Weien Zhou

Xu Liu, Wen Yao, Wei Peng et al.

Physics-informed extreme learning machine (PIELM) has recently received significant attention as a rapid version of physics-informed neural network (PINN) for solving partial differential equations (PDEs). The key characteristic is to fix the input layer weights with random values and use Moore-Penrose generalized inverse for the output layer weights. The framework is effective, but it easily suffers from overfitting noisy data and lacks uncertainty quantification for the solution under noise scenarios.To this end, we develop the Bayesian physics-informed extreme learning machine (BPIELM) to solve both forward and inverse linear PDE problems with noisy data in a unified framework. In our framework, a prior probability distribution is introduced in the output layer for extreme learning machine with physic laws and the Bayesian method is used to estimate the posterior of parameters. Besides, for inverse PDE problems, problem parameters considered as new output layer weights are unified in a framework with forward PDE problems. Finally, we demonstrate BPIELM considering both forward problems, including Poisson, advection, and diffusion equations, as well as inverse problems, where unknown problem parameters are estimated. The results show that, compared with PIELM, BPIELM quantifies uncertainty arising from noisy data and provides more accurate predictions. In addition, BPIELM is considerably cheaper than PINN in terms of the computational cost.

Wei Peng, Weien Zhou, Xiaoya Zhang et al.

Learning solutions of partial differential equations (PDEs) with Physics-Informed Neural Networks (PINNs) is an attractive alternative approach to traditional solvers due to its flexibility and ease of incorporating observed data. Despite the success of PINNs in accurately solving a wide variety of PDEs, the method still requires improvements in terms of computational efficiency. One possible improvement idea is to optimize the generation of training point sets. Residual-based adaptive sampling and quasi-uniform sampling approaches have been each applied to improve the training effects of PINNs, respectively. To benefit from both methods, we propose the Residual-based Adaptive Node Generation (RANG) approach for efficient training of PINNs, which is based on a variable density nodal distribution method for RBF-FD. The method is also enhanced by a memory mechanism to further improve training stability. We conduct experiments on three linear PDEs and three nonlinear PDEs with various node generation methods, through which the accuracy and efficiency of the proposed method compared to the predominant uniform sampling approach is verified numerically.

Jianbo Cui, Jialin Hong, Zhihui Liu et al.

We prove the optimal strong convergence rate of a fully discrete scheme, based on a splitting approach, for a stochastic nonlinear Schrödinger (NLS) equation. The main novelty of our method lies on the uniform a priori estimate and exponential integrability of a sequence of splitting processes which are used to approximate the solution of the stochastic NLS equation. We show that the splitting processes converge to the solution with strong order $1/2$. Then we use the Crank--Nicolson scheme to temporally discretize the splitting process and get the temporal splitting scheme which also possesses strong order $1/2$. To obtain a full discretization, we apply this splitting Crank--Nicolson scheme to the spatially discrete equation which is achieved through the spectral Galerkin approximation. Furthermore, we establish the convergence of this fully discrete scheme with optimal strong convergence rate $\mathcal{O}(N^{-2}+τ^\frac12)$, where $N$ denotes the dimension of the approximate space and $τ$ denotes the time step size. To the best of our knowledge, this is the first result about strong convergence rates of temporally numerical approximations and fully discrete schemes for stochastic NLS equations, or even for stochastic partial differential equations (SPDEs) with non-monotone coefficients. Numerical experiments verify our theoretical result.

Wei Peng, Wen Yao, Weien Zhou et al.

Physics-informed neural networks (PINNs) have been proposed to solve two main classes of problems: data-driven solutions and data-driven discovery of partial differential equations. This task becomes prohibitive when such data is highly corrupted due to the possible sensor mechanism failing. We propose the Least Absolute Deviation based PINN (LAD-PINN) to reconstruct the solution and recover unknown parameters in PDEs - even if spurious data or outliers corrupt a large percentage of the observations. To further improve the accuracy of recovering hidden physics, the two-stage Median Absolute Deviation based PINN (MAD-PINN) is proposed, where LAD-PINN is employed as an outlier detector followed by MAD screening out the highly corrupted data. Then the vanilla PINN or its variants can be subsequently applied to exploit the remaining normal data. Through several examples, including Poisson's equation, wave equation, and steady or unsteady Navier-Stokes equations, we illustrate the generalizability, accuracy and efficiency of the proposed algorithms for recovering governing equations from noisy and highly corrupted measurement data.

Jianbo Cui, Jialin Hong, Zhihui Liu et al.

We indicate that the nonlinear Schrödinger equation with white noise dispersion possesses stochastic symplectic and multi-symplectic structures. Based on these structures, we propose the stochastic symplectic and multi-symplectic methods, which preserve the continuous and discrete charge conservation laws, respectively. Moreover, we show that the proposed methods are convergent with temporal order one in probability. Numerical experiments are presented to verify our theoretical results.

Xiaoyu Zhao, Xiaoqian Chen, Zhiqiang Gong et al.

Perception of the full state is an essential technology to support the monitoring, analysis, and design of physical systems, one of whose challenges is to recover global field from sparse observations. Well-known for brilliant approximation ability, deep neural networks have been attractive to data-driven flow and heat field reconstruction studies. However, limited by network structure, existing researches mostly learn the reconstruction mapping in finite-dimensional space and has poor transferability to variable resolution of outputs. In this paper, we extend the new paradigm of neural operator and propose an end-to-end physical field reconstruction method with both excellent performance and mesh transferability named RecFNO. The proposed method aims to learn the mapping from sparse observations to flow and heat field in infinite-dimensional space, contributing to a more powerful nonlinear fitting capacity and resolution-invariant characteristic. Firstly, according to different usage scenarios, we develop three types of embeddings to model the sparse observation inputs: MLP, mask, and Voronoi embedding. The MLP embedding is propitious to more sparse input, while the others benefit from spatial information preservation and perform better with the increase of observation data. Then, we adopt stacked Fourier layers to reconstruct physical field in Fourier space that regularizes the overall recovered field by Fourier modes superposition. Benefiting from the operator in infinite-dimensional space, the proposed method obtains remarkable accuracy and better resolution transferability among meshes. The experiments conducted on fluid mechanics and thermology problems show that the proposed method outperforms existing POD-based and CNN-based methods in most cases and has the capacity to achieve zero-shot super-resolution.

Weien Zhou, Liying Zhang, Jialin Hong et al.

In this paper, we consider the numerical methods preserving single or multiple conserved quantities, and these methods are able to reach high order of strong convergence simultaneously based on some kinds of projection methods. The mean-square convergence orders of these methods under certain conditions are given, which can reach order 1.5 or even 2 according to the supporting methods embedded in the projection step. Finally, three numerical experiments are taken into account to show the superiority of the projection methods.

Weien Zhou, Jingjing Zhang, Jialin Hong et al.

In this paper, we construct stochastic symplectic Runge--Kutta (SSRK) methods of high strong order for Hamiltonian systems with additive noise. By means of colored rooted tree theory, we combine conditions of mean-square order 1.5 and symplectic conditions to get totally derivative-free schemes. We also achieve mean-square order 2.0 symplectic schemes for a class of second-order Hamiltonian systems with additive noise by similar analysis. Finally, linear and non-linear systems are solved numerically, which verifies the theoretical analysis on convergence order. Especially for the stochastic harmonic oscillator with additive noise, the linear growth property can be preserved exactly over long-time simulation.

Yunyang Zhang, Zhiqiang Gong, Weien Zhou et al.

Temperature field prediction is of great importance in the thermal design of systems engineering, and building the surrogate model is an effective way for the task. Generally, large amounts of labeled data are required to guarantee a good prediction performance of the surrogate model, especially the deep learning model, which have more parameters and better representational ability. However, labeled data, especially high-fidelity labeled data, are usually expensive to obtain and sometimes even impossible. To solve this problem, this paper proposes a pithy deep multi-fidelity model (DMFM) for temperature field prediction, which takes advantage of low-fidelity data to boost the performance with less high-fidelity data. First, a pre-train and fine-tune paradigm are developed in DMFM to train the low-fidelity and high-fidelity data, which significantly reduces the complexity of the deep surrogate model. Then, a self-supervised learning method for training the physics-driven deep multi-fidelity model (PD-DMFM) is proposed, which fully utilizes the physics characteristics of the engineering systems and reduces the dependence on large amounts of labeled low-fidelity data in the training process. Two diverse temperature field prediction problems are constructed to validate the effectiveness of DMFM and PD-DMFM, and the result shows that the proposed method can greatly reduce the dependence of the model on high-fidelity data.

Siyu Ye, Shihang Li, Zhiqiang Gong et al.

Efficient onboard multi-field sparse reconstruction is essential for the autonomous operation of aerospace vehicles. While existing deep learning models exhibit promise for single-field reconstruction, deploying multiple independent models leads to prohibitive model size growth and fails to exploit cross-field correlations, particularly under few-shot conditions. To address these challenges, we first propose a lightweight multi-task Fourier neural operator (MTL-FNO), an end-to-end joint training framework based on hard parameter sharing. In each layer, the parameters are divided into shared and task-specific components to capture common features across fields while preserving task-specific characteristics. Moreover, the task-specific fine-tuning parameters are implemented as low-rank terms, achieving substantial model compression. Second, to address the difficulty of co-optimizing shared and task-specific parameters along with their real and imaginary parts, we revisit the FNO's spectral weight from a polar-form perspective and devise a physically meaningful decoupled optimization scheme. Specifically, we apply polar decomposition to slice-wise disentangle the spectral weight into a unitary tensor encoding phase information and a positive semi-definite tensor characterizing amplitude. By decoupling the optimization of phase and amplitude, our method can effectively mitigate tasks conflict. Meanwhile, to preserve unitary geometric fidelity during training, the Cayley transform is introduced to reparameterize the unitary tensor, converting the constrained optimization problem to an unconstrained one. Finally, the effectiveness of the proposed method under few-shot conditions is validated on two representative engineering cases. Results show that MTL-FNO achieves accuracy comparable to or even surpassing that of standard FNO, while reducing total model size by 76% and 60%, respectively.

Donghua Wang, Wen Yao, Tingsong Jiang et al.

Wide deployment of deep neural networks (DNNs) based applications (e.g., style transfer, cartoonish), stimulating the requirement of copyright protection of such application's production. Although some traditional visible copyright techniques are available, they would introduce undesired traces and result in a poor user experience. In this paper, we propose a novel plug-and-play invisible copyright protection method based on defensive perturbation for DNN-based applications (i.e., style transfer). Rather than apply the perturbation to attack the DNNs model, we explore the potential utilization of perturbation in copyright protection. Specifically, we project the copyright information to the defensive perturbation with the designed copyright encoder, which is added to the image to be protected. Then, we extract the copyright information from the encoded copyrighted image with the devised copyright decoder. Furthermore, we use a robustness module to strengthen the decoding capability of the decoder toward images with various distortions (e.g., JPEG compression), which may be occurred when the user posts the image on social media. To ensure the image quality of encoded images and decoded copyright images, a loss function was elaborately devised. Objective and subjective experiment results demonstrate the effectiveness of the proposed method. We have also conducted physical world tests on social media (i.e., Wechat and Twitter) by posting encoded copyright images. The results show that the copyright information in the encoded image saved from social media can still be correctly extracted.

YiFan Hao, Yang Yang, Junru Song et al.

In the field of robotic control, designing individual controllers for each robot leads to high computational costs. Universal control policies, applicable across diverse robot morphologies, promise to mitigate this challenge. Predominantly, models based on Graph Neural Networks (GNN) and Transformers are employed, owing to their effectiveness in capturing relational dynamics across a robot's limbs. However, these models typically employ homogeneous graph structures that overlook the functional diversity of different limbs. To bridge this gap, we introduce HeteroMorpheus, a novel method based on heterogeneous graph Transformer. This method uniquely addresses limb heterogeneity, fostering better representation of robot dynamics of various morphologies. Through extensive experiments we demonstrate the superiority of HeteroMorpheus against state-of-the-art methods in the capability of policy generalization, including zero-shot generalization and sample-efficient transfer to unfamiliar robot morphologies.

Shihang Li, Zhiqiang Gong, Weien Zhou et al.

Accurate reconstruction of temperature field of heat-source systems (TFR-HSS) is crucial for thermal monitoring and reliability assessment in engineering applications such as electronic devices and aerospace structures. However, the high cost of measurement acquisition and the substantial distributional shifts in temperature field across varying conditions present significant challenges for developing reconstruction models with robust generalization capabilities. Existing DNNs-based methods typically formulate TFR-HSS as a one-to-one regression problem based solely on target sparse measurements, without effectively leveraging reference simulation data that implicitly encode thermal knowledge. To address this limitation, we propose IPTR, an implicit physics-guided temperature field reconstruction framework that introduces sparse monitoring-temperature field pair from reference simulations as priors to enrich physical understanding. To integrate both reference and target information, we design a dual physics embedding module consisting of two complementary branches: an implicit physics-guided branch employing cross-attention to distill latent physics from the reference data, and an auxiliary encoding branch based on Fourier layers to capture the spatial characteristics of the target observation. The fused representation is then decoded to reconstruct the full temperature field. Extensive experiments under single-condition, multi-condition, and few-shot settings demonstrate that IPTR consistently outperforms existing methods, achieving state-of-the-art reconstruction accuracy and strong generalization capability.

Wei Peng, Jun Zhang, Weien Zhou et al.

Physics Informed Neural Network (PINN) is a scientific computing framework used to solve both forward and inverse problems modeled by Partial Differential Equations (PDEs). This paper introduces IDRLnet, a Python toolbox for modeling and solving problems through PINN systematically. IDRLnet constructs the framework for a wide range of PINN algorithms and applications. It provides a structured way to incorporate geometric objects, data sources, artificial neural networks, loss metrics, and optimizers within Python. Furthermore, it provides functionality to solve noisy inverse problems, variational minimization, and integral differential equations. New PINN variants can be integrated into the framework easily. Source code, tutorials, and documentation are available at \url{https://github.com/idrl-lab/idrlnet}.

Hanqing Liu, Jiahuan Long, Junqi Wu et al.

Vision-Language-Action (VLA) models have emerged as promising solutions for robotic manipulation, yet their robustness to real-world physical variations remains critically underexplored. To bridge this gap, we propose Eva-VLA, the first unified framework that systematically evaluates the robustness of VLA models by transforming discrete physical variations into continuous optimization problems. However, comprehensively assessing VLA robustness presents two key challenges: (1) how to systematically characterize diverse physical variations encountered in real-world deployments while maintaining evaluation reproducibility, and (2) how to discover worst-case scenarios without prohibitive real-world data collection costs efficiently. To address the first challenge, we decompose real-world variations into three critical domains: object 3D transformations that affect spatial reasoning, illumination variations that challenge visual perception, and adversarial patches that disrupt scene understanding. For the second challenge, we introduce a continuous black-box optimization framework that transforms discrete physical variations into parameter optimization, enabling systematic exploration of worst-case scenarios. Extensive experiments on state-of-the-art OpenVLA models across multiple benchmarks reveal alarming vulnerabilities: all variation types trigger failure rates exceeding 60%, with object transformations causing up to 97.8% failure in long-horizon tasks. Our findings expose critical gaps between controlled laboratory success and unpredictable deployment readiness, while the Eva-VLA framework provides a practical pathway for hardening VLA-based robotic manipulation models against real-world deployment challenges.

Jiahuan Long, Tingsong Jiang, Wen Yao et al.

Tracking multiple objects in a continuous video stream is crucial for many computer vision tasks. It involves detecting and associating objects with their respective identities across successive frames. Despite significant progress made in multiple object tracking (MOT), recent studies have revealed the vulnerability of existing MOT methods to adversarial attacks. Nevertheless, all of these attacks belong to digital attacks that inject pixel-level noise into input images, and are therefore ineffective in physical scenarios. To fill this gap, we propose PapMOT, which can generate physical adversarial patches against MOT for both digital and physical scenarios. Besides attacking the detection mechanism, PapMOT also optimizes a printable patch that can be detected as new targets to mislead the identity association process. Moreover, we introduce a patch enhancement strategy to further degrade the temporal consistency of tracking results across video frames, resulting in more aggressive attacks. We further develop new evaluation metrics to assess the robustness of MOT against such attacks. Extensive evaluations on multiple datasets demonstrate that our PapMOT can successfully attack various architectures of MOT trackers in digital scenarios. We also validate the effectiveness of PapMOT for physical attacks by deploying printed adversarial patches in the real world.

Xu Liu, Wei Peng, Zhiqiang Gong et al.

Temperature field inversion of heat-source systems (TFI-HSS) with limited observations is essential to monitor the system health. Although some methods such as interpolation have been proposed to solve TFI-HSS, those existing methods ignore correlations between data constraints and physics constraints, causing the low precision. In this work, we develop a physics-informed neural network-based temperature field inversion (PINN-TFI) method to solve the TFI-HSS task and a coefficient matrix condition number based position selection of observations (CMCN-PSO) method to select optima positions of noise observations. For the TFI-HSS task, the PINN-TFI method encodes constrain terms into the loss function, thus the task is transformed into an optimization problem of minimizing the loss function. In addition, we have found that noise observations significantly affect reconstruction performances of the PINN-TFI method. To alleviate the effect of noise observations, the CMCN-PSO method is proposed to find optimal positions, where the condition number of observations is used to evaluate positions. The results demonstrate that the PINN-TFI method can significantly improve prediction precisions and the CMCN-PSO method can find good positions to acquire a more robust temperature field.

Donghua Wang, Tingsong Jiang, Jialiang Sun et al.

Physical adversarial attacks in object detection have attracted increasing attention. However, most previous works focus on hiding the objects from the detector by generating an individual adversarial patch, which only covers the planar part of the vehicle's surface and fails to attack the detector in physical scenarios for multi-view, long-distance and partially occluded objects. To bridge the gap between digital attacks and physical attacks, we exploit the full 3D vehicle surface to propose a robust Full-coverage Camouflage Attack (FCA) to fool detectors. Specifically, we first try rendering the nonplanar camouflage texture over the full vehicle surface. To mimic the real-world environment conditions, we then introduce a transformation function to transfer the rendered camouflaged vehicle into a photo realistic scenario. Finally, we design an efficient loss function to optimize the camouflage texture. Experiments show that the full-coverage camouflage attack can not only outperform state-of-the-art methods under various test cases but also generalize to different environments, vehicles, and object detectors. The code of FCA will be available at: https://idrl-lab.github.io/Full-coverage-camouflage-adversarial-attack/.

Xiaoqian Chen, Zhiqiang Gong, Xiaoyu Zhao et al.

Temperature field reconstruction of heat source systems (TFR-HSS) with limited monitoring sensors occurred in thermal management plays an important role in real time health detection system of electronic equipment in engineering. However, prior methods with common interpolations usually cannot provide accurate reconstruction performance as required. In addition, there exists no public dataset for widely research of reconstruction methods to further boost the reconstruction performance and engineering applications. To overcome this problem, this work develops a machine learning modelling benchmark for TFR-HSS task. First, the TFR-HSS task is mathematically modelled from real-world engineering problem and four types of numerically modellings have been constructed to transform the problem into discrete mapping forms. Then, this work proposes a set of machine learning modelling methods, including the general machine learning methods and the deep learning methods, to advance the state-of-the-art methods over temperature field reconstruction. More importantly, this work develops a novel benchmark dataset, namely Temperature Field Reconstruction Dataset (TFRD), to evaluate these machine learning modelling methods for the TFR-HSS task. Finally, a performance analysis of typical methods is given on TFRD, which can be served as the baseline results on this benchmark.

Xu Liu, Xiaoya Zhang, Wei Peng et al.

Physics-informed neural networks (PINNs) have been widely used to solve various scientific computing problems. However, large training costs limit PINNs for some real-time applications. Although some works have been proposed to improve the training efficiency of PINNs, few consider the influence of initialization. To this end, we propose a New Reptile initialization based Physics-Informed Neural Network (NRPINN). The original Reptile algorithm is a meta-learning initialization method based on labeled data. PINNs can be trained with less labeled data or even without any labeled data by adding partial differential equations (PDEs) as a penalty term into the loss function. Inspired by this idea, we propose the new Reptile initialization to sample more tasks from the parameterized PDEs and adapt the penalty term of the loss. The new Reptile initialization can acquire initialization parameters from related tasks by supervised, unsupervised, and semi-supervised learning. Then, PINNs with initialization parameters can efficiently solve PDEs. Besides, the new Reptile initialization can also be used for the variants of PINNs. Finally, we demonstrate and verify the NRPINN considering both forward problems, including solving Poisson, Burgers, and Schrödinger equations, as well as inverse problems, where unknown parameters in the PDEs are estimated. Experimental results show that the NRPINN training is much faster and achieves higher accuracy than PINNs with other initialization methods.

Zhiqiang Gong, Weien Zhou, Jun Zhang et al.

Temperature monitoring during the life time of heat source components in engineering systems becomes essential to guarantee the normal work and the working life of these components. However, prior methods, which mainly use the interpolate estimation to reconstruct the temperature field from limited monitoring points, require large amounts of temperature tensors for an accurate estimation. This may decrease the availability and reliability of the system and sharply increase the monitoring cost. To solve this problem, this work develops a novel physics-informed deep reversible regression models for temperature field reconstruction of heat-source systems (TFR-HSS), which can better reconstruct the temperature field with limited monitoring points unsupervisedly. First, we define the TFR-HSS task mathematically, and numerically model the task, and hence transform the task as an image-to-image regression problem. Then this work develops the deep reversible regression model which can better learn the physical information, especially over the boundary. Finally, considering the physical characteristics of heat conduction as well as the boundary conditions, this work proposes the physics-informed reconstruction loss including four training losses and jointly learns the deep surrogate model with these losses unsupervisedly. Experimental studies have conducted over typical two-dimensional heat-source systems to demonstrate the effectiveness of the proposed method.

Xianqi Chen, Xiaoyu Zhao, Zhiqiang Gong et al.

Thermal issue is of great importance during layout design of heat source components in systems engineering, especially for high functional-density products. Thermal analysis generally needs complex simulation, which leads to an unaffordable computational burden to layout optimization as it iteratively evaluates different schemes. Surrogate modeling is an effective way to alleviate computation complexity. However, temperature field prediction (TFP) with complex heat source layout (HSL) input is an ultra-high dimensional nonlinear regression problem, which brings great difficulty to traditional regression models. The Deep neural network (DNN) regression method is a feasible way for its good approximation performance. However, it faces great challenges in both data preparation for sample diversity and uniformity in the layout space with physical constraints, and proper DNN model selection and training for good generality, which necessitates efforts of both layout designer and DNN experts. To advance this cross-domain research, this paper proposes a DNN based HSL-TFP surrogate modeling task benchmark. With consideration for engineering applicability, sample generation, dataset evaluation, DNN model, and surrogate performance metrics, are thoroughly studied. Experiments are conducted with ten representative state-of-the-art DNN models. Detailed discussion on baseline results is provided and future prospects are analyzed for DNN based HSL-TFP tasks.

Wei Peng, Weien Zhou, Jun Zhang et al.

Physics-Informed Neural Networks (PINNs) can be regarded as general-purpose PDE solvers, but it might be slow to train PINNs on particular problems, and there is no theoretical guarantee of corresponding error bounds. In this manuscript, we propose a variant called Prior Dictionary based Physics-Informed Neural Networks (PD-PINNs). Equipped with task-dependent dictionaries, PD-PINNs enjoy enhanced representation power on the tasks, which helps to capture features provided by dictionaries so that the proposed neural networks can achieve faster convergence in the process of training. In various numerical simulations, compared with existing PINN methods, combining prior dictionaries can significantly enhance convergence speed. In terms of theory, we obtain the error bounds applicable to PINNs and PD-PINNs for solving elliptic partial differential equations of second order. It is proved that under certain mild conditions, the prediction error made by neural networks can be bounded by expected loss of PDEs and boundary conditions.

Liying Zhang, Weien Zhou, Lihai ji

In this papers, we couple the parareal algorithm with projection methods of the trajectory on a specific manifold, defined by the preservation of some conserved quantities of the differential equations. First, projection methods are introduced as the coarse and fine propagators. Second, we also apply the projection methods for systems with conserved quantities in the correction step of original parareal algorithm. Finally, three numerical experiments are performed by different kinds of algorithms to show the property of convergence in iteration, and preservation in conserved quantities of model systems.