arXiv subjects

Xiao-Ming Fu

Publications and source records attributed to Xiao-Ming Fu.

15 recordsLinked to original sources

arXiv2026

Finite quotients of sousperfectoid adic spaces need not be adic

For every prime $p$ and every perfectoid field $K$ of characteristic $p$, we construct a geometrically normal sousperfectoid affinoid adic space with a $C_p$-action whose quotient in the category of $v$-ringed spaces is not adic. The source is stably uniform and sheafy, while a cofinal sequence of rational neighborhoods at a fixed point acquires new degree-one invariant sections that do not descend by completed rational localization. Consequently, finite quotient stability for affinoid perfectoid spaces does not extend to sousperfectoid spaces.

math.AG↗

arXiv2026

Sharp asymptotics for the tree-completion time in cylindrical Hastings--Levitov$(0)$

Let $\mathrm{CHL}_N$ be the cylindrical Hastings--Levitov aggregation process with parameter $0$ on a cylinder of width $N$ with particles of fixed size $\lambda>0$, and let $\omega_{N,\lambda}$ be its tree-completion time --- the last time at which a new tree is born on the base circle. Chen, Procaccia and Zong proved the sharp upper bound $\mathbb{E}[\omega_{N,\lambda}]\le(1+\varepsilon)(\log N)/(2\lambda)$ and conjectured the matching limit. Here we prove the matching lower bound, and therefore \[ \lim_{N\to\infty}\frac{\mathbb{E}[\omega_{N,\lambda}]}{\log N}=\frac{1}{2\lambda} \qquad\text{for every fixed }\lambda>0 . \]

math.PR↗

arXiv2026

Source-Prior-Driven Selective Adaptation for Efficient Diffusion Model Finetuning

Fine-tuning large diffusion models for new domains or styles involves a trade-off: improving target-specific generation often degrades the pretrained model's broad generative capability. Existing full and parameter-efficient fine-tuning methods typically handle this trade-off only implicitly. In this work, we propose a novel source-prior-driven selective adaptation method to efficiently fine-tune diffusion models, achieving a favorable trade-off. Our method relies on two key observations: (1) the loss of general generative capability is highly inconsistent across pretrained parameters, and (2) parameters that have a relatively small impact on the model's general generative capability remain structurally inconsistent across layers and parameter types. Motivated by these observations, we first learn a static mask to explicitly identify parameters better suited for downstream adaptation, and then construct structured update strategies for the selected subset. Experiments show that our method achieves a better adaptation-retention trade-off than existing strong baselines.

cs.AI↗

arXiv2026

Power-law and log-periodic degree tails for a family of probability generating function equations arising in evolving networks

For a fixed integer $j\ge1$ and $0<p<1$, we study the probability generating function (pgf) equation \[ (1+2p)\,g(x)=2p\,x^{j}+g\bigl(x-px+px^{2}\bigr),\qquad 0\le x\le1 , \] which governs the limiting degree distribution $\{p_k\}$ of a family of evolving network models. The cases $j=1$ and $j=2$ are the treelike fast-growth model of Feng and Hu and the homogeneous evolving network of Feng, Li and Hu. We prove that for every $j$ the equation has a unique pgf solution, of mean $2j$, and we determine its coefficient tail exactly: \[ p_k=k^{-1-\rho}\,\Psi_j(\log_\lambda k)+o\bigl(k^{-1-\rho}\bigr), \] where $\lambda=1+p$, $\rho=\log(1+2p)/\log(1+p)$ is independent of $j$, and $\Psi_j$ is continuous, strictly positive and $1$-periodic, with explicit Fourier coefficients. This resolves two conjectures of Feng and coauthors: (1) the power-law order $p_k=\Theta(k^{-1-\rho})$ and (2) its refinement to the multiplicatively periodic form $p_k\sim\Psi_j(\log_\lambda k)\,k^{-1-\rho}$. The periodic factor is genuinely non-constant for $p$ near $1$, and, for the two network models, for all $p$ outside a discrete set. Consequently, $p_k$ is asymptotic to no constant multiple of $k^{-1-\rho}$. Our method is a self-contained local analysis of the supercritical Galton-Watson process with offspring law $1+\mathrm{Bernoulli}(p)$, inspected at an independent geometric time. This time-changed process solves the equation observed by Feng and coauthors. The main results of this paper were obtained by the multi-agent system Eureka and have subsequently been verified by the authors.

math.PR↗

arXiv2026

Masked BRep Autoencoder via Hierarchical Graph Transformer

We introduce a novel self-supervised learning framework that automatically learns representations from input computer-aided design (CAD) models for downstream tasks, including part classification, modeling segmentation, and machining feature recognition. To train our network, we construct a large-scale, unlabeled dataset of boundary representation (BRep) models. The success of our algorithm relies on two keycomponents. The first is a masked graph autoencoder that reconstructs randomly masked geometries and attributes of BReps for representation learning to enhance the generalization. The second is a hierarchical graph Transformer architecture that elegantly fuses global and local learning by a cross-scale mutual attention block to model long-range geometric dependencies and a graph neural network block to aggregate local topological information. After training the autoencoder, we replace its decoder with a task-specific network trained on a small amount of labeled data for downstream tasks. We conduct experiments on various tasks and achieve high performance, even with a small amount of labeled data, demonstrating the practicality and generalizability of our model. Compared to other methods, our model performs significantly better on downstream tasks with the same amount of training data, particularly when the training data is very limited.

cs.GR↗

arXiv2026

BRepMAE: Self-Supervised Masked BRep Autoencoders for Machining Feature Recognition

We propose a masked self-supervised learning framework, called BRepMAE, for automatically extracting a valuable representation of the input computer-aided design (CAD) model to recognize its machining features. Representation learning is conducted on a large-scale, unlabeled CAD model dataset using the geometric Attributed Adjacency Graph (gAAG) representation, derived from the boundary representation (BRep). The self-supervised network is a masked graph autoencoder (MAE) that focuses on reconstructing geometries and attributes of BRep facets, rather than graph structures. After pre-training, we fine-tune a network that contains both the encoder and a task-specific classification network for machining feature recognition (MFR). In the experiments, our fine-tuned network achieves high recognition rates with only a small amount of data (e.g., 0.1% of the training data), significantly enhancing its practicality in real-world (or private) scenarios where only limited data is available. Compared with other MFR methods, our fine-tuned network achieves a significant improvement in recognition rate with the same amount of training data, especially when the number of training samples is limited.

cs.GR↗

arXiv2025

Efficient Computation of Integer-constrained Cones for Conformal Parameterizations

We propose an efficient method to compute a small set of integer-constrained cone singularities, which induce a rotationally seamless conformal parameterization with low distortion. Since the problem only involves discrete variables, i.e., vertex-constrained positions, integer-constrained angles, and the number of cones, we alternately optimize these three types of variables to achieve tractable convergence. Central to high efficiency is an explicit construction algorithm that reduces the optimization problem scale to be slightly greater than the number of integer variables for determining the optimal angles with fixed positions and numbers, even for high-genus surfaces. In addition, we derive a new derivative formula that allows us to move the cones, effectively reducing distortion until convergence. Combined with other strategies, including repositioning and adding cones to decrease distortion, adaptively selecting a constrained number of integer variables for efficient optimization, and pairing cones to reduce the number, we quickly achieve a favorable tradeoff between the number of cones and the parameterization distortion. We demonstrate the effectiveness and practicability of our cones by using them to generate rotationally seamless and low-distortion parameterizations on a massive test data set. Our method demonstrates an order-of-magnitude speedup (30$\times$ faster on average) compared to state-of-the-art approaches while maintaining comparable cone numbers and parameterization distortion.

cs.GR↗

arXiv2025

Outer Contour-driven Ruled Surface Generation for Linear Hot-wire Rough Machining

We propose a novel method to generate a small set of ruled surfaces that do not collide with the input shape for linear hot-wire rough machining. Central to our technique is a new observation: the ruled surfaces constructed by vertical extrusion from planar smooth curves, which approach the input shape's outer contour lines while having no collisions, are capable of removing materials effectively during rough machining. Accordingly, we develop an iterative algorithm that alternates in each iteration between computing a viewpoint to determine an outer contour line and optimizing a smooth curve to approximate that contour line under the collision-free constraint. Specifically, a view selection approach based on genetic algorithm is used to optimize the viewpoint for removing materials as much as possible, and present an adaptive algorithm to find the constrained curves. The feasibility and practicability of our method are demonstrated through 10 physical examples. Compared with manual designs, our method obtains lower errors with the same number of cuts.

cs.CG↗

arXiv2025

Polynomial 2D Biharmonic Coordinates for High-order Cages

We derive closed-form expressions of biharmonic coordinates for 2D high-order cages, enabling the transformation of the input polynomial curves into polynomial curves of any order. Central to our derivation is the use of the high-order boundary element method. We demonstrate the practicality and effectiveness of our method on various 2D deformations. In practice, users can easily manipulate the Bezier control points to perform the desired intuitive deformation, as the biharmonic coordinates provide an enriched deformation space and encourage the alignment between the boundary cage and its interior geometry.

cs.GR↗

arXiv2024

Polynomial 2D Green Coordinates for High-order Cages

We propose conformal polynomial coordinates for 2D closed high-order cages, which consist of polynomial curves of any order. The coordinates enable the transformation of the input polynomial curves into polynomial curves of any order. We extend the classical 2D Green coordinates to define our coordinates, thereby leading to cage-aware conformal harmonic deformations. We extensively test our method on various 2D deformations, allowing users to manipulate the \Bezier control points to easily generate the desired deformation.

cs.CG↗

arXiv2024

Constructing Boundary-identical Microstructures via Guided Diffusion for Fast Multiscale Topology Optimization

Hierarchical structures exhibit critical features across multiple scales. However, designing multiscale structures demands significant computational resources, and ensuring connectivity between microstructures remains a key challenge. To address these issues, \textit{\textbf{large-range, boundary-identical microstructure datasets}} are successfully constructed, where the microstructures share the same boundaries and exhibit a wide range of elastic moduli. This approach enables highly efficient multiscale topology optimization. Central to our technique adopts a deep generative model, guided diffusion, to generate microstructures under the two conditions, including the specified boundary and homogenized elastic tensor. We generate the desired datasets using active learning approaches, where microstructures with diverse elastic moduli are iteratively added to the dataset, which is then retrained. %We achieve the desired datasets by active learning approaches which are alternately adding microstructures with diverse elastic modulus constructed by the deep generative model into the dataset and retraining the deep generative model. After that, sixteen boundary-identical microstructure datasets with wide ranges of elastic modulus %high property coverage are constructed. We demonstrate the effectiveness and practicability of the obtained datasets over various multiscale design examples. Specifically, in the design of a mechanical cloak, we utilize macrostructures with $30 \times 30$ elements and microstructures filled with $256 \times 256$ elements. The entire reverse design process is completed within one minute, significantly enhancing the efficiency of the multiscale topology optimization.

cs.CE↗

arXiv2024

OpenTM: An Open-source, Single-GPU, Large-scale Thermal Microstructure Design Framework

Thermal microstructures are artificially engineered materials designed to manipulate and control heat flow in unconventional ways. This paper presents an educational framework, called \emph{OpenTM}, to use a single GPU for designing periodic 3D high-resolution thermal microstructures to match the predefined thermal conductivity matrices with volume fraction constraints. Specifically, we use adaptive volume fraction to make the Optimality Criteria (OC) method run stably to obtain the thermal microstructures without a large memory overhead.Practical examples with a high resolution $128 \times 128 \times 128$ run under 90 seconds per structure on an NVIDIA GeForce GTX 4070Ti GPU with a peak GPU memory of 355 MB. Our open-source, high-performance implementation is publicly accessible at \url{https://github.com/quanyuchen2000/OPENTM}, and it is easy to install using Anaconda. Moreover, we provide a Python interface to make OpenTM well-suited for novices in C/C++.

cs.CE↗

arXiv2024

Guided Diffusion for Fast Inverse Design of Density-based Mechanical Metamaterials

Mechanical metamaterial is a synthetic material that can possess extraordinary physical characteristics, such as abnormal elasticity, stiffness, and stability, by carefully designing its internal structure. To make metamaterials contain delicate local structures with unique mechanical properties, it is a potential method to represent them through high-resolution voxels. However, it brings a substantial computational burden. To this end, this paper proposes a fast inverse design method, whose core is an advanced deep generative AI algorithm, to generate voxel-based mechanical metamaterials. Specifically, we use the self-conditioned diffusion model, capable of generating a microstructure with a resolution of $128^3$ to approach the specified homogenized tensor matrix in just 3 seconds. Accordingly, this rapid reverse design tool facilitates the exploration of extreme metamaterials, the sequence interpolation in metamaterials, and the generation of diverse microstructures for multi-scale design. This flexible and adaptive generative tool is of great value in structural engineering or other mechanical systems and can stimulate more subsequent research.

cs.CE↗

arXiv2023

An Optimized, Easy-to-use, Open-source GPU Solver for Large-scale Inverse Homogenization Problems

We propose a high-performance GPU solver for inverse homogenization problems to design high-resolution 3D microstructures. Central to our solver is a favorable combination of data structures and algorithms, making full use of the parallel computation power of today's GPUs through a software-level design space exploration. This solver is demonstrated to optimize homogenized stiffness tensors, such as bulk modulus, shear modulus, and Poisson's ratio, under the constraint of bounded material volume. Practical high-resolution examples with 512^3=134.2 million finite elements run in less than 40 seconds per iteration with a peak GPU memory of 9 GB on an NVIDIA GeForce GTX 1080Ti GPU. Besides, our GPU implementation is equipped with an easy-to-use framework with less than 20 lines of code to support various objective functions defined by the homogenized stiffness tensors. Our open-source high-performance implementation is publicly accessible at https://github.com/lavenklau/homo3d.

math.OC↗

arXiv2019

Voting for Distortion Points in Geometric Processing

Low isometric distortion is often required for mesh parameterizations. A configuration of some vertices, where the distortion is concentrated, provides a way to mitigate isometric distortion, but determining the number and placement of these vertices is non-trivial. We call these vertices distortion points. We present a novel and automatic method to detect distortion points using a voting strategy. Our method integrates two components: candidate generation and candidate voting. Given a closed triangular mesh, we generate candidate distortion points by executing a three-step procedure repeatedly: (1) randomly cut an input to a disk topology; (2) compute a low conformal distortion parameterization; and (3) detect the distortion points. Finally, we count the candidate points and generate the final distortion points by voting. We demonstrate that our algorithm succeeds when employed on various closed meshes with a genus of zero or higher. The distortion points generated by our method are utilized in three applications, including planar parameterization, semi-automatic landmark correspondence, and isotropic remeshing. Compared to other state-of-the-art methods, our method demonstrates stronger practical robustness in distortion point detection.

cs.GR↗