{"ID":2874252,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.05117","arxiv_id":"2509.05117","title":"HyPINO: Multi-Physics Neural Operators via HyperPINNs and the Method of Manufactured Solutions","abstract":"We present HyPINO, a multi-physics neural operator designed for zero-shot generalization across a broad class of PDEs without requiring task-specific fine-tuning. Our approach combines a Swin Transformer-based hypernetwork with mixed supervision: (i) labeled data from analytical solutions generated via the Method of Manufactured Solutions (MMS), and (ii) unlabeled samples optimized using physics-informed objectives. The model maps PDE parameterizations to target Physics-Informed Neural Networks (PINNs) and can handle linear elliptic, hyperbolic, and parabolic equations in two dimensions with varying source terms, geometries, and mixed Dirichlet/Neumann boundary conditions, including interior boundaries. HyPINO achieves strong zero-shot accuracy on seven benchmark problems from PINN literature, outperforming U-Nets, Poseidon, and Physics-Informed Neural Operators (PINO). Further, we introduce an iterative refinement procedure that treats the residual of the generated PINN as \"delta PDE\" and performs another forward pass to generate a corrective PINN. Summing their contributions and repeating this process forms an ensemble whose combined solution progressively reduces the error on six benchmarks and achieves a \u003e100x lower $L_2$ loss in the best case, while retaining forward-only inference. Additionally, we evaluate the fine-tuning behavior of PINNs initialized by HyPINO and show that they converge faster and to lower final error than both randomly initialized and Reptile-meta-learned PINNs on five benchmarks, performing on par on the remaining two. Our results highlight the potential of this scalable approach as a foundation for extending neural operators toward solving increasingly complex, nonlinear, and high-dimensional PDE problems. The code and model weights are publicly available at https://github.com/rbischof/hypino.","short_abstract":"We present HyPINO, a multi-physics neural operator designed for zero-shot generalization across a broad class of PDEs without requiring task-specific fine-tuning. Our approach combines a Swin Transformer-based hypernetwork with mixed supervision: (i) labeled data from analytical solutions generated via the Method of Ma...","url_abs":"https://arxiv.org/abs/2509.05117","url_pdf":"https://arxiv.org/pdf/2509.05117v4","authors":"[\"Rafael Bischof\",\"Michal Piovarči\",\"Michael A. Kraus\",\"Siddhartha Mishra\",\"Bernd Bickel\"]","published":"2025-09-05T13:59:25Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[\"Transformer\"]","has_code":false,"code_links":[{"ID":610123,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_id":2874252,"paper_url":"https://arxiv.org/abs/2509.05117","paper_title":"HyPINO: Multi-Physics Neural Operators via HyperPINNs and the Method of Manufactured Solutions","repo_url":"https://github.com/rbischof/hypino","is_official":false,"mentioned_in_paper":false,"mentioned_in_github":true,"github_stars":0}]}