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Zijian Zhou

Publications and source records attributed to Zijian Zhou.

101 records · Page 6Linked to original sources
arXiv2022

Data-driven discoveries of Bäcklund transforms and soliton evolution equations via deep neural network learning schemes

We introduce a deep neural network learning scheme to learn the Bäcklund transforms (BTs) of soliton evolution equations and an enhanced deep learning scheme for data-driven soliton equation discovery based on the known BTs, respectively. The first scheme takes advantage of some solution (or soliton equation) information to study the data-driven BT of sine-Gordon equation, and complex and real Miura transforms between the defocusing (focusing) mKdV equation and KdV equation, as well as the data-driven mKdV equation discovery via the Miura transforms. The second deep learning scheme uses the explicit/implicit BTs generating the higher-order solitons to train the data-driven discovery of mKdV and sine-Gordon equations, in which the high-order solution informations are more powerful for the enhanced leaning soliton equations with higher accurates.

cs.LG↗
arXiv2021

Deep neural networks for solving forward and inverse problems of (2+1)-dimensional nonlinear wave equations with rational solitons

In this paper, we investigate the forward problems on the data-driven rational solitons for the (2+1)-dimensional KP-I equation and spin-nonlinear Schrödinger (spin-NLS) equation via the deep neural networks leaning. Moreover, the inverse problems of the (2+1)-dimensional KP-I equation and spin-NLS equation are studied via deep learning. The main idea of the data-driven forward and inverse problems is to use the deep neural networks with the activation function to approximate the solutions of the considered (2+1)-dimensional nonlinear wave equations by optimizing the chosen loss functions related to the considered nonlinear wave equations.

nlin.PS↗
arXiv2021

Deep learning neural networks for the third-order nonlinear Schrodinger equation: Solitons, breathers, and rogue waves

The third-order nonlinear Schrodinger equation (alias the Hirota equation) is investigated via deep leaning neural networks, which describes the strongly dispersive ion-acoustic wave in plasma and the wave propagation of ultrashort light pulses in optical fibers, as well as broader-banded waves on deep water. In this paper, we use the physics-informed neural networks (PINNs) deep learning method to explore the data-driven solutions (e.g., soliton, breather, and rogue waves) of the Hirota equation when the two types of the unperturbated and unperturbated (a 2% noise) training data are considered. Moreover, we use the PINNs deep learning to study the data-driven discovery of parameters appearing in the Hirota equation with the aid of solitons.

nlin.PS↗
arXiv2021

Randomized Ensembled Double Q-Learning: Learning Fast Without a Model

Using a high Update-To-Data (UTD) ratio, model-based methods have recently achieved much higher sample efficiency than previous model-free methods for continuous-action DRL benchmarks. In this paper, we introduce a simple model-free algorithm, Randomized Ensembled Double Q-Learning (REDQ), and show that its performance is just as good as, if not better than, a state-of-the-art model-based algorithm for the MuJoCo benchmark. Moreover, REDQ can achieve this performance using fewer parameters than the model-based method, and with less wall-clock run time. REDQ has three carefully integrated ingredients which allow it to achieve its high performance: (i) a UTD ratio >> 1; (ii) an ensemble of Q functions; (iii) in-target minimization across a random subset of Q functions from the ensemble. Through carefully designed experiments, we provide a detailed analysis of REDQ and related model-free algorithms. To our knowledge, REDQ is the first successful model-free DRL algorithm for continuous-action spaces using a UTD ratio >> 1.

cs.LG↗
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↗