{"ID":2875202,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.03757","arxiv_id":"2509.03757","title":"ARDO: A Weak Formulation Deep Neural Network Method for Elliptic and Parabolic PDEs Based on Random Differences of Test Functions","abstract":"We propose ARDO method for solving PDEs and PDE-related problems with deep learning techniques. This method uses a weak adversarial formulation but transfers the random difference operator onto the test function. The main advantage of this framework is that it is fully derivative-free with respect to the solution neural network. This framework is particularly suitable for Fokker-Planck type second-order elliptic and parabolic PDEs.","short_abstract":"We propose ARDO method for solving PDEs and PDE-related problems with deep learning techniques. This method uses a weak adversarial formulation but transfers the random difference operator onto the test function. The main advantage of this framework is that it is fully derivative-free with respect to the solution neura...","url_abs":"https://arxiv.org/abs/2509.03757","url_pdf":"https://arxiv.org/pdf/2509.03757v1","authors":"[\"Wei Cai\",\"Andrew Qing He\"]","published":"2025-09-03T22:54:12Z","proceeding":"math.NA","tasks":"[\"math.NA\",\"cs.AI\"]","methods":"[]","has_code":false}