Jun Zhang

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}.

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.

Liwei Hu, Yu Xiang, Jun Zhan et al.

The quality of datasets is one of the key factors that affect the accuracy of aerodynamic data models. For example, in the uniformly sampled Burgers' dataset, the insufficient high-speed data is overwhelmed by massive low-speed data. Predicting high-speed data is more difficult than predicting low-speed data, owing to that the number of high-speed data is limited, i.e. the quality of the Burgers' dataset is not satisfactory. To improve the quality of datasets, traditional methods usually employ the data resampling technology to produce enough data for the insufficient parts in the original datasets before modeling, which increases computational costs. Recently, the mixtures of experts have been used in natural language processing to deal with different parts of sentences, which provides a solution for eliminating the need for data resampling in aerodynamic data modeling. Motivated by this, we propose the multi-task learning (MTL), a datasets quality-adaptive learning scheme, which combines task allocation and aerodynamic characteristics learning together to disperse the pressure of the entire learning task. The task allocation divides a whole learning task into several independent subtasks, while the aerodynamic characteristics learning learns these subtasks simultaneously to achieve better precision. Two experiments with poor quality datasets are conducted to verify the data quality-adaptivity of the MTL to datasets. The results show than the MTL is more accurate than FCNs and GANs in poor quality datasets.

Liwei Hu, Wenyong Wang, Yu Xiang et al.

Nonlinear sparse data regression and generation have been a long-term challenge, to cite the flow field reconstruction as a typical example. The huge computational cost of computational fluid dynamics (CFD) makes it much expensive for large scale CFD data producing, which is the reason why we need some cheaper ways to do this, of which the traditional reduced order models (ROMs) were promising but they couldn't generate a large number of full domain flow field data (FFD) to realize high-precision flow field reconstructions. Motivated by the problems of existing approaches and inspired by the success of the generative adversarial networks (GANs) in the field of computer vision, we prove an optimal discriminator theorem that the optimal discriminator of a GAN is a radial basis function neural network (RBFNN) while dealing with nonlinear sparse FFD regression and generation. Based on this theorem, two radial basis function-based GANs (RBF-GAN and RBFC-GAN), for regression and generation purposes, are proposed. Three different datasets are applied to verify the feasibility of our models. The results show that the performance of the RBF-GAN and the RBFC-GAN are better than that of GANs/cGANs by means of both the mean square error (MSE) and the mean square percentage error (MSPE). Besides, compared with GANs/cGANs, the stability of the RBF-GAN and the RBFC-GAN improve by 34.62% and 72.31%, respectively. Consequently, our proposed models can be used to generate full domain FFD from limited and sparse datasets, to meet the requirement of high-precision flow field reconstructions.

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.