Xü Liu

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.

Yongheng Zhang, Xu Liu, Ruihan Tao et al.

Video understanding plays a vital role in bridging low-level visual signals with high-level cognitive reasoning, and is fundamental to applications such as autonomous driving, embodied AI, and the broader pursuit of AGI. The rapid development of large language models (LLMs), particularly those utilizing Chain-of-Thought (CoT) technology, has significantly advanced video reasoning capabilities. However, current approaches primarily depend on textual information for reasoning, overlooking the visual modality in the actual video reasoning process. In contrast, humans naturally re-examine visual content while reasoning. Motivated by this, we introduce a novel video reasoning paradigm: Video-Text Interleaved CoT (ViTCoT), which facilitates more intuitive and cognitively aligned reasoning. To the end, first, we construct the Video-Text Interleaved Benchmark (ViTIB), which is created using MLLMs for key-video selection and manually verified. Furthermore, we extensively explore the potential of the ViTCoT paradigm in the video understanding field. Extensive experiments demonstrate that ViTCoT significantly enhances performance compared to the traditional text-only CoT paradigm and effectively activates more neuron values in MLLMs.

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.

Zhicheng Guo, Jiaxuan Zhao, Licheng Jiao et al.

We propose a balanced coarsening scheme for multilevel hypergraph partitioning. In addition, an initial partitioning algorithm is designed to improve the quality of k-way hypergraph partitioning. By assigning vertex weights through the LPT algorithm, we generate a prior hypergraph under a relaxed balance constraint. With the prior hypergraph, we have defined the Wasserstein discrepancy to coordinate the optimal transport of coarsening process. And the optimal transport matrix is solved by Sinkhorn algorithm. Our coarsening scheme fully takes into account the minimization of connectivity metric (objective function). For the initial partitioning stage, we define a normalized cut function induced by Fiedler vector, which is theoretically proved to be a concave function. Thereby, a three-point algorithm is designed to find the best cut under the balance constraint.