[2603.21534] Generalization Limits of In-Context Operator Networks for Higher-Order Partial Differential Equations

Computer Science > Machine Learning arXiv:2603.21534 (cs) [Submitted on 23 Mar 2026] Title:Generalization Limits of In-Context Operator Networks for Higher-Order Partial Differential Equations Authors:Jamie Mahowald, Tan Bui-Thanh View a PDF of the paper titled Generalization Limits of In-Context Operator Networks for Higher-Order Partial Differential Equations, by Jamie Mahowald and 1 other authors View PDF HTML (experimental) Abstract:We investigate the generalization capabilities of In-Context Operator Networks (ICONs), a new class of operator networks that build on the principles of in-context learning, for higher-order partial differential equations. We extend previous work by expanding the type and scope of differential equations handled by the foundation model. We demonstrate that while processing complex inputs requires some new computational methods, the underlying machine learning techniques are largely consistent with simpler cases. Our implementation shows that although point-wise accuracy degrades for higher-order problems like the heat equation, the model retains qualitative accuracy in capturing solution dynamics and overall behavior. This demonstrates the model's ability to extrapolate fundamental solution characteristics to problems outside its training regime. Comments: Subjects: Machine Learning (cs.LG); Numerical Analysis (math.NA) Cite as: arXiv:2603.21534 [cs.LG]   (or arXiv:2603.21534v1 [cs.LG] for this version)   https://doi.org/10.48550/arXiv.2603....