Jia Zhang

Xinquan Huang, Wenlei Shi, Xiaotian Gao et al.

Neural operators, as a powerful approximation to the non-linear operators between infinite-dimensional function spaces, have proved to be promising in accelerating the solution of partial differential equations (PDE). However, it requires a large amount of simulated data, which can be costly to collect. This can be avoided by learning physics from the physics-constrained loss, which we refer to it as mean squared residual (MSR) loss constructed by the discretized PDE. We investigate the physical information in the MSR loss, which we called long-range entanglements, and identify the challenge that the neural network requires the capacity to model the long-range entanglements in the spatial domain of the PDE, whose patterns vary in different PDEs. To tackle the challenge, we propose LordNet, a tunable and efficient neural network for modeling various entanglements. Inspired by the traditional solvers, LordNet models the long-range entanglements with a series of matrix multiplications, which can be seen as the low-rank approximation to the general fully-connected layers and extracts the dominant pattern with reduced computational cost. The experiments on solving Poisson's equation and (2D and 3D) Navier-Stokes equation demonstrate that the long-range entanglements from the MSR loss can be well modeled by the LordNet, yielding better accuracy and generalization ability than other neural networks. The results show that the Lordnet can be $40\times$ faster than traditional PDE solvers. In addition, LordNet outperforms other modern neural network architectures in accuracy and efficiency with the smallest parameter size.

Lin Huang, Qiyuan Dong, Lijun Wu et al.

As a specific semantic segmentation task, aerial imagery segmentation has been widely employed in high spatial resolution (HSR) remote sensing images understanding. Besides common issues (e.g. large scale variation) faced by general semantic segmentation tasks, aerial imagery segmentation has some unique challenges, the most critical one among which lies in foreground-background imbalance. There have been some recent efforts that attempt to address this issue by proposing sophisticated neural network architectures, since they can be used to extract informative multi-scale feature representations and increase the discrimination of object boundaries. Nevertheless, many of them merely utilize those multi-scale representations in ad-hoc measures but disregard the fact that the semantic meaning of objects with various sizes could be better identified via receptive fields of diverse ranges. In this paper, we propose Adaptive Focus Framework (AF$_2$), which adopts a hierarchical segmentation procedure and focuses on adaptively utilizing multi-scale representations generated by widely adopted neural network architectures. Particularly, a learnable module, called Adaptive Confidence Mechanism (ACM), is proposed to determine which scale of representation should be used for the segmentation of different objects. Comprehensive experiments show that AF$_2$ has significantly improved the accuracy on three widely used aerial benchmarks, as fast as the mainstream method.