Wen Yao

Zeyu Cao, Wen Yao, Wei Peng et al.

The rapid analysis of thermal stress and deformation plays a pivotal role in the thermal control measures and optimization of the structural design of satellites. For achieving real-time thermal stress and thermal deformation analysis of satellite motherboards, this paper proposes a novel Multi-Task Attention UNet (MTA-UNet) neural network which combines the advantages of both Multi-Task Learning (MTL) and U-Net with attention mechanism. Besides, a physics-informed strategy is used in the training process, where partial differential equations (PDEs) are integrated into the loss functions as residual terms. Finally, an uncertainty-based loss balancing approach is applied to weight different loss functions of multiple training tasks. Experimental results show that the proposed MTA-UNet effectively improves the prediction accuracy of multiple physics tasks compared with Single-Task Learning (STL) models. In addition, the physics-informed method brings less error in the prediction of each task, especially on small data sets. The code can be downloaded at: \url{https://github.com/KomorebiTso/MTA-UNet}.

Xiaoyu Zhao, Xiaoqian Chen, Zhiqiang Gong et al.

Few-shot segmentation enables the model to recognize unseen classes with few annotated examples. Most existing methods adopt prototype learning architecture, where support prototype vectors are expanded and concatenated with query features to perform conditional segmentation. However, such framework potentially focuses more on query features while may neglect the similarity between support and query features. This paper proposes a contrastive enhancement approach using latent prototypes to leverage latent classes and raise the utilization of similarity information between prototype and query features. Specifically, a latent prototype sampling module is proposed to generate pseudo-mask and novel prototypes based on features similarity. The module conveniently conducts end-to-end learning and has no strong dependence on clustering numbers like cluster-based method. Besides, a contrastive enhancement module is developed to drive models to provide different predictions with the same query features. Our method can be used as an auxiliary module to flexibly integrate into other baselines for a better segmentation performance. Extensive experiments show our approach remarkably improves the performance of state-of-the-art methods for 1-shot and 5-shot segmentation, especially outperforming baseline by 5.9% and 7.3% for 5-shot task on Pascal-5^i and COCO-20^i. Source code is available at https://github.com/zhaoxiaoyu1995/CELP-Pytorch

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.

Kairui Bao, Wen Yao, Xiaoya Zhang et al.

In the whole aircraft structural optimization loop, thermal analysis plays a very important role. But it faces a severe computational burden when directly applying traditional numerical analysis tools, especially when each optimization involves repetitive parameter modification and thermal analysis followed. Recently, with the fast development of deep learning, several Convolutional Neural Network (CNN) surrogate models have been introduced to overcome this obstacle. However, for temperature field prediction on irregular geometric domains (TFP-IGD), CNN can hardly be competent since most of them stem from processing for regular images. To alleviate this difficulty, we propose a novel physics and data co-driven surrogate modeling method. First, after adapting the Bezier curve in geometric parameterization, a body-fitted coordinate mapping is introduced to generate coordinate transforms between the irregular physical plane and regular computational plane. Second, a physics-driven CNN surrogate with partial differential equation (PDE) residuals as a loss function is utilized for fast meshing (meshing surrogate); then, we present a data-driven surrogate model based on the multi-level reduced-order method, aiming to learn solutions of temperature field in the above regular computational plane (thermal surrogate). Finally, combining the grid position information provided by the meshing surrogate with the scalar temperature field information provided by the thermal surrogate (combined model), we reach an end-to-end surrogate model from geometric parameters to temperature field prediction on an irregular geometric domain. Numerical results demonstrate that our method can significantly improve accuracy prediction on a smaller dataset while reducing the training time when compared with other CNN methods.

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.

Yao Wen, Guopeng Zhang, Kezhi Wang et al.

To alleviate the shortage of computing power faced by clients in training deep neural networks (DNNs) using federated learning (FL), we leverage the edge computing and split learning to propose a model-splitting allowed FL (SFL) framework, with the aim to minimize the training latency without loss of test accuracy. Under the synchronized global update setting, the latency to complete a round of global training is determined by the maximum latency for the clients to complete a local training session. Therefore, the training latency minimization problem (TLMP) is modelled as a minimizing-maximum problem. To solve this mixed integer nonlinear programming problem, we first propose a regression method to fit the quantitative-relationship between the cut-layer and other parameters of an AI-model, and thus, transform the TLMP into a continuous problem. Considering that the two subproblems involved in the TLMP, namely, the cut-layer selection problem for the clients and the computing resource allocation problem for the parameter-server are relative independence, an alternate-optimization-based algorithm with polynomial time complexity is developed to obtain a high-quality solution to the TLMP. Extensive experiments are performed on a popular DNN-model EfficientNetV2 using dataset MNIST, and the results verify the validity and improved performance of the proposed SFL framework.

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.

Yanfang Lyu, Xiaoyu Zhao, Zhiqiang Gong et al.

Data-driven prediction of fluid flow and temperature distribution in marine and aerospace engineering has received extensive research and demonstrated its potential in real-time prediction recently. However, usually large amounts of high-fidelity data are required to describe and accurately predict the complex physical information, while in reality, only limited high-fidelity data is available due to the high experiment/computational cost. Therefore, this work proposes a novel multi-fidelity learning method based on the Fourier Neural Operator by jointing abundant low-fidelity data and limited high-fidelity data under transfer learning paradigm. First, as a resolution-invariant operator, the Fourier Neural Operator is first and gainfully applied to integrate multi-fidelity data directly, which can utilize the scarce high-fidelity data and abundant low-fidelity data simultaneously. Then, the transfer learning framework is developed for the current task by extracting the rich low-fidelity data knowledge to assist high-fidelity modeling training, to further improve data-driven prediction accuracy. Finally, three typical fluid and temperature prediction problems are chosen to validate the accuracy of the proposed multi-fidelity model. The results demonstrate that our proposed method has high effectiveness when compared with other high-fidelity models, and has the high modeling accuracy of 99% for all the selected physical field problems. Significantly, the proposed multi-fidelity learning method has the potential of a simple structure with high precision, which can provide a reference for the construction of the subsequent model.

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.

Xiaohu Zheng, Wen Yao, Yunyang Zhang et al.

Polynomial chaos expansion (PCE) is a powerful surrogate model-based reliability analysis method. Generally, a PCE model with a higher expansion order is usually required to obtain an accurate surrogate model for some complex non-linear stochastic systems. However, the high-order PCE increases the number of labeled data required for solving the expansion coefficients. To alleviate this problem, this paper proposes a consistency regularization-based deep polynomial chaos neural network (Deep PCNN) method, including the low-order adaptive PCE model (the auxiliary model) and the high-order polynomial chaos neural network (the main model). The expansion coefficients of the main model are parameterized into the learnable weights of the polynomial chaos neural network, realizing iterative learning of expansion coefficients to obtain more accurate high-order PCE models. The auxiliary model uses a proposed consistency regularization loss function to assist in training the main model. The consistency regularization-based Deep PCNN method can significantly reduce the number of labeled data in constructing a high-order PCE model without losing accuracy by using few labeled data and abundant unlabeled data. A numerical example validates the effectiveness of the consistency regularization-based Deep PCNN method, and then this method is applied to analyze the reliability of two aerospace engineering systems.

Yunyang Zhang, Zhiqiang Gong, Xiaohu Zheng et al.

As a powerful way of realizing semi-supervised segmentation, the cross supervision method learns cross consistency based on independent ensemble models using abundant unlabeled images. However, the wrong pseudo labeling information generated by cross supervision would confuse the training process and negatively affect the effectiveness of the segmentation model. Besides, the training process of ensemble models in such methods also multiplies the cost of computation resources and decreases the training efficiency. To solve these problems, we propose a novel cross supervision method, namely uncertainty-guided self cross supervision (USCS). In addition to ensemble models, we first design a multi-input multi-output (MIMO) segmentation model which can generate multiple outputs with shared model and consequently impose consistency over the outputs, saving the cost on parameters and calculations. On the other hand, we employ uncertainty as guided information to encourage the model to focus on the high confident regions of pseudo labels and mitigate the effects of wrong pseudo labeling in self cross supervision, improving the performance of the segmentation model. Extensive experiments show that our method achieves state-of-the-art performance while saving 40.5% and 49.1% cost on parameters and calculations.

Yunyang Zhang, Zhiqiang Gong, Xiaoyu Zhao et al.

Recovering a globally accurate complex physics field from limited sensor is critical to the measurement and control in the aerospace engineering. General reconstruction methods for recovering the field, especially the deep learning with more parameters and better representational ability, usually require large amounts of labeled data which is unaffordable. To solve the problem, this paper proposes Uncertainty Guided Ensemble Self-Training (UGE-ST), using plentiful unlabeled data to improve reconstruction performance. A novel self-training framework with the ensemble teacher and pretraining student designed to improve the accuracy of the pseudo-label and remedy the impact of noise is first proposed. On the other hand, uncertainty-guided learning is proposed to encourage the model to focus on the highly confident regions of pseudo-labels and mitigate the effects of wrong pseudo-labeling in self-training, improving the performance of the reconstruction model. Experiments include the pressure velocity field reconstruction of airfoil and the temperature field reconstruction of aircraft system indicate that our UGE-ST can save up to 90% of the data with the same accuracy as supervised learning.

Zixue Xiang, Wei Peng, Wen Yao

Physics-informed neural networks (PINNs) have lately received significant attention as a representative deep learning-based technique for solving partial differential equations (PDEs). Most fully connected network-based PINNs use automatic differentiation to construct loss functions that suffer from slow convergence and difficult boundary enforcement. In addition, although convolutional neural network (CNN)-based PINNs can significantly improve training efficiency, CNNs have difficulty in dealing with irregular geometries with unstructured meshes. Therefore, we propose a novel framework based on graph neural networks (GNNs) and radial basis function finite difference (RBF-FD). We introduce GNNs into physics-informed learning to better handle irregular domains with unstructured meshes. RBF-FD is used to construct a high-precision difference format of the differential equations to guide model training. Finally, we perform numerical experiments on Poisson and wave equations on irregular domains. We illustrate the generalizability, accuracy, and efficiency of the proposed algorithms on different PDE parameters, numbers of collection points, and several types of RBFs.

Jialiang Sun, Wen Yao, Tingsong Jiang et al.

The robustness of deep neural networks (DNN) models has attracted increasing attention due to the urgent need for security in many applications. Numerous existing open-sourced tools or platforms are developed to evaluate the robustness of DNN models by ensembling the majority of adversarial attack or defense algorithms. Unfortunately, current platforms do not possess the ability to optimize the architectures of DNN models or the configuration of adversarial attacks to further enhance the robustness of models or the performance of adversarial attacks. To alleviate these problems, in this paper, we first propose a novel platform called auto adversarial attack and defense ($A^{3}D$), which can help search for robust neural network architectures and efficient adversarial attacks. In $A^{3}D$, we employ multiple neural architecture search methods, which consider different robustness evaluation metrics, including four types of noises: adversarial noise, natural noise, system noise, and quantified metrics, resulting in finding robust architectures. Besides, we propose a mathematical model for auto adversarial attack, and provide multiple optimization algorithms to search for efficient adversarial attacks. In addition, we combine auto adversarial attack and defense together to form a unified framework. Among auto adversarial defense, the searched efficient attack can be used as the new robustness evaluation to further enhance the robustness. In auto adversarial attack, the searched robust architectures can be utilized as the threat model to help find stronger adversarial attacks. Experiments on CIFAR10, CIFAR100, and ImageNet datasets demonstrate the feasibility and effectiveness of the proposed platform, which can also provide a benchmark and toolkit for researchers in the application of automated machine learning in evaluating and improving the DNN model robustnesses.

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, Wenzhe Zhang, Ning Wang et al.

Physical field reconstruction (PFR) aims to predict the state distribution of physical quantities (e.g., velocity, pressure, and temperature) based on limited sensor measurements. It plays a critical role in domains such as fluid dynamics and thermodynamics. However, existing deep learning methods often fail to capture long-range temporal dependencies, resulting in suboptimal performance on time-evolving physical systems. To address this, we propose FR-Mamba, a novel spatiotemporal flow field reconstruction framework based on state space modeling. Specifically, we design a hybrid neural network architecture that combines Fourier Neural Operator (FNO) and State Space Model (SSM) to capture both global spatial features and long-range temporal dependencies. We adopt Mamba, a recently proposed efficient SSM architecture, to model long-range temporal dependencies with linear time complexity. In parallel, the FNO is employed to capture non-local spatial features by leveraging frequency-domain transformations. The spatiotemporal representations extracted by these two components are then fused to reconstruct the full-field distribution of the physical system. Extensive experiments demonstrate that our approach significantly outperforms existing PFR methods in flow field reconstruction tasks, achieving high-accuracy performance on long sequences.

Jialiang Sun, Wen Yao, Tingsong Jiang et al.

Neural architecture search (NAS) has emerged as one successful technique to find robust deep neural network (DNN) architectures. However, most existing robustness evaluations in NAS only consider $l_{\infty}$ norm-based adversarial noises. In order to improve the robustness of DNN models against multiple types of noises, it is necessary to consider a comprehensive evaluation in NAS for robust architectures. But with the increasing number of types of robustness evaluations, it also becomes more time-consuming to find comprehensively robust architectures. To alleviate this problem, we propose a novel efficient search of comprehensively robust neural architectures via multi-fidelity evaluation (ES-CRNA-ME). Specifically, we first search for comprehensively robust architectures under multiple types of evaluations using the weight-sharing-based NAS method, including different $l_{p}$ norm attacks, semantic adversarial attacks, and composite adversarial attacks. In addition, we reduce the number of robustness evaluations by the correlation analysis, which can incorporate similar evaluations and decrease the evaluation cost. Finally, we propose a multi-fidelity online surrogate during optimization to further decrease the search cost. On the basis of the surrogate constructed by low-fidelity data, the online high-fidelity data is utilized to finetune the surrogate. Experiments on CIFAR10 and CIFAR100 datasets show the effectiveness of our proposed method.

Xiaohu Zheng, Wen Yao, Zhiqiang Gong et al.

Temperature field reconstruction is essential for analyzing satellite heat reliability. As a representative machine learning model, the deep convolutional neural network (DCNN) is a powerful tool for reconstructing the satellite temperature field. However, DCNN needs a lot of labeled data to learn its parameters, which is contrary to the fact that actual satellite engineering can only acquire noisy unlabeled data. To solve the above problem, this paper proposes an unsupervised method, i.e., the physics-informed deep Monte Carlo quantile regression method, for reconstructing temperature field and quantifying the aleatoric uncertainty caused by data noise. For one thing, the proposed method combines a deep convolutional neural network with the known physics knowledge to reconstruct an accurate temperature field using only monitoring point temperatures. For another thing, the proposed method can quantify the aleatoric uncertainty by the Monte Carlo quantile regression. Based on the reconstructed temperature field and the quantified aleatoric uncertainty, this paper models an interval multilevel Bayesian Network to analyze satellite heat reliability. Two case studies are used to validate the proposed method.

Xiaohu Zheng, Wen Yao, Zhiqiang Gong et al.

For the temperature field reconstruction (TFR), a complex image-to-image regression problem, the convolutional neural network (CNN) is a powerful surrogate model due to the convolutional layer's good image feature extraction ability. However, a lot of labeled data is needed to train CNN, and the common CNN can not quantify the aleatoric uncertainty caused by data noise. In actual engineering, the noiseless and labeled training data is hardly obtained for the TFR. To solve these two problems, this paper proposes a deep Monte Carlo quantile regression (Deep MC-QR) method for reconstructing the temperature field and quantifying aleatoric uncertainty caused by data noise. On the one hand, the Deep MC-QR method uses physical knowledge to guide the training of CNN. Thereby, the Deep MC-QR method can reconstruct an accurate TFR surrogate model without any labeled training data. On the other hand, the Deep MC-QR method constructs a quantile level image for each input in each training epoch. Then, the trained CNN model can quantify aleatoric uncertainty by quantile level image sampling during the prediction stage. Finally, the effectiveness of the proposed Deep MC-QR method is validated by many experiments, and the influence of data noise on TFR is analyzed.

Xingwen Peng, Xingchen Li, Zhiqiang Gong et al.

Physical field reconstruction is highly desirable for the measurement and control of engineering systems. The reconstruction of the temperature field from limited observation plays a crucial role in thermal management for electronic equipment. Deep learning has been employed in physical field reconstruction, whereas the accurate estimation for the regions with large gradients is still diffcult. To solve the problem, this work proposes a novel deep learning method based on patchwise training to reconstruct the temperature field of electronic equipment accurately from limited observation. Firstly, the temperature field reconstruction (TFR) problem of the electronic equipment is modeled mathematically and transformed as an image-to-image regression task. Then a patchwise training and inference framework consisting of an adaptive UNet and a shallow multilayer perceptron (MLP) is developed to establish the mapping from the observation to the temperature field. The adaptive UNet is utilized to reconstruct the whole temperature field while the MLP is designed to predict the patches with large temperature gradients. Experiments employing finite element simulation data are conducted to demonstrate the accuracy of the proposed method. Furthermore, the generalization is evaluated by investigating cases under different heat source layouts, different power intensities, and different observation point locations. The maximum absolute errors of the reconstructed temperature field are less than 1K under the patchwise training approach.

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/.

Wen Yao, Xiaohu Zheng, Jun Zhang et al.

The surrogate model-based uncertainty quantification method has drawn much attention in many engineering fields. Polynomial chaos expansion (PCE) and deep learning (DL) are powerful methods for building a surrogate model. However, PCE needs to increase the expansion order to improve the accuracy of the surrogate model, which causes more labeled data to solve the expansion coefficients, and DL also requires a lot of labeled data to train the deep neural network (DNN). First of all, this paper proposes the adaptive arbitrary polynomial chaos (aPC) and proves two properties about the adaptive expansion coefficients. Based on the adaptive aPC, a semi-supervised deep adaptive arbitrary polynomial chaos expansion (Deep aPCE) method is proposed to reduce the training data cost and improve the surrogate model accuracy. For one hand, the Deep aPCE method uses two properties of the adaptive aPC to assist in training the DNN based on only a small amount of labeled data and many unlabeled data, significantly reducing the training data cost. On the other hand, the Deep aPCE method adopts the DNN to fine-tune the adaptive expansion coefficients dynamically, improving the Deep aPCE model accuracy with lower expansion order. Besides, the Deep aPCE method can directly construct accurate surrogate models of the high dimensional stochastic systems without complex dimension-reduction and model decomposition operations. Five numerical examples and an actual engineering problem are used to verify the effectiveness of the Deep aPCE method.

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.