Deflation-PINNs: Learning Multiple Solutions for PDEs and Landau-de Gennes
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| Format: | Preprint |
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2026
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| _version_ | 1866910090985996288 |
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| author | Disarò, Sean Maity, Ruma Rani Bacho, Aras |
| author_facet | Disarò, Sean Maity, Ruma Rani Bacho, Aras |
| contents | Nonlinear Partial Differential Equations (PDEs) are ubiquitous in mathematical physics and engineering. Although Physics-Informed Neural Networks (PINNs) have emerged as a powerful tool for solving PDE problems, they typically struggle to identify multiple distinct solutions, since they are designed to find one solution at a time. To address this limitation, we introduce Deflation-PINNs, a novel framework that integrates a deflation loss with an architecture based on PINNs and Deep Operator Networks (DeepONets). By incorporating a deflation term into the loss function, our method systematically forces the Deflation-PINN to seek and converge upon distinct finitely many solution branches. We provide theoretical evidence on the convergence of our model and demonstrate the efficacy of Deflation-PINNs through numerical experiments on the Landau-de Gennes model of liquid crystals, a system renowned for its complex energy landscape and multiple equilibrium states. Our results show that Deflation-PINNs can successfully identify and characterize multiple distinct crystal structures. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_27936 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Deflation-PINNs: Learning Multiple Solutions for PDEs and Landau-de Gennes Disarò, Sean Maity, Ruma Rani Bacho, Aras Numerical Analysis Machine Learning Nonlinear Partial Differential Equations (PDEs) are ubiquitous in mathematical physics and engineering. Although Physics-Informed Neural Networks (PINNs) have emerged as a powerful tool for solving PDE problems, they typically struggle to identify multiple distinct solutions, since they are designed to find one solution at a time. To address this limitation, we introduce Deflation-PINNs, a novel framework that integrates a deflation loss with an architecture based on PINNs and Deep Operator Networks (DeepONets). By incorporating a deflation term into the loss function, our method systematically forces the Deflation-PINN to seek and converge upon distinct finitely many solution branches. We provide theoretical evidence on the convergence of our model and demonstrate the efficacy of Deflation-PINNs through numerical experiments on the Landau-de Gennes model of liquid crystals, a system renowned for its complex energy landscape and multiple equilibrium states. Our results show that Deflation-PINNs can successfully identify and characterize multiple distinct crystal structures. |
| title | Deflation-PINNs: Learning Multiple Solutions for PDEs and Landau-de Gennes |
| topic | Numerical Analysis Machine Learning |
| url | https://arxiv.org/abs/2603.27936 |