Shiqi Gong

Peiyan Hu, Qi Meng, Bingguang Chen et al.

Stochastic partial differential equations (SPDEs) are significant tools for modeling dynamics in many areas including atmospheric sciences and physics. Neural Operators, generations of neural networks with capability of learning maps between infinite-dimensional spaces, are strong tools for solving parametric PDEs. However, they lack the ability to modeling SPDEs which usually have poor regularity due to the driving noise. As the theory of regularity structure has achieved great successes in analyzing SPDEs and provides the concept model feature vectors that well-approximate SPDEs' solutions, we propose the Neural Operator with Regularity Structure (NORS) which incorporates the feature vectors for modeling dynamics driven by SPDEs. We conduct experiments on various of SPDEs including the dynamic Phi41 model and the 2d stochastic Navier-Stokes equation, and the results demonstrate that the NORS is resolution-invariant, efficient, and achieves one order of magnitude lower error with a modest amount of data.

Qi Dai, Beixiong Zheng, Yanhua Tan et al.

Unlike conventional fixed-antenna architectures, rotatable antenna (RA) has shown great potential in enhancing wireless communication performance by exploiting additional spatial degrees of freedom (DoFs) in a cost-effective manner. In this letter, we propose a novel RA-enabled covert communication system, where an RA array-based transmitter (Alice) sends covert information to a legitimate user (Bob) in the presence of multiple wardens (Willies). To maximize the covert rate, we optimize the transmit beamforming vector and the rotational angles of individual RAs, subject to the constraints on covertness, transmit power, and antenna rotational range. To address the non-convex formulated problem, we decompose it into two subproblems and propose an efficient alternating optimization (AO) algorithm to solve the two subproblems iteratively, where the second-order cone programming (SOCP) method and successive convex approximation (SCA) approach are applied separately. Simulation results demonstrate that the proposed RA-enabled covert communication system can provide significantly superior covertness performance to other benchmark schemes.

Shiqi Gong, Qi Meng, Yue Wang et al.

Learning dynamics governed by differential equations is crucial for predicting and controlling the systems in science and engineering. Neural Ordinary Differential Equation (NODE), a deep learning model integrated with differential equations, is popular in learning dynamics recently due to its robustness to irregular samples and its flexibility to high-dimensional input. However, the training of NODE is sensitive to the precision of the numerical solver, which makes the convergence of NODE unstable, especially for ill-conditioned dynamical systems. In this paper, to reduce the reliance on the numerical solver, we propose to enhance the supervised signal in the training of NODE. Specifically, we pre-train a neural differential operator (NDO) to output an estimation of the derivatives to serve as an additional supervised signal. The NDO is pre-trained on a class of basis functions and learns the mapping between the trajectory samples of these functions to their derivatives. To leverage both the trajectory signal and the estimated derivatives from NDO, we propose an algorithm called NDO-NODE, in which the loss function contains two terms: the fitness on the true trajectory samples and the fitness on the estimated derivatives that are outputted by the pre-trained NDO. Experiments on various kinds of dynamics show that our proposed NDO-NODE can consistently improve the forecasting accuracy with one pre-trained NDO. Especially for the stiff ODEs, we observe that NDO-NODE can capture the transitions in the dynamics more accurately compared with other regularization methods.

Qi Meng, Shiqi Gong, Wei Chen et al.

Stochastic gradient descent (SGD) and its variants are mainstream methods to train deep neural networks. Since neural networks are non-convex, more and more works study the dynamic behavior of SGD and the impact to its generalization, especially the escaping efficiency from local minima. However, these works take the over-simplified assumption that the covariance of the noise in SGD is (or can be upper bounded by) constant, although it is actually state-dependent. In this work, we conduct a formal study on the dynamic behavior of SGD with state-dependent noise. Specifically, we show that the covariance of the noise of SGD in the local region of the local minima is a quadratic function of the state. Thus, we propose a novel power-law dynamic with state-dependent diffusion to approximate the dynamic of SGD. We prove that, power-law dynamic can escape from sharp minima exponentially faster than flat minima, while the previous dynamics can only escape sharp minima polynomially faster than flat minima. Our experiments well verified our theoretical results. Inspired by our theory, we propose to add additional state-dependent noise into (large-batch) SGD to further improve its generalization ability. Experiments verify that our method is effective.