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math.NA2026
Least-Squares Neural Network (LSNN) Method for Scalar Hyperbolic Partial Differential Equations
Min Liu, Zhiqiang Cai
This chapter offers a comprehensive introduction to the least-squares neural network (LSNN) method introduced in [14,16], for solving scalar first-order hyperbolic partial differen…
math.NA2021★ 1 cited
Adaptive Two-Layer ReLU Neural Network: II. Ritz Approximation to Elliptic PDEs
Min Liu, Zhiqiang Cai
In this paper, we study adaptive neuron enhancement (ANE) method for solving self-adjoint second-order elliptic partial differential equations (PDEs). The ANE method is a self-adap…