Yao Li

Shengzhu Shi, Yao Li, Zhichang Guo et al.

Physics-informed neural networks (PINNs) have shown great promise in solving partial differential equations (PDEs). However, vanilla PINNs often face challenges when solving complex PDEs, especially those involving multi-scale behaviors or solutions with sharp or oscillatory characteristics. To precisely and adaptively locate the critical regions that fail in the solving process we propose a sampling strategy grounded in white-box adversarial attacks, referred to as WbAR. WbAR search for failure regions in the direction of the loss gradient, thus directly locating the most critical positions. WbAR generates adversarial samples in a random walk manner and iteratively refines PINNs to guide the model's focus towards dynamically updated critical regions during training. We implement WbAR to the elliptic equation with multi-scale coefficients, Poisson equation with multi-peak solutions, high-dimensional Poisson equations, and Burgers equation with sharp solutions. The results demonstrate that WbAR can effectively locate and reduce failure regions. Moreover, WbAR is suitable for solving complex PDEs, since locating failure regions through adversarial attacks is independent of the size of failure regions or the complexity of the distribution.

Xiu-Shen Wei, Chen-Lin Zhang, Yao Li et al.

Reusable model design becomes desirable with the rapid expansion of machine learning applications. In this paper, we focus on the reusability of pre-trained deep convolutional models. Specifically, different from treating pre-trained models as feature extractors, we reveal more treasures beneath convolutional layers, i.e., the convolutional activations could act as a detector for the common object in the image co-localization problem. We propose a simple but effective method, named Deep Descriptor Transforming (DDT), for evaluating the correlations of descriptors and then obtaining the category-consistent regions, which can accurately locate the common object in a set of images. Empirical studies validate the effectiveness of the proposed DDT method. On benchmark image co-localization datasets, DDT consistently outperforms existing state-of-the-art methods by a large margin. Moreover, DDT also demonstrates good generalization ability for unseen categories and robustness for dealing with noisy data.