Surface-from-gradients (SfG) aims to recover a three-dimensional (3D) surface from its gradients. Traditional methods encounter significant challenges in achieving high accuracy and handling high-resolution inputs, particularly facing the complex nature of discontinuities and the inefficiencies associated with large-scale linear solvers. Although recent advances in deep learning, such as photometric stereo, have enhanced normal estimation accuracy, they do not fully address the intricacies of gradient-based surface reconstruction. To overcome these limitations, we propose a Fourier neural operator-based Numerical Integration Network (FNIN) within a two-stage optimization framework. In the first stage, our approach employs an iterative architecture for numerical integration, harnessing an advanced Fourier neural operator to approximate the solution operator in Fourier space. Additionally, a self-learning attention mechanism is incorporated to effectively detect and handle discontinuities. In the second stage, we refine the surface reconstruction by formulating a weighted least squares problem, addressing the identified discontinuities rationally. Extensive experiments demonstrate that our method achieves significant improvements in both accuracy and efficiency compared to current state-of-the-art solvers. This is particularly evident in handling high-resolution images with complex data, achieving errors of fewer than 0.1 mm on tested objects.

The traditional robust principal component analysis (RPCA) model is based on the nuclear norm, which usually underestimates the singular values of the low‐rank matrix. As a consequence, the restoration image experiences serious interference by Gaussian noise, and the image quality degenerates during the denoising process. Therefore, an improved RPCA method via non‐convex regularisation terms is proposed to remedy the above shortcomings. First, in order to estimate the singular value of the low‐rank matrix more accurately, the authors employ the non‐convex penalty function and add a weight vector to it. Then, the regularisation with non‐convex penalty function and its weighted version are used to replace the nuclear norm and entry‐wise norm in original RPCA, respectively, to establish an improved model. Finally, an optimal solution algorithm is derived by developing the alternating direction multiplier method. Experimental results show that the proposed method has better performance in terms of both quantitative measurement and visual perception quality than other several state‐of‐the‐art image denoising methods.

In order to use remote wind power/solar energy, the scale of power grid interconnection grow rapidly. If transient stability can be increased when faults happen on tie lines, the transmission capacity can be increased too. Dynamic braking can increase transient stability by increasing deceleration area, but it's difficult to coordinate several braking devices and calculate braking amount in real time. Things are no longer so after rotor angle droop (RAD) controllers are deployed across the power system. Since all rotor angles of generators will be fixed in rotating coordination system determined by global position system (GPS) pulse per second (PPS) signal, dynamic braking amount can be calculated by RAD controller by using local speed and rotor measurement. This paper shows the revised equal area criteria (EAC) when this kind of dynamic braking is used. The relationships between RAD controller parameter (saturation threshold) and the braking effect are also investigated. Simulation results in IEEE 68 nodes system show that, by applying dynamic braking on several generators simultaneously, critical clearing time can be increased dramatically when faults happen on tie lines.