# A Robust In-Context Model for Conservation Laws: Injecting Context into Flux Neural Operators via Recurrent Vision Transformers

arXiv: https://arxiv.org/abs/2605.05488 · HTML: https://mlsanity.com/paper/2605.05488/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 34 references that are in the map.
- First posted on arXiv 6 May 2026.

## Builds on (most cited first, 25 of 25)

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- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
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- [Magnitude Invariant Parametrizations Improve Hypernetwork Learning](https://mlsanity.com/paper/2304.07645/) (2023)
- [Approximating Numerical Fluxes Using Fourier Neural Operators for Hyperbolic Conservation Laws](https://mlsanity.com/paper/2401.01783/) (2024)
- [TRecViT: A Recurrent Video Transformer](https://mlsanity.com/paper/2412.14294/) (2024)
- [Neural Operators Learn the Local Physics of Magnetohydrodynamics](https://mlsanity.com/paper/2404.16015/) (2024)

## Abstract (arXiv)

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 https://github.com/xx257xx/CONTEXT_FLUX_NO.