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Neural Network Convergence for Variational Inequalities
Yun Zhao, Harry Zheng
https://arxiv.org/abs/2509.26535 https://arxiv.org/pdf/2509.26535

Neural Network Convergence for Variational Inequalities
We propose an approach to applying neural networks on linear parabolic variational inequalities. We use loss functions that directly incorporate the variational inequality on the whole domain to bypass the need to determine the stopping region in advance and prove the existence of neural networks whose losses converge to zero. We also prove the functional convergence in the Sobolev space. We then apply our approach to solving an optimal investment and stopping problem in finance. By leveraging …