Abstract:We propose an architecture that augments the Flux Neural Operator (Flux NO), which combines the classical finite volume method (FVM) with neural operators, with ViT-based context injection. Our model is formulated as a hypernetwork: it extracts solution dynamics over a finite temporal window, encodes them with a recurrent Vision Transformer, and generates the parameters of a context-conditioned neural operator. This enables the model to infer and solve conservation laws without explicit access to the governing equation or PDE coefficients. Experimentally, we show that the proposed method preserves the robustness, generalization ability, and long-time prediction advantages of Flux NO over standard neural operators, while delivering reliable numerical solutions across a broad range of conservative systems, including previously unseen fluxes. Our code is available at this https URL.
| Comments: | 14 pages, 3 figures |
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2605.05488 [cs.LG] |
| (or arXiv:2605.05488v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.05488 arXiv-issued DOI via DataCite (pending registration) |
From: Taeyoung Kim [view email]
[v1]
Wed, 6 May 2026 22:23:07 UTC (527 KB)
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