Jian Cao

Abstract Accurate and efficient determination of crystal plasticity (CP) material parameters is essential for predictive simulations that link microstructures, manufacturing processes, and material properties. This study presents a graphical processing unit (GPU)-accelerated pipeline for calibrating CP material parameters, integrating automatic differentiation (AD)-based sensitivities with gradient-based optimization, built upon our open-source jax-cpfem package. This method eliminates reliance on finite differences in gradient-based approaches while improving efficiency over gradient-free optimization. The effectiveness of the pipeline is demonstrated through five case studies covering various crystal structures and boundary conditions. First, the AD-based sensitivity analysis achieves over 10 × speedup compared to finite difference while maintaining accuracy for complex, nonlinear constitutive laws. Second, a comprehensive analysis of initial starting points on gradient-based optimization demonstrates that using appropriate bounds mitigates potential issues. Across both single-crystal and polycrystalline cases calibrating six material parameters, our pipeline requires approximately 7 × fewer iterations and achieves 3 × higher efficiency over popular gradient-free methods like Bayesian optimization, regardless of geometry complexity. Furthermore, the successful calibration of 12 parameters in a dual-phase steel model highlights the capability of the pipeline to handle high-dimensional optimization problems, which is challenging for gradient-free optimization. Finally, the robustness of our pipeline is validated using noisy synthetic data and experimental tensile data for wrought IN625 over a finite strain range. These results illustrate the applicability of our pipeline to real-world scenarios and its potential for high-dimensional optimization and promising applications in integrated computational materials engineering workflows.

Stem cells hold great promise for repairing degenerated nucleus pulposus (NP) in intervertebral disc degeneration (IVDD) via differentiating into NP-like cells and replenishing the extracellular matrix (ECM). However, the harsh environment in degenerated NP contributes to poor survival, low differentiation efficiency, and matrix catabolism, hampering stem cells' long-term transplantation and efficacy. Herein, a hyaluronic acid (HA)-based hydrogel (Pep-aGel) functionalized with collagen mimetic peptide and amination is fabricated to deliver glycoengineered stem cells for NP repair. The peptide (GFOGER), which contains the integrin recognition sequence of collagen, is selectively bound to the upregulated integrin-β1 of glycoengineered stem cells, thereby promoting their NP-like differentiation. The amination introduced amino groups in hydrogel and further enhanced the integration of cell-secreted glycosaminoglycans (GAGs) on the HA chains, which mimicked the biosynthesis of Aggrecan, creating an NP-like nanostructure in the hydrogel. Pep-aGel loading with glycoengineered cells showed injectable properties and significantly improved disc height, extracellular matrix content, and GAG deposition in rat degenerated discs. This approach established a self-sufficient system that consists of NP cell replenishment, in situ ECM supply, and GAG anchoring, which may offer a concise, yet synergistic, strategy for the regeneration of IVDD.

Abstract Ultrashort pulse laser (USPL) with its excellent properties of ultrashort pulse width and extremely high peak power is widely applied in precision machining, microfabrication, and biomedicine. In recent years, there is a growing trend in using USPL in the field of welding. This emerging welding technology is primarily applied to the welding of transparent materials. By focusing USPL at the welding interface, laser energy transfers to substrates within a narrow area through the nonlinear absorption process, accompanied with large amount of heat release to achieve the melting and bonding. Due to the extremely short pulse width and limited energy input, thermal diffusion around the joint is minimal, resulting in the diminished welding region, lower thermal stress, and enhanced welding precision. This method holds significant promise for welding samples with a large coefficient of thermal expansion (CTE) difference. In this review, the welding of transparent materials is first introduced, including the welding process, mechanism, and process optimization. Following this, the welding of transparent materials‐opaque materials and opaque materials‐opaque materials are described. The current progress in the applications of USPL welding is then presented. Finally, the development prospects of USPL welding technology are summarized and discussed.

Abstract Additive manufacturing (AM) is an important addition to fabrication technology due to its flexibility in shape and material processing and ability to reduce waste compared to other fabrication methods. However, the tribological performance of the as-built surface roughness of AM parts has not yet been thoroughly studied. This review aims toward defining the intersection of AM and tribological research by exploring the qualities of AM surfaces, how they are altered with various postprocessing methods, and how they are measured and quantified. Through this exploration, directions of future work on the tribology of AM surfaces can be laid out. The limitations and areas of improvement for AM parts with respect to their surface quality and behavior are assessed from this point of view.

Computational science and engineering are shifting toward data-centric, optimization-based, and self-correcting solvers with artificial intelligence. This transition faces challenges such as low accuracy with sparse data, poor scalability, and high computational cost in complex system design. This work introduces Interpolating Neural Network (INN)-a network architecture blending interpolation theory and tensor decomposition. INN significantly reduces computational effort and memory requirements while maintaining high accuracy. Thus, it outperforms traditional partial differential equation (PDE) solvers, machine learning (ML) models, and physics-informed neural networks (PINNs). It also efficiently handles sparse data and enables dynamic updates of nonlinear activation. Demonstrated in metal additive manufacturing, INN rapidly constructs an accurate surrogate model of Laser Powder Bed Fusion (L-PBF) heat transfer simulation. It achieves sub-10-micrometer resolution for a 10 mm path in under 15 minutes on a single GPU, which is 5-8 orders of magnitude faster than competing ML models. This offers a new perspective for addressing challenges in computational science and engineering.

This study investigates the microstructure and properties of multi-layer Inconel 625 alloy cladding on alloy steel under different post-weld heat treatment conditions. Results indicate that the cladding microstructure primarily consists of dendritic and cellular austenite, with a distinct bright-white fusion zone between layers. As post-weld heat treatment temperature increases, cellular grains grow significantly and distribute more uniformly, while columnar grain size decreases. The fusion zone width gradually increases, along with the quantity and size of planar grains. Dendritic segregation in the cladding layer causes enrichment of Ni, Cr, and Mo in intergranular regions. post-weld heat treatment promotes the diffusion of Fe, Ni, Cr, and Mo, balancing their distribution between grain interiors and boundaries. With rising post-weld heat treatment temperature, cladding hardness slightly increases but exhibits greater fluctuation, while the hardness of the heat-affected zone (HAZ) and base metal (BM) decreases. Considering the comprehensive impact of heat treatment on cladding and substrate properties, 645°C is identified as the optimal post-weld heat treatment temperature. This temperature enhances corrosion resistance of the cladding while maintaining high compatibility with the substrate.

In this paper, combining the theory of discrete exponential dichotomy, Krasnoselskii's fixed point theorem and decomposition technique, we establish two new existent theorems for asymptotically almost periodic solutions of discrete dynamical systems. Our results generalize and improve some previous results, and are implemented for some economical, biological and mathematical models.

PURPOSE: To characterize corneal biomechanics in post-small-incision lenticule extraction (SMILE), post-laser-assisted subepithelial keratomileusis (LASEK), and normal eyes using Brillouin microscopy. METHODS: This study included myopic patients who underwent corneal refractive surgery (SMILE or LASEK) at least 1 month prior to ensure corneal stability. A total of 177 eyes (79 post-SMILE, 24 post-LASEK, and 74 untreated normal eyes) from 177 patients were evaluated using Pentacam HR and Brillouin microscopy for morphological and biomechanical assessment, respectively. Among them, 30 eyes (20 post-SMILE and 10 post-LASEK) from 30 participants underwent both pre- and post-operative Brillouin and Pentacam examinations, enabling within-subject comparisons. Corneal biomechanics were assessed using Brillouin modulus (BM), where lower values indicate weaker biomechanical properties. RESULTS: No significant differences were observed in Central BM, Mean BM, or Max BM among the groups. Compared with the normal eyes, Min BM was significantly lower in the post-SMILE and post-LASEK groups (P = 0.004 and 0.002, respectively) and Max-Min BM significantly increased after SMILE and LASEK (both P < 0.001). In post-SMILE corneas, standardized deviation BM was significantly higher than in normal corneas (P < 0.001). Within-subjects comparisons (pre- vs post-operation) further confirmed above results. Multiple linear regression analysis revealed a negative correlation between Central BM and post-operative corneal thickness in post-SMILE corneas (coefficient = -0.016, P = 0.025). In the post-LASEK group, Max-Min BM showed a positive correlation with mean corneal curvature (coefficient = 0.031, P = 0.001). CONCLUSION: SMILE and LASEK can induce localized changes in corneal biomechanics, as observed by Brillouin microscopy, while maintaining overall corneal biomechanics.

Purpose To summarize recent progress in the clinical and experimental applications of Brillouin microscopy in ophthalmology, highlighting its potential to advance biomechanical understanding in these contexts. Methods Literature review. Results Employing low-power lasers across visible to near-infrared wavelengths, Brillouin microscopy enables the assessment of tissue's longitudinal modulus or viscoelasticity by analyzing the Brillouin frequency shift. This technique provides valuable insights into the cornea's hydration state and anisotropic biomechanics, improving our understanding of its intrinsic characteristics. Numerous studies have demonstrated the diagnostic potential of Brillouin microscopy for corneal diseases. Experimental research has also shown significant changes in Brillouin biomechanics properties following procedures like corneal flap formation and corneal cross-linking. Additionally, Brillouin microscopy offers a novel perspective on age-related changes in both Brillouin biomechanics and morphology of crystalline lenses. Successful Brillouin measurements have been performed on other ocular tissues, including the limbus, sclera, and retina, in ex vivo studies. Conclusions Brillouin microscopy holds great promise as an ophthalmology tool. It offers unique insights into the biomechanical properties, disease-related alterations in ocular tissues, and intrinsic characteristics of biological specimens. The application of stimulated Brillouin microscopy, along with the integration of laser pump and machine learning techniques, can further enhance the acquisition speed and resolution of biological imaging. [ J Refract Surg . 2025;41(7):e731–e746.]

Abstract Additive manufacturing has enabled the fabrication of functionally graded materials (FGMs), such as compositionally graded alloys (CGAs), offering unprecedented flexibility in structural design. CGAs hold significant potential for thermal-elastic applications, yet existing design methods often overlook temperature-dependent material properties due to the complexity of coupled physics, design-dependent temperature fields, and local constraints. To address these challenges, we propose a topology optimization (TO) framework that concurrently designs geometry and graded material composition while accounting for temperature-dependent material behaviors and nonlinear thermal analysis. Our method employs a radial basis function (RBF)-based interpolation scheme to model material properties as functions of both temperature and material composition. Additionally, we leverage automatic differentiation and adjoint sensitivity analysis for computational efficiency and extensibility to GPU acceleration. Numerical examples demonstrate the effectiveness of our approach, underscoring (1) the critical role of temperature-dependent material properties in thermal-elastic structure optimization and (2) the benefits of continuous material grading in enhancing structural performance.

A data-free, predictive scientific AI model, Tensor-decomposition-based A Priori Surrogate (TAPS), is proposed for tackling ultra large-scale engineering simulations with significant speedup, memory savings, and storage gain. TAPS can effectively obtain surrogate models for high-dimensional parametric problems with equivalent zetta-scale ($10^{21}$) degrees of freedom (DoFs). TAPS achieves this by directly obtaining reduced-order models through solving governing equations with multiple independent variables such as spatial coordinates, parameters, and time. The paper first introduces an AI-enhanced finite element-type interpolation function called convolution hierarchical deep-learning neural network (C-HiDeNN) with tensor decomposition (TD). Subsequently, the generalized space-parameter-time Galerkin weak form and the corresponding matrix form are derived. Through the choice of TAPS hyperparameters, an arbitrary convergence rate can be achieved. To show the capabilities of this framework, TAPS is then used to simulate a large-scale additive manufacturing process as an example and achieves around 1,370x speedup, 14.8x memory savings, and 955x storage gain compared to the finite difference method with $3.46$ billion spatial degrees of freedom (DoFs). As a result, the TAPS framework opens a new avenue for many challenging ultra large-scale engineering problems, such as additive manufacturing and integrated circuit design, among others.

This paper systematically investigates the impact of different k-mer tokenization strategies on sequence feature representation and model performance. Using the TCR-epitope affinity prediction task as an example, we integrated data from public databases (VDJdb, IEDB Receptor, PIRD, McPAS) to construct a large-scale dataset and randomly extracted <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{1 0, 0 0 0}$</tex> samples (small-scale), 200,000 samples (medium-scale), and used the full dataset (422,164 samples, large-scale). Under a unified simple convolutional neural network, four tokenization strategies (1-mer, 2-mer, 3-mer, and 4-mer) were compared. Experimental results show that smaller <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{k}$</tex> values converge faster on small-scale datasets, while the 3-mer strategy, which captures more contextual information, achieves the highest AUC on the large-scale dataset. Although 4-mer tokenization captures longer local features, its training time increases significantly with only limited performance gains. These findings provide data-driven guidance for selecting appropriate <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{k}$</tex>-mer tokenization strategies in bioinformatics tasks.

Abstract This study investigates the impact of surface texturing on the durability of slippery liquid-infused porous surface (SLIPS) coatings applied to sheet metal substrates by the double-sided incremental forming (DSIF) process. Toolmarks generated during the DSIF process were leveraged as an efficient method for texturing, enabling both the formation and texturing of surfaces using a single set of universal tools. The effects of texture patterns, spacing, and tool movement on the SLIPS performance were evaluated by comparing samples generated in the presence and absence of tool spinning/rotation. The results indicate that textures with dimple patterns significantly improve coating durability by acting as lubricant reservoirs, reducing oil depletion, and supporting self-healing. In contrast, continuous grooves were less effective due to limited capillary action and increased edge effects. Tool spinning further enhanced the surface topography, producing an undulating texture that minimized contact line pinning and improved the surface hydrophobicity. Low-speed spinning (approximately 10 rpm) facilitated a transition to mixed sliding–rolling friction, resulting in smoother textures and extended coating durability. Combining dimple patterns and controlled spinning provides a synergistic approach for optimizing SLIPS coatings, offering a practical solution for enhancing durability without requiring additional equipment. This study underscores the potential of controlled texturing and tool movement to improve the SLIPS efficacy and broaden its applications in industrial, clinical, and consumer environments.

• The degradation behavior of Mg, Zn and Fe was investigated in human duodenal fluid (HDF). • Organics in HDF hinder the degradation of these metals in different ways. • Zn is nearly immune to degradation in HDF. • Compared to their degradation rates in popular pseudo-humoral media (e. g. HBSS, DMEM), Mg degrades faster in HDF, and Zn and Fe more slowly. Biodegradable metals have been of great interest in making gastrointestinal implants these years. The most researched biodegradable metal is magnesium (Mg), followed by zinc (Zn) and iron (Fe). However, due to the limitations of in vivo experiments and the complex component of the gastrointestinal fluid, their degradation mechanisms in such an environment are still ambiguous. In this work, the human duodenal fluid (HDF) was used to investigate their in vitro degradation behaviors, with a simulated duodenal fluid (SDF) prepared for the control group based on the HDF ionic composition. After immersion of these metals for 7 days, it is found that HDF shows a stronger pH buffering effect than SDF due to the presence of organics. These organics can also hinder the degradation of metals by affecting their product formation in different ways. On the one hand, the adsorption of organics and their effects on the fluid dominate their degradation inhibition effect on Mg and Zn in HDF. On the other hand, they can hinder the further oxidation of the degradation products of Fe, which is the main mechanism resulting in a lower degradation rate of Fe in HDF rather than in SDF. Among the three metals, Mg unsurprisingly shows the highest degradation rate in both fluids. Interestingly, Zn is nearly immune to degradation in HDF, while it presents typical pitting corrosion in SDF. Compared to their degradation rates in popular pseudo-humoral media (e. g. Hanks’ Balanced Salt Solutions, Dulbecco's modified Eagle's medium) reported previously, Mg degrades faster, and Zn and Fe more slowly in HDF. The higher in vitro degradation rate of Fe than that of Zn is influenced by oxygen and ions in the degradation environment.

Digital Twin – a virtual replica of a physical system enabling real-time monitoring, model updating, prediction, and decision-making – combined with recent advances in machine learning, offers new opportunities for proactive control strategies in autonomous manufacturing. However, achieving real-time decision-making with Digital Twins requires efficient optimization driven by accurate predictions of highly nonlinear manufacturing systems. This paper presents a simultaneous multi-step Model Predictive Control (MPC) framework for real-time decision-making, using a multivariate deep neural network, named Time-Series Dense Encoder (TiDE), as the surrogate model. Unlike conventional MPC models which only provide one-step ahead prediction, TiDE is capable of predicting future states within the prediction horizon in one shot (multi-step), significantly accelerating the MPC. Using Directed Energy Deposition (DED) additive manufacturing as a case study, we demonstrate the effectiveness of the proposed MPC in achieving melt pool temperature tracking to ensure part quality, while reducing porosity defects by regulating laser power to maintain melt pool depth constraints. In this work, we first show that TiDE is capable of accurately predicting melt pool temperature and depth. Second, we demonstrate that the proposed MPC achieves precise temperature tracking while satisfying melt pool depth constraints within a targeted dilution range (10%–30%), reducing potential porosity defects. Compared to Proportional–Integral–Derivative (PID) controller, the MPC results in smoother and less fluctuating laser power profiles with competitive or superior melt pool temperature control performance. This demonstrates the MPC’s proactive control capabilities, leveraging time-series prediction and real-time optimization, positioning it as a powerful tool for future Digital Twin applications and real-time process optimization in manufacturing. • Simultaneous multi-step MPC accelerates real-time decision-making in Digital Twin. • Surrogate using Time-Series Dense Encoder (TiDE) enables multistep-ahead prediction. • Accurate predictions for melt pool temperature and depths using multivariate TiDE. • MPC improves melt pool temperature tracking while enforcing depth constraints in DED. • Real-time decision-making is supported by auto-differentiation. • Proactive defect mitigation enhances part quality by maintaining dilution range.

This paper focuses on the development and application of an intelligent basic platform for intermediate experiments, serving the oil production process. Through a series of methods such as hardware intelligent upgrading and transformation, establishing connections between programmable logic controllers and hardware devices based on Modbus protocol, designing configuration software to read and control display data in real time, the intelligent basic platform for intermediate experiments has been successfully developed. The research and development achievements include the design and completion of three sets of configuration systems, intelligent control of hardware working status, and real-time data reading and graphical display, providing efficient and intelligent platform support for experimental research in the industry.

We present the formulation and applications of JAX-CPFEM, an open-source, GPU-accelerated, and differentiable 3-D crystal plasticity finite element method (CPFEM) software package. Leveraging the modern computing architecture JAX, JAX-CPFEM features high performance through array programming and GPU acceleration, achieving a 39× speedup in a polycrystal case with ~52,000 degrees of freedom compared to MOOSE with MPI (8 cores). Furthermore, JAX-CPFEM utilizes the automatic differentiation technique, enabling users to handle complex, non-linear constitutive materials laws without manually deriving the case-specific Jacobian matrix. Beyond solving forward problems, JAX-CPFEM demonstrates its potential in an inverse design pipeline, where initial crystallographic orientations of polycrystal copper are optimized to achieve targeted mechanical properties under deformations. The end-to-end differentiability of JAX-CPFEM allows automatic sensitivity calculations and high-dimensional inverse design using gradient-based optimization. The concept of differentiable JAX-CPFEM provides an affordable, flexible, and multi-purpose tool, advancing efficient and accessible computational tools for inverse design in smart manufacturing.

Discovering manufacturing processes has been largely experienced-based. We propose a shift to a systematic approach driven by dependencies between energy inputs and performance outputs. Uncovering these dependencies across diverse process classes requires a universal language that characterizes process inputs and performances. Traditional manufacturing languages, with their individualized syntax and terminology, hinder the characterization across varying length scales and energy inputs. To enable the evaluation of process dependencies, we propose a broad manufacturing language that facilitates the characterization of diverse process classes, which include energy inputs, tool-material interactions, material compatibility, and performance outputs. We analyze the relationships between these characteristics by constructing a dataset of over 50 process classes, which we use to train a variational autoencoder (VAE) model. This generative model encodes our dataset into a 2D latent space, where we can explore, select, and generate processes based on desired performances and retrieve the corresponding process characteristics. After verifying the dependencies derived from the VAE model match with existing knowledge on manufacturing processes, we demonstrate the usefulness of using the model to discover new potential manufacturing processes through three illustrative cases.

Recent trends in next-item recommendation systems have focused on modeling user intents. Traditional methods often extract users' inherent intents from the most representative items in a session, overlooking “unexpected items” that deviate from the majority in various contextual aspects. These unexpected items, frequently present, can be crucial indicators of a user's inclination towards exploring new options, signaling emerging intents that warrant significant attention. In response, we introduce DbMei, a novel approach that decouples user behaviors and emphasizes the modeling of emerging intents. DbMei distinguishes between two user behavior types: “focused shopping”, which aligns with users' inherent intents, and”wandering shopping”, which aligns with emerging intents. Focused shopping is analyzed using topic modeling and hypergraph learning while wandering shopping is explored through session neighbor retrieval. An exploitation-exploration mechanism is employed to determine the behavioral probability distribution for upcoming items. This integrated modeling of focused and wandering shopping behaviors drives our recommendation process. Extensive empirical studies on two real-world datasets, Amazon-KDD and Beauty, showcase DbMei's superiority over leading methods regarding Recall and MRR metrics. Our code is publicly available at https://github.com/sunlingdan-123/DbMei.

Introducing trace rare earth elements (REEs) into L1 2 dispersoids (Al 3 (Sc,Zr)) can markedly enhance the mechanical properties of aluminum alloys, However, excessive amounts may cause adverse impacts. This study explores Ti and Cu as transition metal candidates for Al-Zn-Mg-X alloys, aiming to enhance mechanical properties, elucidate microstructure evolution, and identify optimization mechanisms. The addition of Ti to the Al-6.8Zn-2.2Mg-0.2Sc-0.1Zr (AS) alloy results in a notable refinement of the grain size, reducing it from 170 μm to 47 μm. This refinement of Ti can be attributed to its role as a nucleating agent during solidification, its promotion of dynamic recrystallization during hot-rolling, and its inhibition of static recrystallization during solid solution treatment stage. The formation of a new Ti-containing layer, which substitutes Al sites adjacent to Al 3 Zr dispersoids, leads to an increase in the phase size from 16 nm to 25 nm. In addition, Cu significantly decreases the aging activation energy of the GP zone and η’ precipitate, thereby facilitating their nucleation and growth, which enhances the mechanical properties of the alloy. Ti markedly improves the hardness and strength of the alloy through grain refinement strengthening, Orowan strengthening and solid solution strengthening, while Cu predominantly enhances solid solution strengthening. Our findings suggest that Ti and Cu microalloying profoundly influences the properties and the microstructures of Al-Zn-Mg-X alloys across various scales offering a promising approach for the advancement of high-performance aluminum alloys.

Software systems often record important runtime information in logs to help with troubleshooting. Log-based anomaly detection has become a key research area that aims to identify system issues through log data, ultimately enhancing the reliability of software systems. Traditional deep learning methods often struggle to capture the semantic information embedded in log data, which is typically organized in natural language. In this paper, we propose LogLLM, a log-based anomaly detection framework that leverages large language models (LLMs). LogLLM employs BERT for extracting semantic vectors from log messages, while utilizing Llama, a transformer decoder-based model, for classifying log sequences. Additionally, we introduce a projector to align the vector representation spaces of BERT and Llama, ensuring a cohesive understanding of log semantics. Unlike conventional methods that require log parsers to extract templates, LogLLM preprocesses log messages with regular expressions, streamlining the entire process. Our framework is trained through a novel three-stage procedure designed to enhance performance and adaptability. Experimental results across four public datasets demonstrate that LogLLM outperforms state-of-the-art methods. Even when handling unstable logs, it effectively captures the semantic meaning of log messages and detects anomalies accurately.

Model heterogeneity poses a significant challenge in Heterogeneous Federated Learning (HtFL). In scenarios with diverse model architectures, directly aggregating model parameters is impractical, leading HtFL methods to incorporate an extra objective alongside the original local objective on each client to facilitate collaboration. However, this often results in a mismatch between the extra and local objectives. To resolve this, we propose Federated Learning-to-Guide (FedL2G), a method that adaptively learns to guide local training in a federated manner, ensuring the added objective aligns with each client's original goal. With theoretical guarantees, FedL2G utilizes only first-order derivatives w.r.t. model parameters, achieving a non-convex convergence rate of O(1/T). We conduct extensive experiments across two data heterogeneity and six model heterogeneity settings, using 14 heterogeneous model architectures (e.g., CNNs and ViTs). The results show that FedL2G significantly outperforms seven state-of-the-art methods.