arXiv subjects

Zidong Wang

Publications and source records attributed to Zidong Wang.

At least 37 records · Page 2Linked to original sources

arXiv2025

PhyMPGN: Physics-encoded Message Passing Graph Network for spatiotemporal PDE systems

Solving partial differential equations (PDEs) serves as a cornerstone for modeling complex dynamical systems. Recent progresses have demonstrated grand benefits of data-driven neural-based models for predicting spatiotemporal dynamics (e.g., tremendous speedup gain compared with classical numerical methods). However, most existing neural models rely on rich training data, have limited extrapolation and generalization abilities, and suffer to produce precise or reliable physical prediction under intricate conditions (e.g., irregular mesh or geometry, complex boundary conditions, diverse PDE parameters, etc.). To this end, we propose a new graph learning approach, namely, Physics-encoded Message Passing Graph Network (PhyMPGN), to model spatiotemporal PDE systems on irregular meshes given small training datasets. Specifically, we incorporate a GNN into a numerical integrator to approximate the temporal marching of spatiotemporal dynamics for a given PDE system. Considering that many physical phenomena are governed by diffusion processes, we further design a learnable Laplace block, which encodes the discrete Laplace-Beltrami operator, to aid and guide the GNN learning in a physically feasible solution space. A boundary condition padding strategy is also designed to improve the model convergence and accuracy. Extensive experiments demonstrate that PhyMPGN is capable of accurately predicting various types of spatiotemporal dynamics on coarse unstructured meshes, consistently achieves the state-of-the-art results, and outperforms other baselines with considerable gains.

cs.LG↗

arXiv2025

Exploring Representation-Aligned Latent Space for Better Generation

Generative models serve as powerful tools for modeling the real world, with mainstream diffusion models, particularly those based on the latent diffusion model paradigm, achieving remarkable progress across various tasks, such as image and video synthesis. Latent diffusion models are typically trained using Variational Autoencoders (VAEs), interacting with VAE latents rather than the real samples. While this generative paradigm speeds up training and inference, the quality of the generated outputs is limited by the latents' quality. Traditional VAE latents are often seen as spatial compression in pixel space and lack explicit semantic representations, which are essential for modeling the real world. In this paper, we introduce ReaLS (Representation-Aligned Latent Space), which integrates semantic priors to improve generation performance. Extensive experiments show that fundamental DiT and SiT trained on ReaLS can achieve a 15% improvement in FID metric. Furthermore, the enhanced semantic latent space enables more perceptual downstream tasks, such as segmentation and depth estimation.

cs.LG↗

arXiv2025

PDEformer: Towards a Foundation Model for One-Dimensional Partial Differential Equations

This paper introduces PDEformer, a neural solver for partial differential equations (PDEs) capable of simultaneously addressing various types of PDEs. We propose to represent the PDE in the form of a computational graph, facilitating the seamless integration of both symbolic and numerical information inherent in a PDE. A graph Transformer and an implicit neural representation (INR) are employed to generate mesh-free predicted solutions. Following pretraining on data exhibiting a certain level of diversity, our model achieves zero-shot accuracies on benchmark datasets that is comparable to those of specifically trained expert models. Additionally, PDEformer demonstrates promising results in the inverse problem of PDE coefficient recovery.

math.NA↗

arXiv2025

PDEformer-1: A Foundation Model for One-Dimensional Partial Differential Equations

This paper introduces PDEformer-1, a versatile neural solver capable of simultaneously addressing various partial differential equations (PDEs). With the PDE represented as a computational graph, we facilitate the seamless integration of symbolic and numeric information inherent in a PDE. A graph Transformer and an implicit neural representation (INR) are employed subsequently to generate mesh-free predicted solutions. We generated a dataset with up to three million samples involving diverse one-dimensional PDEs to pretrain our model. Compared with baseline models trained specifically on benchmark datasets, our pretrained model achieves comparable accuracy via zero-shot inference, and the advantage expands after finetuning. For PDEs new or unseen in the pretraining stage, our model can adapt quickly by finetuning on a relatively small set of examples from the target equation. Additionally, PDEformer-1 demonstrates promising results in the inverse problem of PDE scalar coefficient recovery and coefficient field recovery.

math.NA↗

arXiv2025

Conservation-informed Graph Learning for Spatiotemporal Dynamics Prediction

Data-centric methods have shown great potential in understanding and predicting spatiotemporal dynamics, enabling better design and control of the object system. However, deep learning models often lack interpretability, fail to obey intrinsic physics, and struggle to cope with the various domains. While geometry-based methods, e.g., graph neural networks (GNNs), have been proposed to further tackle these challenges, they still need to find the implicit physical laws from large datasets and rely excessively on rich labeled data. In this paper, we herein introduce the conservation-informed GNN (CiGNN), an end-to-end explainable learning framework, to learn spatiotemporal dynamics based on limited training data. The network is designed to conform to the general conservation law via symmetry, where conservative and non-conservative information passes over a multiscale space enhanced by a latent temporal marching strategy. The efficacy of our model has been verified in various spatiotemporal systems based on synthetic and real-world datasets, showing superiority over baseline models. Results demonstrate that CiGNN exhibits remarkable accuracy and generalizability, and is readily applicable to learning for prediction of various spatiotemporal dynamics in a spatial domain with complex geometry.

cs.LG↗

arXiv2024

P$^2$C$^2$Net: PDE-Preserved Coarse Correction Network for efficient prediction of spatiotemporal dynamics

When solving partial differential equations (PDEs), classical numerical methods often require fine mesh grids and small time stepping to meet stability, consistency, and convergence conditions, leading to high computational cost. Recently, machine learning has been increasingly utilized to solve PDE problems, but they often encounter challenges related to interpretability, generalizability, and strong dependency on rich labeled data. Hence, we introduce a new PDE-Preserved Coarse Correction Network (P$^2$C$^2$Net) to efficiently solve spatiotemporal PDE problems on coarse mesh grids in small data regimes. The model consists of two synergistic modules: (1) a trainable PDE block that learns to update the coarse solution (i.e., the system state), based on a high-order numerical scheme with boundary condition encoding, and (2) a neural network block that consistently corrects the solution on the fly. In particular, we propose a learnable symmetric Conv filter, with weights shared over the entire model, to accurately estimate the spatial derivatives of PDE based on the neural-corrected system state. The resulting physics-encoded model is capable of handling limited training data (e.g., 3--5 trajectories) and accelerates the prediction of PDE solutions on coarse spatiotemporal grids while maintaining a high accuracy. P$^2$C$^2$Net achieves consistent state-of-the-art performance with over 50\% gain (e.g., in terms of relative prediction error) across four datasets covering complex reaction-diffusion processes and turbulent flows.

math.NA↗

arXiv2024

FiT: Flexible Vision Transformer for Diffusion Model

Nature is infinitely resolution-free. In the context of this reality, existing diffusion models, such as Diffusion Transformers, often face challenges when processing image resolutions outside of their trained domain. To overcome this limitation, we present the Flexible Vision Transformer (FiT), a transformer architecture specifically designed for generating images with unrestricted resolutions and aspect ratios. Unlike traditional methods that perceive images as static-resolution grids, FiT conceptualizes images as sequences of dynamically-sized tokens. This perspective enables a flexible training strategy that effortlessly adapts to diverse aspect ratios during both training and inference phases, thus promoting resolution generalization and eliminating biases induced by image cropping. Enhanced by a meticulously adjusted network structure and the integration of training-free extrapolation techniques, FiT exhibits remarkable flexibility in resolution extrapolation generation. Comprehensive experiments demonstrate the exceptional performance of FiT across a broad range of resolutions, showcasing its effectiveness both within and beyond its training resolution distribution. Repository available at https://github.com/whlzy/FiT.

cs.CV↗

arXiv2024

Diffusion Models Need Visual Priors for Image Generation

Conventional class-guided diffusion models generally succeed in generating images with correct semantic content, but often struggle with texture details. This limitation stems from the usage of class priors, which only provide coarse and limited conditional information. To address this issue, we propose Diffusion on Diffusion (DoD), an innovative multi-stage generation framework that first extracts visual priors from previously generated samples, then provides rich guidance for the diffusion model leveraging visual priors from the early stages of diffusion sampling. Specifically, we introduce a latent embedding module that employs a compression-reconstruction approach to discard redundant detail information from the conditional samples in each stage, retaining only the semantic information for guidance. We evaluate DoD on the popular ImageNet-$256 \times 256$ dataset, reducing 7$\times$ training cost compared to SiT and DiT with even better performance in terms of the FID-50K score. Our largest model DoD-XL achieves an FID-50K score of 1.83 with only 1 million training steps, which surpasses other state-of-the-art methods without bells and whistles during inference.

cs.CV↗

arXiv2024

EEGUnity: Open-Source Tool in Facilitating Unified EEG Datasets Towards Large-Scale EEG Model

The increasing number of dispersed EEG dataset publications and the advancement of large-scale Electroencephalogram (EEG) models have increased the demand for practical tools to manage diverse EEG datasets. However, the inherent complexity of EEG data, characterized by variability in content data, metadata, and data formats, poses challenges for integrating multiple datasets and conducting large-scale EEG model research. To tackle the challenges, this paper introduces EEGUnity, an open-source tool that incorporates modules of 'EEG Parser', 'Correction', 'Batch Processing', and 'Large Language Model Boost'. Leveraging the functionality of such modules, EEGUnity facilitates the efficient management of multiple EEG datasets, such as intelligent data structure inference, data cleaning, and data unification. In addition, the capabilities of EEGUnity ensure high data quality and consistency, providing a reliable foundation for large-scale EEG data research. EEGUnity is evaluated across 25 EEG datasets from different sources, offering several typical batch processing workflows. The results demonstrate the high performance and flexibility of EEGUnity in parsing and data processing. The project code is publicly available at github.com/Baizhige/EEGUnity.

eess.SP↗

arXiv2024

BDAN: Mitigating Temporal Difference Across Electrodes in Cross-Subject Motor Imagery Classification via Generative Bridging Domain

Because of "the non-repeatability of the experiment settings and conditions" and "the variability of brain patterns among subjects", the data distributions across sessions and electrodes are different in cross-subject motor imagery (MI) studies, eventually reducing the performance of the classification model. Systematically summarised based on the existing studies, a novel temporal-electrode data distribution problem is investigated under both intra-subject and inter-subject scenarios in this paper. Based on the presented issue, a novel bridging domain adaptation network (BDAN) is proposed, aiming to minimise the data distribution difference across sessions in the aspect of the electrode, thus improving and enhancing model performance. In the proposed BDAN, deep features of all the EEG data are extracted via a specially designed spatial feature extractor. With the obtained spatio-temporal features, a special generative bridging domain is established, bridging the data from all the subjects across sessions. The difference across sessions and electrodes is then minimized using the customized bridging loss functions, and the known knowledge is automatically transferred through the constructed bridging domain. To show the effectiveness of the proposed BDAN, comparison experiments and ablation studies are conducted on a public EEG dataset. The overall comparison results demonstrate the superior performance of the proposed BDAN compared with the other advanced deep learning and domain adaptation methods.

cs.HC↗

arXiv2024

Smart Help: Strategic Opponent Modeling for Proactive and Adaptive Robot Assistance in Households

Despite the significant demand for assistive technology among vulnerable groups (e.g., the elderly, children, and the disabled) in daily tasks, research into advanced AI-driven assistive solutions that genuinely accommodate their diverse needs remains sparse. Traditional human-machine interaction tasks often require machines to simply help without nuanced consideration of human abilities and feelings, such as their opportunity for practice and learning, sense of self-improvement, and self-esteem. Addressing this gap, we define a pivotal and novel challenge Smart Help, which aims to provide proactive yet adaptive support to human agents with diverse disabilities and dynamic goals in various tasks and environments. To establish this challenge, we leverage AI2-THOR to build a new interactive 3D realistic household environment for the Smart Help task. We introduce an innovative opponent modeling module that provides a nuanced understanding of the main agent's capabilities and goals, in order to optimize the assisting agent's helping policy. Rigorous experiments validate the efficacy of our model components and show the superiority of our holistic approach against established baselines. Our findings illustrate the potential of AI-imbued assistive robots in improving the well-being of vulnerable groups.

cs.RO↗

arXiv2024

A Distance Metric Learning Model Based On Variational Information Bottleneck

In recent years, personalized recommendation technology has flourished and become one of the hot research directions. The matrix factorization model and the metric learning model which proposed successively have been widely studied and applied. The latter uses the Euclidean distance instead of the dot product used by the former to measure the latent space vector. While avoiding the shortcomings of the dot product, the assumption of Euclidean distance is neglected, resulting in limited recommendation quality of the model. In order to solve this problem, this paper combines the Variationl Information Bottleneck with metric learning model for the first time, and proposes a new metric learning model VIB-DML (Variational Information Bottleneck Distance Metric Learning) for rating prediction, which limits the mutual information of the latent space feature vector to improve the robustness of the model and satisfiy the assumption of Euclidean distance by decoupling the latent space feature vector. In this paper, the experimental results are compared with the root mean square error (RMSE) on the three public datasets. The results show that the generalization ability of VIB-DML is excellent. Compared with the general metric learning model MetricF, the prediction error is reduced by 7.29%. Finally, the paper proves the strong robustness of VIBDML through experiments.

cs.IR↗

arXiv2024

On Time-Varying Delayed Stochastic Differential Systems with Non-Markovian Switching Parameters

This paper focuses on time-varying delayed stochastic differential systems with stochastically switching parameters formulated by a unified switching behavior combining a discrete adapted process and a Cox process. Unlike prior studies limited to stationary and ergodic switching scenarios, our research emphasizes non-Markovian, non-stationary, and non-ergodic cases. It arrives at more general results regarding stability analysis with a more rigorous methodology. The theoretical results are validated through numerical examples.

math.DS↗

arXiv2023

Unsupervisedly Prompting AlphaFold2 for Few-Shot Learning of Accurate Folding Landscape and Protein Structure Prediction

Data-driven predictive methods which can efficiently and accurately transform protein sequences into biologically active structures are highly valuable for scientific research and medical development. Determining accurate folding landscape using co-evolutionary information is fundamental to the success of modern protein structure prediction methods. As the state of the art, AlphaFold2 has dramatically raised the accuracy without performing explicit co-evolutionary analysis. Nevertheless, its performance still shows strong dependence on available sequence homologs. Based on the interrogation on the cause of such dependence, we presented EvoGen, a meta generative model, to remedy the underperformance of AlphaFold2 for poor MSA targets. By prompting the model with calibrated or virtually generated homologue sequences, EvoGen helps AlphaFold2 fold accurately in low-data regime and even achieve encouraging performance with single-sequence predictions. Being able to make accurate predictions with few-shot MSA not only generalizes AlphaFold2 better for orphan sequences, but also democratizes its use for high-throughput applications. Besides, EvoGen combined with AlphaFold2 yields a probabilistic structure generation method which could explore alternative conformations of protein sequences, and the task-aware differentiable algorithm for sequence generation will benefit other related tasks including protein design.

cs.LG↗

arXiv2023

Adaptive Rotated Convolution for Rotated Object Detection

Rotated object detection aims to identify and locate objects in images with arbitrary orientation. In this scenario, the oriented directions of objects vary considerably across different images, while multiple orientations of objects exist within an image. This intrinsic characteristic makes it challenging for standard backbone networks to extract high-quality features of these arbitrarily orientated objects. In this paper, we present Adaptive Rotated Convolution (ARC) module to handle the aforementioned challenges. In our ARC module, the convolution kernels rotate adaptively to extract object features with varying orientations in different images, and an efficient conditional computation mechanism is introduced to accommodate the large orientation variations of objects within an image. The two designs work seamlessly in rotated object detection problem. Moreover, ARC can conveniently serve as a plug-and-play module in various vision backbones to boost their representation ability to detect oriented objects accurately. Experiments on commonly used benchmarks (DOTA and HRSC2016) demonstrate that equipped with our proposed ARC module in the backbone network, the performance of multiple popular oriented object detectors is significantly improved (\eg +3.03\% mAP on Rotated RetinaNet and +4.16\% on CFA). Combined with the highly competitive method Oriented R-CNN, the proposed approach achieves state-of-the-art performance on the DOTA dataset with 81.77\% mAP. Code is available at \url{https://github.com/LeapLabTHU/ARC}.

cs.CV↗

arXiv2023

Composite Disturbance Filtering: A Novel State Estimation Scheme for Systems With Multi-Source, Heterogeneous, and Isomeric Disturbances

State estimation has long been a fundamental problem in signal processing and control areas. The main challenge is to design filters with ability to reject or attenuate various disturbances. With the arrival of big data era, the disturbances of complicated systems are physically multi-source, mathematically heterogenous, affecting the system dynamics via isomeric (additive, multiplicative and recessive) channels, and deeply coupled with each other. In traditional filtering schemes, the multi-source heterogenous disturbances are usually simplified as a lumped one so that the "single" disturbance can be either rejected or attenuated. Since the pioneering work in 2012, a novel state estimation methodology called {\it composite disturbance filtering} (CDF) has been proposed, which deals with the multi-source, heterogenous, and isomeric disturbances based on their specific characteristics. With the CDF, enhanced anti-disturbance capability can be achieved via refined quantification, effective separation, and simultaneous rejection and attenuation of the disturbances. In this paper, an overview of the CDF scheme is provided, which includes the basic principle, general design procedure, application scenarios (e.g. alignment, localization and navigation), and future research directions. In summary, it is expected that the CDF offers an effective tool for state estimation, especially in the presence of multi-source heterogeneous disturbances.

eess.SY↗

arXiv2023

Learning to simulate partially known spatio-temporal dynamics with trainable difference operators

Recently, using neural networks to simulate spatio-temporal dynamics has received a lot of attention. However, most existing methods adopt pure data-driven black-box models, which have limited accuracy and interpretability. By combining trainable difference operators with black-box models, we propose a new hybrid architecture explicitly embedded with partial prior knowledge of the underlying PDEs named PDE-Net++. Furthermore, we introduce two distinct options called the trainable flipping difference layer (TFDL) and the trainable dynamic difference layer (TDDL) for the difference operators. Numerous numerical experiments have demonstrated that PDE-Net++ has superior prediction accuracy and better extrapolation performance than black-box models.

cs.LG↗

arXiv2023

Analysis of the Decoder Width for Parametric Partial Differential Equations

Recently, Meta-Auto-Decoder (MAD) was proposed as a novel reduced order model (ROM) for solving parametric partial differential equations (PDEs), and the best possible performance of this method can be quantified by the decoder width. This paper aims to provide a theoretical analysis related to the decoder width. The solution sets of several parametric PDEs are examined, and the upper bounds of the corresponding decoder widths are estimated. In addition to the elliptic and the parabolic equations on a fixed domain, we investigate the advection equations that present challenges for classical linear ROMs, as well as the elliptic equations with the computational domain shape as a variable PDE parameter. The resulting fast decay rates of the decoder widths indicate the promising potential of MAD in addressing these problems.

math.NA↗