwhile we can obtain Grothendieck rings of Gelaki's Hopf algebras and Radford's Hopf algebras $U_{(N,\nu,\omega)}$ in \cite{R}, and non-isomorphic Hopf algebras with isomorphic Grothendieck rings.

math.QA↗