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math.NA2021★ 32 cited
MOD-Net: A Machine Learning Approach via Model-Operator-Data Network for Solving PDEs
Lulu Zhang, Tao Luo, Yaoyu Zhang +3
In this paper, we propose a a machine learning approach via model-operator-data network (MOD-Net) for solving PDEs. A MOD-Net is driven by a model to solve PDEs based on operator r…
math.NA2020
Fourier-domain Variational Formulation and Its Well-posedness for Supervised Learning
Tao Luo, Zheng Ma, Zhiwei Wang +2
A supervised learning problem is to find a function in a hypothesis function space given values on isolated data points. Inspired by the frequency principle in neural networks, we…
math.NA2020★ 50 cited
Two-Layer Neural Networks for Partial Differential Equations: Optimization and Generalization Theory
Tao Luo, Haizhao Yang
The problem of solving partial differential equations (PDEs) can be formulated into a least-squares minimization problem, where neural networks are used to parametrize PDE solution…