Hailong Guo

Hailong Guo, Zhimin Zhang, Ren Zhao

In this article, we propose and analyze an effective Hessian recovery strategy for the Lagrangian finite element of arbitrary order $k$. We prove that the proposed Hessian recovery preserves polynomials of degree $k+1$ on general unstructured meshes and superconverges at rate $O(h^k)$ on mildly structured meshes. In addition, the method preserves polynomials of degree $k+2$ on translation invariant meshes and produces a symmetric Hessian matrix when the sampling points for recovery are selected with symmetry. Numerical examples are presented to support our theoretical results.

Hailong Guo, Zhimin Zhang, Qingsong Zou

In this paper, we develop a straightforward $C^0$ linear finite element method for sixth-order elliptic equations. The basic idea is to use gradient recovery techniques to generate higher-order numerical derivatives from a $C^0$ linear finite element function. Both theoretical analysis and numerical experiments show that the proposed method has the optimal convergence rate under the energy norm. The method avoids complicated construction of conforming $C^2$ finite element basis or nonconforming penalty terms and has a low computational cost.

Minqiang Xu, Hailong Guo, Qingsong Zou

In this paper, we propose a novel recovery based finite element method for the Cahn-Hilliard equation. One distinguishing feature of the method is that we discretize the fourth-order differential operator in a standard $C^0$ linear finite elements space. Precisely, we first transform the fourth-order Cahn-Hilliard equation to its variational formulation in which only first-order and second-order derivatives are involved and then we compute the and second-order derivatives of a linear finite element function by a least-squares fitting recovery procedure. The intrinsic link between the second-order derivatives (Hessian matrix) recovery scheme and the finite difference method is studied in the paper. In particular, for the first time, we discover that the Laplace recovery scheme is exactly the well-known five-point stencil over uniform meshes. The proposed discretization for the Cahn-Hilliard equation can be regarded as a combination of the finite difference scheme and the finite element scheme. In addition, special considerations are put on different methods for imposing Neumann type boundary conditions. The optimal-order convergence and energy stability are numerically proved through a series of benchmark tests.

Hailong Guo, Xu Yang, Zhimin Zhang

The contribution of this paper contains two parts: first, we prove a supercloseness result for the partially penalized immersed finite element (PPIFE) method in [T. Lin, Y. Lin, and X. Zhang, SIAM J. Numer. Anal., 53 (2015), 1121--1144]; then based on the supercloseness result, we show that the gradient recovery method proposed in our previous work [H. Guo and X. Yang, arXiv: 1608.00063] can be applied to the PPIFE method and the recovered gradient converges to the exact gradient with a superconvergent rate $\mathcal{O}(h^{3/2})$. Hence, the gradient recovery method provides an asymptotically exact a posteriori error estimator for the PPIFE method. Several numerical examples are presented to verify our theoretical result.

Hailong Guo, Xu Yang, Yi Zhu

Photonic graphene, a photonic crystal with honeycomb structures, has been intensively studied in both theoretical and applied fields. Similar to graphene which admits Dirac Fermions and topological edge states, photonic graphene supports novel and subtle propagating modes (edge modes) of electromagnetic waves. These modes have wide applications in many optical systems. In this paper, we propose a novel gradient recovery method based on Bloch theory for the computation of topological edge modes in the honeycomb structure. Compared to standard finite element methods, this method provides higher order accuracy with the help of gradient recovery technique. This high order accuracy is highly desired for constructing the propagating electromagnetic modes in applications. We analyze the accuracy and prove the superconvergence of this method. Numerical examples are presented to show the efficiency by computing the edge mode for the $\mathcal{P}$-symmetry and $\mathcal{C}$-symmetry breaking cases in honeycomb structures.

Hailong Guo, Xu Yang

This is the third paper on the study of gradient recovery for elliptic interface problem. In our previous works [H. Guo and X. Yang, 2016, arXiv:1607.05898 and {\it J. Comput. Phys.}, 338 (2017), 606--619], we developed {gradient recovery methods} for elliptic interface problem based on body-fitted meshes and immersed finite element methods. Despite the efficiency and accuracy that these methods bring to recover the gradient, there are still some cases in unfitted meshes where skinny triangles appear in the generated local body-fitted triangulation that destroy the accuracy of recovered gradient near the interface. In this paper, we propose a gradient recovery technique based on Nitsche's method for elliptic interface problem, which avoids the loss of accuracy of gradient near the interface caused by skinny triangles. We analyze the supercloseness between the gradient of the numerical solution by the Nitsche's method and the gradient of interpolation of the exact solution, which leads to the superconvergence of the proposed gradient recovery method. We also present several numerical examples to validate the theoretical results.

Fangtai Wu, Hailong Guo, Shijie Huang et al.

Customized image editing aims to equip pre-trained diffusion models with specific visual effects using limited paired data, typically via Low-Rank Adaptation (LoRA). As the number of desired effects grows, storing and dynamically loading numerous these effect LoRAs significantly increases deployment overhead. Furthermore, current pipelines typically cascade these effect LoRAs with acceleration modules for fast generation, which triggers severe parameter interference and results in concept bleeding and style degradation. We propose CollectionLoRA, a multi-teacher on-policy distillation framework capable of distilling the concepts of up to 50 different effect LoRAs along with few-step generation capabilities into a single LoRA. This fundamentally resolves the feature interference issue and significantly reduces deployment costs. Specifically, the method introduces (i) a Probabilistic Dual-Stream Routing mechanism that enables the model to randomly switch between data sources during training, effectively enhancing its generalization in unseen scenarios; (ii) an Asymmetric Orthogonal Prompting strategy to achieve concept isolation within the prompt space; (iii) a Coarse-to-Fine Distillation Objective to mitigate the distribution gap between the teacher and student models. Extensive evaluations show that CollectionLoRA distills all customized effects and few-step generation into a single LoRA, reducing deployment overhead while achieving concept fidelity comparable to or better than independently trained teacher models.

Yubo Huang, Hailong Guo, Fangtai Wu et al.

Existing diffusion-based video generation methods are fundamentally constrained by sequential computation and long-horizon inconsistency, limiting their practical adoption in real-time, streaming audio-driven avatar synthesis. We present Live Avatar, an algorithm-system co-designed framework that enables efficient, high-fidelity, and infinite-length avatar generation using a 14-billion-parameter diffusion model. Our approach introduces Timestep-forcing Pipeline Parallelism (TPP), a distributed inference paradigm that pipelines denoising steps across multiple GPUs, effectively breaking the autoregressive bottleneck and ensuring stable, low-latency real-time streaming. To further enhance temporal consistency and mitigate identity drift and color artifacts, we propose the Rolling Sink Frame Mechanism (RSFM), which maintains sequence fidelity by dynamically recalibrating appearance using a cached reference image. Additionally, we leverage Self-Forcing Distribution Matching Distillation to facilitate causal, streamable adaptation of large-scale models without sacrificing visual quality. Live Avatar demonstrates state-of-the-art performance, reaching 20 FPS end-to-end generation on 5 H800 GPUs, and, to the best of our knowledge, is the first to achieve practical, real-time, high-fidelity avatar generation at this scale. Our work establishes a new paradigm for deploying advanced diffusion models in industrial long-form video synthesis applications.

Liwei Lu, Hailong Guo, Xu Yang et al.

In this paper, we propose a deep learning framework for solving high-dimensional partial integro-differential equations (PIDEs) based on the temporal difference learning. We introduce a set of Levy processes and construct a corresponding reinforcement learning model. To simulate the entire process, we use deep neural networks to represent the solutions and non-local terms of the equations. Subsequently, we train the networks using the temporal difference error, termination condition, and properties of the non-local terms as the loss function. The relative error of the method reaches O(10^{-3}) in 100-dimensional experiments and O(10^{-4}) in one-dimensional pure jump problems. Additionally, our method demonstrates the advantages of low computational cost and robustness, making it well-suited for addressing problems with different forms and intensities of jumps.

Guozhi Dong, Hailong Guo

This paper investigates gradient recovery schemes for data defined on discretized manifolds. The proposed method, parametric polynomial preserving recovery (PPPR), does not require the tangent spaces of the exact manifolds, and they have been assumed for some significant gradient recovery methods in the literature. Another advantage of PPPR is that superconvergence is guaranteed without the symmetric condition which has been asked in the existing techniques. There is also numerical evidence that the superconvergence by PPPR is high curvature stable, which distinguishes itself from the others. As an application, we show its capability of constructing an asymptotically exact \textit{a posteriori} error estimator. Several numerical examples on two-dimensional surfaces are presented to support the theoretical results and comparisons with existing methods are documented.

Hailong Guo

This paper is concerned with the nonconforming finite element discretization of geometric partial differential equations. In specific, we construct a surface Crouzeix-Raviart element on the linear approximated surface, analogous to a flat surface. The optimal error estimations are established even though the presentation of the geometric error. By taking the intrinsic viewpoint of manifolds, we introduce a new superconvergent gradient recovery method for the surface Crouzeix-Raviart element using only the information of discretization surface. The potential of serving as an asymptotically exact {\it a posteriori} error estimator is also exploited. A series of benchmark numerical examples are presented to validate the theoretical results and numerically demonstrate the superconvergence of the gradient recovery method.

Hailong Guo, Bohan Zeng, Yiren Song et al.

Image-based virtual try-on (VTON) aims to generate a virtual try-on result by transferring an input garment onto a target person's image. However, the scarcity of paired garment-model data makes it challenging for existing methods to achieve high generalization and quality in VTON. Also, it limits the ability to generate mask-free try-ons. To tackle the data scarcity problem, approaches such as Stable Garment and MMTryon use a synthetic data strategy, effectively increasing the amount of paired data on the model side. However, existing methods are typically limited to performing specific try-on tasks and lack user-friendliness. To enhance the generalization and controllability of VTON generation, we propose Any2AnyTryon, which can generate try-on results based on different textual instructions and model garment images to meet various needs, eliminating the reliance on masks, poses, or other conditions. Specifically, we first construct the virtual try-on dataset LAION-Garment, the largest known open-source garment try-on dataset. Then, we introduce adaptive position embedding, which enables the model to generate satisfactory outfitted model images or garment images based on input images of different sizes and categories, significantly enhancing the generalization and controllability of VTON generation. In our experiments, we demonstrate the effectiveness of our Any2AnyTryon and compare it with existing methods. The results show that Any2AnyTryon enables flexible, controllable, and high-quality image-based virtual try-on generation. https://logn-2024.github.io/Any2anyTryonProjectPage

Rui Wang, Hailong Guo, Jiaming Liu et al.

In this paper, we introduce StableGarment, a unified framework to tackle garment-centric(GC) generation tasks, including GC text-to-image, controllable GC text-to-image, stylized GC text-to-image, and robust virtual try-on. The main challenge lies in retaining the intricate textures of the garment while maintaining the flexibility of pre-trained Stable Diffusion. Our solution involves the development of a garment encoder, a trainable copy of the denoising UNet equipped with additive self-attention (ASA) layers. These ASA layers are specifically devised to transfer detailed garment textures, also facilitating the integration of stylized base models for the creation of stylized images. Furthermore, the incorporation of a dedicated try-on ControlNet enables StableGarment to execute virtual try-on tasks with precision. We also build a novel data engine that produces high-quality synthesized data to preserve the model's ability to follow prompts. Extensive experiments demonstrate that our approach delivers state-of-the-art (SOTA) results among existing virtual try-on methods and exhibits high flexibility with broad potential applications in various garment-centric image generation.

Shijie Huang, Yiren Song, Yuxuan Zhang et al.

We introduce PhotoDoodle, a novel image editing framework designed to facilitate photo doodling by enabling artists to overlay decorative elements onto photographs. Photo doodling is challenging because the inserted elements must appear seamlessly integrated with the background, requiring realistic blending, perspective alignment, and contextual coherence. Additionally, the background must be preserved without distortion, and the artist's unique style must be captured efficiently from limited training data. These requirements are not addressed by previous methods that primarily focus on global style transfer or regional inpainting. The proposed method, PhotoDoodle, employs a two-stage training strategy. Initially, we train a general-purpose image editing model, OmniEditor, using large-scale data. Subsequently, we fine-tune this model with EditLoRA using a small, artist-curated dataset of before-and-after image pairs to capture distinct editing styles and techniques. To enhance consistency in the generated results, we introduce a positional encoding reuse mechanism. Additionally, we release a PhotoDoodle dataset featuring six high-quality styles. Extensive experiments demonstrate the advanced performance and robustness of our method in customized image editing, opening new possibilities for artistic creation.

Hailong Guo, Xu Yang

This is the second paper on the study of gradient recovery for elliptic interface problem. In our previous work [H. Guo and X. Yang, 2016, arXiv:1607.05898], we developed gradient recovery finite element method based on body-fitted mesh. In this paper, we propose new gradient recovery methods based on two immersed interface finite element methods: symmetric and consistent immersed finite method [H. Ji, J. Chen and Z. Li, J. Sci. Comput., 61 (2014), 533--557] and Petrov-Galerkin immersed finite element method [T.Y. Hou, X.-H. Wu and Y. Zhang, Commun. Math. Sci., 2 (2004), 185--205, and S. Hou and X.-D. Liu, J. Comput. Phys., 202 (2005), 411--445]. Compared to body-fitted mesh based gradient recover methods, immersed finite element methods provide a uniform way of recovering gradient on regular meshes. Numerical examples are presented to confirm the superconvergence of both gradient recovery methods. Moreover, they provide asymptotically exact a posteriori error estimators for both immersed finite element methods.

Hailong Guo, Xu Yang

In this paper, we propose a novel gradient recovery method for elliptic interface problem using body-fitted mesh in two dimension. Due to the lack of regularity of solution at interface, standard gradient recovery methods fail to give superconvergent results, and thus will lead to overrefinement when served as a posteriori error estimator. This drawback is overcome by designing an immersed gradient recovery operator in our method. We prove the superconvergence of this method for both mildly unstructured mesh and adaptive mesh, and present several numerical examples to verify the superconvergence and its robustness as a posteriori error estimator.

Hailong Guo, Zhimin Zhang, Ren Zhao

Some numerical algorithms for elliptic eigenvalue problems are proposed, analyzed, and numerically tested. The methods combine advantages of the two-grid algorithm, two-space method, the shifted inverse power method, and the polynomial preserving recovery technique . Our new algorithms compare favorably with some existing methods and enjoy superconvergence property.