no code implementations • 1 Jul 2024 • Zhiqiang Cai, Anastassia Doktorova, Robert D. Falgout, César Herrera

We present a factorization of the mass matrix that enables solving the systems of linear equations in ${\cal O}(n)$ operations.

no code implementations • 29 May 2024 • Zhiqiang Cai, Yu Cao, Yuanfei Huang, Xiang Zhou

Sampling invariant distributions from an Ito diffusion process presents a significant challenge in stochastic simulation.

no code implementations • 7 Apr 2024 • Zhiqiang Cai, Tong Ding, Min Liu, Xinyu Liu, Jianlin Xia

In this paper, we propose a structure-guided Gauss-Newton (SgGN) method for solving least squares problems using a shallow ReLU neural network.

no code implementations • 7 Mar 2024 • Jialin Chen, Zhiqiang Cai, Ke Xu, Di wu, Wei Cao

Considering the noise level limit, one crucial aspect for quantum machine learning is to design a high-performing variational quantum circuit architecture with small number of quantum gates.

no code implementations • 9 Sep 2022 • Jiayue Han, Zhiqiang Cai, Zhiyou Wu, Xiang Zhou

Thus, we propose the Residual-Quantile Adjustment (RQA) method for a better weight choice for each training sample.

no code implementations • 19 Nov 2021 • Zhiqiang Cai, Ling Lin, Xiang Zhou

We propose a reinforcement learning (RL) approach to compute the expression of quasi-stationary distribution.

no code implementations • 21 Oct 2021 • Zhiqiang Cai, Jingshuang Chen, Min Liu

A least-squares neural network (LSNN) method was introduced for solving scalar linear and nonlinear hyperbolic conservation laws (HCLs) in [7, 6].

no code implementations • 29 Sep 2021 • Min Liu, Zhiqiang Cai, Karthik Ramani

This paper presents RitzNet, an unsupervised learning method which takes any point in the computation domain as input, and learns a neural network model to output its corresponding function value satisfying the underlying governing PDEs.

no code implementations • 7 Sep 2021 • Zhiqiang Cai, Jingshuang Chen, Min Liu

Designing an optimal deep neural network for a given task is important and challenging in many machine learning applications.

no code implementations • 25 May 2021 • Zhiqiang Cai, Jingshuang Chen, Min Liu

We introduced the least-squares ReLU neural network (LSNN) method for solving the linear advection-reaction problem with discontinuous solution and showed that the method outperforms mesh-based numerical methods in terms of the number of degrees of freedom.

no code implementations • 25 May 2021 • Zhiqiang Cai, Jingshuang Chen, Min Liu

This paper studies least-squares ReLU neural network method for solving the linear advection-reaction problem with discontinuous solution.

1 code implementation • 5 Nov 2019 • Zhiqiang Cai, Jingshuang Chen, Min Liu, Xinyu Liu

This paper studies an unsupervised deep learning-based numerical approach for solving partial differential equations (PDEs).

no code implementations • 12 Feb 2016 • Tai Wang, Xiangen Hu, Keith Shubeck, Zhiqiang Cai, Jie Tang

The relationship between reading and writing (RRW) is one of the major themes in learning science.

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