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Zijian Zhou

Publications and source records attributed to Zijian Zhou.

97 records · Page 6Linked to original sources
arXiv2020

Solving forward and inverse problems of the logarithmic nonlinear Schrodinger equation with PT-symmetric harmonic potential via deep learning

In this paper, we investigate the logarithmic nonlinear Schrödinger (LNLS) equation with the parity-time (PT)-symmetric harmonic potential, which is an important physical model in many fields such as nuclear physics, quantum optics, magma transport phenomena, and effective quantum gravity. Three types of initial value conditions and periodic boundary conditions are chosen to solve the LNLS equation with PT -symmetric harmonic potential via the physics-informed neural networks (PINNs) deep learning method, and these obtained results are compared with ones deduced from the Fourier spectral method. Moreover, we also investigate the effectiveness of the PINNs deep learning for the LNLS equation with PT symmetric potential by choosing the distinct space widths or distinct optimized steps. Finally, we use the PINNs deep learning method to effectively tackle the data-driven discovery of the LNLS equation with PT -symmetric harmonic potential such that the coefficients of dispersion and nonlinear terms or the amplitudes of PT -symmetric harmonic potential can be approximately found.

nlin.PS↗
arXiv2020

BAIL: Best-Action Imitation Learning for Batch Deep Reinforcement Learning

There has recently been a surge in research in batch Deep Reinforcement Learning (DRL), which aims for learning a high-performing policy from a given dataset without additional interactions with the environment. We propose a new algorithm, Best-Action Imitation Learning (BAIL), which strives for both simplicity and performance. BAIL learns a V function, uses the V function to select actions it believes to be high-performing, and then uses those actions to train a policy network using imitation learning. For the MuJoCo benchmark, we provide a comprehensive experimental study of BAIL, comparing its performance to four other batch Q-learning and imitation-learning schemes for a large variety of batch datasets. Our experiments show that BAIL's performance is much higher than the other schemes, and is also computationally much faster than the batch Q-learning schemes.

cs.LG↗
arXiv2020

Gaussian Vector: An Efficient Solution for Facial Landmark Detection

Significant progress has been made in facial landmark detection with the development of Convolutional Neural Networks. The widely-used algorithms can be classified into coordinate regression methods and heatmap based methods. However, the former loses spatial information, resulting in poor performance while the latter suffers from large output size or high post-processing complexity. This paper proposes a new solution, Gaussian Vector, to preserve the spatial information as well as reduce the output size and simplify the post-processing. Our method provides novel vector supervision and introduces Band Pooling Module to convert heatmap into a pair of vectors for each landmark. This is a plug-and-play component which is simple and effective. Moreover, Beyond Box Strategy is proposed to handle the landmarks out of the face bounding box. We evaluate our method on 300W, COFW, WFLW and JD-landmark. That the results significantly surpass previous works demonstrates the effectiveness of our approach.

cs.CV↗
arXiv2020

Ekedahl-Oort strata of curves of genus four in characteristic three

We study the induced Ekedahl-Oort stratification on the moduli space $\mathcal{M}_4$ of curves of genus $4$ in characteristic $3$. By constructing families of curves with given Ekedahl-Oort type and by computing the dimension of the intersection of the induced Ekedahl-Oort strata and the boundary divisor classes, we show that for certain induced Ekedahl-Oort strata in $\mathcal{M}_4$, they have the same codimension in $\mathcal{M}_4$ as the corresponding Ekedahl-Oort strata in moduli space $\mathcal{A}_4$ of principally polarized abelian varieties of dimension $4$.

math.AG↗