Wei Peng

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.

Maonian Wu, Bang Chen, Shaojun Zhu et al.

A recommendation system assists users in finding items that are relevant to them. Existing recommendation models are primarily based on predicting relationships between users and items and use complex matching models or incorporate extensive external information to capture association patterns in data. However, recommendation is not only a problem of inductive statistics using data; it is also a cognitive task of reasoning decisions based on knowledge extracted from information. Hence, a logic system could naturally be incorporated for the reasoning in a recommendation task. However, although hard-rule approaches based on logic systems can provide powerful reasoning ability, they struggle to cope with inconsistent and incomplete knowledge in real-world tasks, especially for complex tasks such as recommendation. Therefore, in this paper, we propose a neuro-symbolic recommendation model, which transforms the user history interactions into a logic expression and then transforms the recommendation prediction into a query task based on this logic expression. The logic expressions are then computed based on the modular logic operations of the neural network. We also construct an implicit logic encoder to reasonably reduce the complexity of the logic computation. Finally, a user's interest items can be queried in the vector space based on the computation results. Experiments on three well-known datasets verified that our method performs better compared to state of the art shallow, deep, session, and reasoning models.

Wei Peng, Kang Liu, Jianchen Hu et al.

Prompt learning is one of the most effective paradigms for adapting pre-trained vision-language models (VLMs) to the biomedical image classification tasks in few shot scenarios. However, most of the current prompt learning methods only used the text prompts and ignored the particular structures (such as the complex anatomical structures and subtle pathological features) in the biomedical images. In this work, we propose Biomed-DPT, a knowledge-enhanced dual modality prompt tuning technique. In designing the text prompt, Biomed-DPT constructs a dual prompt including the template-driven clinical prompts and the large language model (LLM)-driven domain-adapted prompts, then extracts the clinical knowledge from the domain-adapted prompts through the knowledge distillation technique. In designing the vision prompt, Biomed-DPT introduces the zero vector as a soft prompt to leverage attention re-weighting so that the focus on non-diagnostic regions and the recognition of non-critical pathological features are avoided. Biomed-DPT achieves an average classification accuracy of 66.14\% across 11 biomedical image datasets covering 9 modalities and 10 organs, with performance reaching 78.06\% in base classes and 75.97\% in novel classes, surpassing the Context Optimization (CoOp) method by 6.20\%, 3.78\%, and 8.04\%, respectively. Our code are available at \underline{https://github.com/Kanyooo/Biomed-DPT}.

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}.

Xiutian Zhao, Ke Wang, Wei Peng

Despite large language models' (LLMs) recent advancements, their bias and hallucination issues persist, and their ability to offer consistent preferential rankings remains underexplored. This study investigates the capacity of LLMs to provide consistent ordinal preferences, a crucial aspect in scenarios with dense decision space or lacking absolute answers. We introduce a formalization of consistency based on order theory, outlining criteria such as transitivity, asymmetry, reversibility, and independence from irrelevant alternatives. Our diagnostic experiments on selected state-of-the-art LLMs reveal their inability to meet these criteria, indicating a strong positional bias and poor transitivity, with preferences easily swayed by irrelevant alternatives. These findings highlight a significant inconsistency in LLM-generated preferential rankings, underscoring the need for further research to address these limitations.

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.

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.

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.

Weibo Huang, Peng Wei

To coupe with the difficulties in the process of inspection and classification of defects in Printed Circuit Board (PCB), other researchers have proposed many methods. However, few of them published their dataset before, which hindered the introduction and comparison of new methods. In this paper, we published a synthesized PCB dataset containing 1386 images with 6 kinds of defects for the use of detection, classification and registration tasks. Besides, we proposed a reference based method to inspect and trained an end-to-end convolutional neural network to classify the defects. Unlike conventional approaches that require pixel-by-pixel processing, our method firstly locate the defects and then classify them by neural networks, which shows superior performance on our dataset.