arXiv subjects

Ye Ji

Publications and source records attributed to Ye Ji.

13 recordsLinked to original sources

arXiv2026

Bijectivity analysis of rational T-spline surfaces via Bernstein representations

Ensuring the bijectivity of spline-based parameterizations is fundamental in geometric modeling and isogeometric analysis, as invalid mappings may lead to self-intersections, singular Jacobians, and numerical instability. While T-splines offer enhanced flexibility through local refinement, this flexibility also makes bijectivity verification significantly more challenging. In this work, we propose a rigorous and efficient framework for bijectivity analysis of rational T-spline surfaces based on B\'ezier extraction. The key idea is to reformulate the T-spline representation into a collection of element-wise rational B\'ezier patches, on which the Gram determinant of the mapping admits a Bernstein polynomial representation. This enables a coefficient-based analysis of local regularity by exploiting the convex hull and positivity properties of the Bernstein basis. Based on this formulation, we derive a sufficient condition for bijectivity from the nonnegativity of Bernstein coefficients, together with a necessary condition based on the sign consistency of corner coefficients. For cases where these conditions are inconclusive, we introduce a hierarchical subdivision strategy that progressively localizes ambiguous regions and resolves them through refinement. The proposed method provides a certified and adaptive procedure for bijectivity verification that avoids dense numerical sampling and remains computationally efficient. Numerical experiments on complex T-spline geometries demonstrate that the approach accurately detects both valid and near-degenerate configurations, while scaling effectively to large models with thousands of rational B\'ezier patches. The framework is fully compatible with standard isogeometric analysis workflows.

math.NA↗

arXiv2026

Laguna M.1/XS.2 Technical Report

We present Laguna M.1 and Laguna XS.2, two Mixture-of-Experts foundation models built for long-horizon, agentic coding: M.1 has $225.8$B total parameters ($23.4$B activated per token) and XS.2 has $33.4$B total ($3$B activated). Both models were trained from scratch end-to-end inside the same internal system that we refer to as our Model Factory: a tightly-integrated stack of versioned data, training, evaluation, and inference components that turn model development into an industrial process. We describe the principles and design choices of the Model Factory and also detail the end-to-end training process of our models, throughout pre-training data and architecture, post-training stages, evaluation, and quantization. On agentic software engineering and terminal benchmarks (SWE-bench Verified, SWE-bench Multilingual, SWE-Bench Pro, and Terminal-Bench 2.0) M.1 and XS.2 are competitive with state-of-the-art open models in their respective weight classes. Laguna XS.2 weights are released under Apache~2.0 at https://huggingface.co/collections/poolside/laguna-xs2.

cs.AI↗

arXiv2026

Parameterization-driven arbitrary Lagrangian-Eulerian method for large-deformation isogeometric fluid-structure interaction

Body-fitted arbitrary Lagrangian-Eulerian (ALE) methods provide a sharp representation of the fluid-structure interface but rely on mesh-update strategies that incrementally deform a reference configuration. To address this issue, we reformulate the ALE mesh-motion problem in the isogeometric setting as a sequence of independent domain parameterization problems. At each time step, a multi-patch spline parameterization of the fluid domain is constructed from the current interface geometry. Three technical components realize this framework: (i) a barrier-function-based spline parameterization that enforces a strictly positive Jacobian at every time step; (ii) a tangential-slip reparameterization that handles unbounded cumulative rotations of closed domains, where no fixed boundary-to-parameter correspondence is admissible; and (iii) a constant-preserving quasi-interpolation operator for solution transfer between consecutive parameterizations, ensuring that the discrete geometric conservation law holds algebraically. We validate the method on three two-dimensional FSI benchmarks, covering standard and large-rotation regimes, and on a three-dimensional rotor problem. On a rotating-square benchmark, the tangential-slip strategy enables simulations under sustained rotation far beyond the range accessible to classical mesh-update schemes--a regime that is fundamentally inaccessible to any mesh-deformation formulation, not merely numerically difficult. A three-dimensional rotor example further demonstrates that the framework extends naturally to volumetric spline parameterizations. Finally, we show that the per-step spline parameterizations can be used directly within a standard finite element solver.

math.NA↗

arXiv2025

Regularity analysis and verification of Coons volume mappings

The Coons volume provides a classical approach for constructing three-dimensional parametric mappings via boundary surface interpolation and is widely employed in volumetric mesh generation, computer-aided geometric design, and isogeometric analysis. However, due to curvature variations and continuity limitations of the boundary surfaces, the Jacobian determinant of a Coons volume may locally vanish or become negative, resulting in a non-regular mapping. This undermines mesh quality and compromises the stability of subsequent numerical computations. Ensuring the regularity of Coons volumes is therefore critical for robust parametric modeling. This paper develops a systematic framework for analyzing and verifying the regularity of Coons volumes. We first derive a general sufficient condition applicable to arbitrary boundary parameterizations, independent of specific analytical forms. For B\'ezier-form Coons volumes, we introduce a criterion based on the B\'ezier coefficients of the Jacobian determinant, transforming the verification problem into checking the positivity of control coefficients. Furthermore, we construct a necessary condition by applying a subdivision strategy combined with the B\'ezier blossoming technique, ensuring that regularity is preserved in all subdomains. By integrating these conditions, we design an efficient verification algorithm whose correctness and computational performance are validated through numerical experiments. We observe that the regularity of a Coons volume is closely related to the geometric similarity of its opposite boundary surfaces. Moreover, through B\'ezier extraction, the algorithm is extended to multi-patch B-spline volumes of arbitrary topology. Numerical tests show that the method completes regularity verification in milliseconds, enabling real-time application.

math.NA↗

arXiv2025

Efficient thermal simulation in metal additive manufacturing via semi-analytical isogeometric analysis

Thermal modeling of Laser Powder Bed Fusion (LPBF) is challenging due to steep, rapidly moving thermal gradients induced by the laser, which are difficult to resolve accurately with conventional Finite Element Methods. Highly refined, dynamically adaptive spatial discretization is typically required, leading to prohibitive computational costs. Semi-analytical approaches mitigate this by decomposing the temperature field into an analytical point-source solution and a complementary numerical field that enforces boundary conditions. However, state-of-the-art implementations either necessitate extensive mesh refinement near boundaries or rely on restrictive image source techniques, limiting their efficiency and applicability to complex geometries. This study presents a novel reformulation of the semi-analytical framework using Isogeometric Analysis. The laser heat input is captured by the analytical point-source solution, while the complementary correction field, which imposes boundary conditions, is solved using a spline-based IGA discretization. The governing heat equation for the correction field is cast in a weak form, discretized with NURBS basis functions, and advanced in time using an implicit $\theta$-scheme. This approach leverages IGA's key advantages: exact geometry representation, higher-order continuity, and superior accuracy per degree of freedom. These features unlock efficient thermal modeling of realistic parts with complex contours. Our strategy eliminates the need for scan-wise remeshing and robustly handles intricate geometric features like sharp corners and varying cross-sections. Numerical examples demonstrate that the proposed semi-analytical IGA method delivers accurate temperature predictions and achieves substantial computational efficiency gains compared to standard FEM, establishing it as a powerful new tool for high-fidelity thermal simulation in LPBF.

math.NA↗

arXiv2025

IGA-LBM: Isogeometric lattice Boltzmann method

The lattice Boltzmann method (LBM) offers intrinsic parallelism and simple boundary treatment, but Cartesian lattices approximate curved boundaries by stair steps, causing spurious forces and boundary-layer errors. We present an isogeometric collocation lattice Boltzmann method (IGA-LBM) that solves the discrete-velocity BGK system in strong form on body-fitted B-spline and NURBS geometries. Distribution functions are collocated at Greville points, advection is evaluated with high-order operators on the exact spline mapping, and time integration uses a four-stage Runge-Kutta scheme. Exact geometric metrics preserve a uniform free stream to machine precision on curved grids while retaining formal accuracy. The analysis recovers the incompressible Navier-Stokes equations with viscosity nu = cs^2 tau and shows that the main isogeometric advantage is exact geometry rather than a new interior stencil. Centered collocation is stabilized by a high-order filter, a physical-node closure restores fourth-order accuracy near clustered walls, and stiff collision limits the explicit step to dt <= 2.785 tau, scaling as O(Re^-1). Tests confirm the predicted accuracy and the O(Ma^2) compressibility floor. Validation covers the Ghia lid-driven cavity, steady and unsteady flow past a circular cylinder, and a body-fitted NACA0012 airfoil. For the cylinder, recirculation length is within about 9 percent and the Strouhal number within about 2.5 percent of reference values; drag is 6-12 percent above consensus and decreases with refinement, with stable wakes up to Re = 1000. For NACA0012 at Re = 500 and 10 degrees incidence, surface pressure and skin friction agree with reference data within a few percent. The method provides a high-order, free-stream-preserving LBM for curved-boundary flows based on exact B-spline and NURBS geometry, with demonstrated accuracy, stability, and geometric fidelity.

math.NA↗

arXiv2025

Hierarchical Intent-guided Optimization with Pluggable LLM-Driven Semantics for Session-based Recommendation

Session-based Recommendation (SBR) aims to predict the next item a user will likely engage with, using their interaction sequence within an anonymous session. Existing SBR models often focus only on single-session information, ignoring inter-session relationships and valuable cross-session insights. Some methods try to include inter-session data but struggle with noise and irrelevant information, reducing performance. Additionally, most models rely on item ID co-occurrence and overlook rich semantic details, limiting their ability to capture fine-grained item features. To address these challenges, we propose a novel hierarchical intent-guided optimization approach with pluggable LLM-driven semantic learning for session-based recommendations, called HIPHOP. First, we introduce a pluggable embedding module based on large language models (LLMs) to generate high-quality semantic representations, enhancing item embeddings. Second, HIPHOP utilizes graph neural networks (GNNs) to model item transition relationships and incorporates a dynamic multi-intent capturing module to address users' diverse interests within a session. Additionally, we design a hierarchical inter-session similarity learning module, guided by user intent, to capture global and local session relationships, effectively exploring users' long-term and short-term interests. To mitigate noise, an intent-guided denoising strategy is applied during inter-session learning. Finally, we enhance the model's discriminative capability by using contrastive learning to optimize session representations. Experiments on multiple datasets show that HIPHOP significantly outperforms existing methods, demonstrating its effectiveness in improving recommendation quality. Our code is available: https://github.com/hjx159/HIPHOP.

cs.IR↗

arXiv2024

Boundary parameter matching for isogeometric analysis using Schwarz-Christoffel mapping

Isogeometric analysis has brought a paradigm shift in integrating computational simulations with geometric designs across engineering disciplines. This technique necessitates analysis-suitable parameterization of physical domains to fully harness the synergy between Computer-Aided Design and Computer-Aided Engineering analyses. The existing methods often fix boundary parameters, leading to challenges in elongated geometries such as fluid channels and tubular reactors. This paper presents an innovative solution for the boundary parameter matching problem, specifically designed for analysis-suitable parameterizations. We employ a sophisticated Schwarz-Christoffel mapping technique, which is instrumental in computing boundary correspondences. A refined boundary curve reparameterization process complements this. Our dual-strategy approach maintains the geometric exactness and continuity of input physical domains, overcoming limitations often encountered with the existing reparameterization techniques. By employing our proposed boundary parameter method, we show that even a simple linear interpolation approach can effectively construct a satisfactory analysis-suitable parameterization. Our methodology offers significant improvements over traditional practices, enabling the generation of analysis-suitable and geometrically precise models, which is crucial for ensuring accurate simulation results. Numerical experiments show the capacity of the proposed method to enhance the quality and reliability of isogeometric analysis workflows.

math.NA↗

arXiv2023

A U-Net-Based Self-Stitching Method for Generating Periodic Grain Structures

When modeling microstructures, the computational resource requirements increase rapidly as the simulation domain becomes larger. As a result, simulating a small representative fraction under periodic boundary conditions is often a necessary simplification. However, the truncated structures leave nonphysical boundaries, which are detrimental to numerical modeling. Here, we propose a self-stitching algorithm for generating periodic structures, demonstrated in a grain structure. The main idea of our algorithm is to artificially add structural information between mismatched boundary pairs, using the hierarchical spatial predictions of the U-Net. The algorithm provides an automatic and unbiased way to obtain periodic boundaries in grain structures and can be applied to porous microstructures in a similar way.

cond-mat.mtrl-sci↗

arXiv2023

A short report on preconditioned Anderson acceleration method

In this report, we present a versatile and efficient preconditioned Anderson acceleration (PAA) method for fixed-point iterations. The proposed framework offers flexibility in balancing convergence rates (linear, super-linear, or quadratic) and computational costs related to the Jacobian matrix. Our approach recovers various fixed-point iteration techniques, including Picard, Newton, and quasi-Newton iterations. The PAA method can be interpreted as employing Anderson acceleration (AA) as its own preconditioner or as an accelerator for quasi-Newton methods when their convergence is insufficient. Adaptable to a wide range of problems with differing degrees of nonlinearity and complexity, the method achieves improved convergence rates and robustness by incorporating suitable preconditioners. We test multiple preconditioning strategies on various problems and investigate a delayed update strategy for preconditioners to further reduce the computational costs.

math.NA↗

arXiv2018

Skyrmion ratchet effect driven by a biharmonic force

Based on micromagnetic simulation and analysis of Thiele's equation, in this work we demonstrate that ratchet motion of skyrmion can be induced by a biharmonic in-plane magnetic field hx(t) = h1sin(mwt) + h2sin(nwt + phi), provided that integers m and n are coprime and that m + n is odd. Remarkably, the speed and direction of the ratchet motion can be readily adjusted by the field amplitude, frequency and phase, with the maximum speed being over 5 m/s and the direction rotatable over 360 degree. The origin of the skyrmion ratchet motion is analyzed by tracing the excitation spectra of the dissipation parameter D and the skyrmion position R, and it shows that the dissipative force plays a key role in the appearance of ratchet motion. Such a ratchet motion of skyrmion is distinguished from those caused by single-frequency ac drives reported in the literature, and from that driven by pulsed magnetic fields as also predicted in this work. Our results show that skyrmion ratchet effect under biharmonic forces shares some common features of those found in many soliton systems, and the facile controllability of both the skyrmion speed and direction should be useful in practice.

cond-mat.mtrl-sci↗

arXiv2014

Cross-Modal Learning via Pairwise Constraints

In multimedia applications, the text and image components in a web document form a pairwise constraint that potentially indicates the same semantic concept. This paper studies cross-modal learning via the pairwise constraint, and aims to find the common structure hidden in different modalities. We first propose a compound regularization framework to deal with the pairwise constraint, which can be used as a general platform for developing cross-modal algorithms. For unsupervised learning, we propose a cross-modal subspace clustering method to learn a common structure for different modalities. For supervised learning, to reduce the semantic gap and the outliers in pairwise constraints, we propose a cross-modal matching method based on compound ?21 regularization along with an iteratively reweighted algorithm to find the global optimum. Extensive experiments demonstrate the benefits of joint text and image modeling with semantically induced pairwise constraints, and show that the proposed cross-modal methods can further reduce the semantic gap between different modalities and improve the clustering/retrieval accuracy.

cs.CV↗

arXiv2011

Image Retrieval Method Using Top-surf Descriptor

This report presents the results and details of a content-based image retrieval project using the Top-surf descriptor. The experimental results are preliminary, however, it shows the capability of deducing objects from parts of the objects or from the objects that are similar. This paper uses a dataset consisting of 1200 images of which 800 images are equally divided into 8 categories, namely airplane, beach, motorbike, forest, elephants, horses, bus and building, while the other 400 images are randomly picked from the Internet. The best results achieved are from building category.

cs.CV↗