Weidong Zhao

Shuixin Fang, Yue Qiu, Weidong Zhao

The Butcher theory provides a powerful tool for analyzing order conditions of Runge-Kutta schemes for ordinary differential equations (ODEs); however, such a theory has not yet been well established for backward stochastic differential equations (BSDEs) -- motivating the current work to address this gap. Specifically, we propose a new class of explicit Runge-Kutta schemes for BSDEs. These schemes admit a concise formulation that closely mirrors their ODE counterparts. Building on this formulation, we extend the Butcher theory to the proposed schemes, thereby enabling a symbolic derivation of Taylor expansions for the local truncation errors, and yielding the order conditions. Our approach preserves the elegance and generality of the original Butcher theory: it avoids stage-by-stage error expansions and provides a systematic, stage-inductive analysis, applicable to schemes with any number of stages and any target order. Numerical experiments support the theoretical results.

Yang Li, Jie Yang, Weidong Zhao

The Crank-Nicolson (short for C-N) scheme for solving {\it backward stochastic differential equation} (BSDE), driven by Brownian motions, was first developed by the authors W. Zhao, L. Chen and S. Peng [SIAM J. Sci. Comput., 28 (2006), 1563--1581], and numerical experiments showed that the accuracy of this C-N scheme was of second order for solving BSDE. This C-N scheme was extended to solve decoupled {\it forward-backward stochastic differential equations} (FBSDEs) by W. Zhao, Y. Li and Y. Fu [Sci. China. Math., 57 (2014), 665--686], and it was numerically shown that the accuracy of the extended C-N scheme was also of second order. To our best knowledge, among all one-step (two-time level) numerical schemes with second-order accuracy for solving BSDE or FBSDEs, such as the ones in the above two papers and the one developed by the authors D. Crisan and K. Manolarakis [Ann. Appl. Probab., 24, 2 (2014), 652--678], the C-N scheme is the simplest one in applications. The theoretical proofs of second-order error estimates reported in the literature for these schemes for solving decoupled FBSDEs did not include the C-N scheme. The purpose of this work is to theoretically analyze the error estimate of the C-N scheme for solving decoupled FBSDEs. Based on the Taylor and Itô-Taylor expansions, the Malliavin calculus theory (e.g., the multiple Malliavin integration-by-parts formula), and our new truncation error cancelation techniques, we rigorously prove that the strong convergence rate of the C-N scheme is of second order for solving decoupled FBSDEs, which fills the gap between the second-order numerical and theoretical analysis of the C-N scheme.

Xin Chen, Yuwen Qin, Weidong Zhao et al.

Accurate state-of-health (SOH) estimation is critical to guarantee the safety, efficiency and reliability of battery-powered applications. Most SOH estimation methods focus on the 0-100\% full state-of-charge (SOC) range that has similar distributions. However, the batteries in real-world applications usually work in the partial SOC range under shallow-cycle conditions and follow different degradation profiles with no labeled data available, thus making SOH estimation challenging. To estimate shallow-cycle battery SOH, a novel unsupervised deep transfer learning method is proposed to bridge different domains using self-attention distillation module and multi-kernel maximum mean discrepancy technique. The proposed method automatically extracts domain-variant features from charge curves to transfer knowledge from the large-scale labeled full cycles to the unlabeled shallow cycles. The CALCE and SNL battery datasets are employed to verify the effectiveness of the proposed method to estimate the battery SOH for different SOC ranges, temperatures, and discharge rates. The proposed method achieves a root-mean-square error within 2\% and outperforms other transfer learning methods for different SOC ranges. When applied to batteries with different operating conditions and from different manufacturers, the proposed method still exhibits superior SOH estimation performance. The proposed method is the first attempt at accurately estimating battery SOH under shallow-cycle conditions without needing a full-cycle characteristic test.

Ziqi Xie, Weidong Zhao, Xianhui Liu et al.

Deep learning-based image stitching pipelines are typically divided into three cascading stages: registration, fusion, and rectangling. Each stage requires its own network training and is tightly coupled to the others, leading to error propagation and posing significant challenges to parameter tuning and system stability. This paper proposes the Simple and Robust Stitcher (SRStitcher), which revolutionizes the image stitching pipeline by simplifying the fusion and rectangling stages into a unified inpainting model, requiring no model training or fine-tuning. We reformulate the problem definitions of the fusion and rectangling stages and demonstrate that they can be effectively integrated into an inpainting task. Furthermore, we design the weighted masks to guide the reverse process in a pre-trained largescale diffusion model, implementing this integrated inpainting task in a single inference. Through extensive experimentation, we verify the interpretability and generalization capabilities of this unified model, demonstrating that SRStitcher outperforms state-of-the-art methods in both performance and stability. Code: https://github.com/yayoyo66/SRStitcher

Ziqi Xie, Xiao Lai, Weidong Zhao et al.

Current image stitching methods often produce noticeable seams in challenging scenarios such as uneven hue and large parallax. To tackle this problem, we propose the Reference-Driven Inpainting Stitcher (RDIStitcher), which reformulates the image fusion and rectangling as a reference-based inpainting model, incorporating a larger modification fusion area and stronger modification intensity than previous methods. Furthermore, we introduce a self-supervised model training method, which enables the implementation of RDIStitcher without requiring labeled data by fine-tuning a Text-to-Image (T2I) diffusion model. Recognizing difficulties in assessing the quality of stitched images, we present the Multimodal Large Language Models (MLLMs)-based metrics, offering a new perspective on evaluating stitched image quality. Compared to the state-of-the-art (SOTA) method, extensive experiments demonstrate that our method significantly enhances content coherence and seamless transitions in the stitched images. Especially in the zero-shot experiments, our method exhibits strong generalization capabilities. Code: https://github.com/yayoyo66/RDIStitcher

Gong Gao, Weidong Zhao, Xianhui Liu et al.

Existing value-based online reinforcement learning (RL) algorithms suffer from slow policy exploitation due to ineffective exploration and delayed policy updates. To address these challenges, we propose an algorithm called Instant Retrospect Action (IRA). Specifically, we propose Q-Representation Discrepancy Evolution (RDE) to facilitate Q-network representation learning, enabling discriminative representations for neighboring state-action pairs. In addition, we adopt an explicit method to policy constraints by enabling Greedy Action Guidance (GAG). This is achieved through backtracking historical actions, which effectively enhances the policy update process. Our proposed method relies on providing the learning algorithm with accurate $k$-nearest-neighbor action value estimates and learning to design a fast-adaptable policy through policy constraints. We further propose the Instant Policy Update (IPU) mechanism, which enhances policy exploitation by systematically increasing the frequency of policy updates. We further discover that the early-stage training conservatism of the IRA method can alleviate the overestimation bias problem in value-based RL. Experimental results show that IRA can significantly improve the learning efficiency and final performance of online RL algorithms on eight MuJoCo continuous control tasks.

Anci Lin, Xiaohong Liu, Zhiwen Zhang et al.

Nonconvex multi-well energies in cell-induced phase transitions give rise to sharp interfaces, fine-scale microstructures, and distance-dependent inter-cell coupling, all of which pose significant challenges for physics-informed learning. Existing methods often suffer from over-smoothing in near-field patterns. To address this, we propose biomimetic physics-informed neural networks (Bio-PINNs), a variational framework that encodes temporal causality into explicit spatial causality via a progressive distance gate. Furthermore, Bio-PINNs leverage a deformation-uncertainty proxy for the interfacial length scale to target microstructure-prone regions, providing a computationally efficient alternative to explicit second-derivative regularization. We provide theoretical guarantees for the resulting uncertainty-driven ``retain-resample-release" adaptive collocation strategy, which ensures persistent coverage under gating and establishing a quantitative near-to-far growth bound. Across single- and multi-cell benchmarks, diverse separations, and various regularization regimes, Bio-PINNs consistently recover sharp transition layers and tether morphologies, significantly outperforming state-of-the-art adaptive and ungated baselines.

Jiayin Wang, Mingfeng Yao, Yanran Wei et al.

For Minimally Invasive Surgical (MIS) robots, accurate haptic interaction force feedback is essential for ensuring the safety of interacting with soft tissue. However, most existing MIS robotic systems cannot facilitate direct measurement of the interaction force with hardware sensors due to space limitations. This letter introduces an effective vision-based scheme that utilizes a One-Shot structured light projection with a designed pattern on soft tissue coupled with haptic information processing through a trained image-to-force neural network. The images captured from the endoscopic stereo camera are analyzed to reconstruct high-resolution 3D point clouds for soft tissue deformation. Based on this, a modified PointNet-based force estimation method is proposed, which excels in representing the complex mechanical properties of soft tissue. Numerical force interaction experiments are conducted on three silicon materials with different stiffness. The results validate the effectiveness of the proposed scheme.

Gong Gao, Zekai Wang, Jian Zhao et al.

Face Attribute Recognition (FAR) plays a crucial role in applications such as person re-identification, face retrieval, and face editing. Conventional multi-task attribute recognition methods often process the entire feature map for feature extraction and attribute classification, which can produce redundant features due to reliance on global regions. To address these challenges, we propose a novel approach emphasizing the selection of specific feature regions for efficient feature learning. We introduce the Mask-Guided Multi-Task Network (MGMTN), which integrates Adaptive Mask Learning (AML) and Group-Global Feature Fusion (G2FF) to address the aforementioned limitations. Leveraging a pre-trained keypoint annotation model and a fully convolutional network, AML accurately localizes critical facial parts (e.g., eye and mouth groups) and generates group masks that delineate meaningful feature regions, thereby mitigating negative transfer from global region usage. Furthermore, G2FF combines group and global features to enhance FAR learning, enabling more precise attribute identification. Extensive experiments on two challenging facial attribute recognition datasets demonstrate the effectiveness of MGMTN in improving FAR performance.

Gong Gao, Zekai Wang, Xianhui Liu et al.

To enhance the generalization performance of Multi-Task Networks (MTN) in Face Attribute Recognition (FAR), it is crucial to share relevant information across multiple related prediction tasks effectively. Traditional MTN methods create shared low-level modules and distinct high-level modules, causing an exponential increase in model parameters with the addition of tasks. This approach also limits feature interaction at the high level, hindering the exploration of semantic relations among attributes, thereby affecting generalization negatively. In response, this study introduces FAR-AMTN, a novel Attention Multi-Task Network for FAR. It incorporates a Weight-Shared Group-Specific Attention (WSGSA) module with shared parameters to minimize complexity while improving group feature representation. Furthermore, a Cross-Group Feature Fusion (CGFF) module is utilized to foster interactions between attribute groups, enhancing feature learning. A Dynamic Weighting Strategy (DWS) is also introduced for synchronized task convergence. Experiments on the CelebA and LFWA datasets demonstrate that the proposed FAR-AMTN demonstrates superior accuracy with significantly fewer parameters compared to existing models.

Yu Fu, Weidong Zhao, Tao Zhou

This is the second part in a series of papers on multi-step schemes for solving coupled forward backward stochastic differential equations (FBSDEs). We extend the basic idea in our former paper [W. Zhao, Y. Fu and T. Zhou, SIAM J. Sci. Comput., 36 (2014), pp. A1731-A1751] to solve high-dimensional FBSDEs, by using the spectral sparse grid approximations. The main issue for solving high dimensional FBSDEs is to build an efficient spatial discretization, and deal with the related high dimensional conditional expectations and interpolations. In this work, we propose the sparse grid spatial discretization. We use the sparse grid Gaussian-Hermite quadrature rule to approximate the conditional expectations. And for the associated high dimensional interpolations, we adopt an spectral expansion of functions in polynomial spaces with respect to the spatial variables, and use the sparse grid approximations to recover the expansion coefficients. The FFT algorithm is used to speed up the recovery procedure, and the entire algorithm admits efficient and high accurate approximations in high-dimensions, provided that the solutions are sufficiently smooth. Several numerical examples are presented to demonstrate the efficiency of the proposed methods.