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math.NA2025
On understanding and overcoming spectral biases of deep neural network learning methods for solving PDEs
Zhi-Qin John Xu, Lulu Zhang, Wei Cai
In this review, we survey the latest approaches and techniques developed to overcome the spectral bias towards low frequency of deep neural network learning methods in learning mul…
math.NA2024
Deep Neural Networks with Symplectic Preservation Properties
Qing He, Wei Cai
We propose a deep neural network architecture designed such that its output forms an invertible symplectomorphism of the input. This design draws an analogy to the real-valued non-…