用视觉变压器注入上下文，让神经算子自动解守恒律方程。
A Robust In-Context Model for Conservation Laws: Injecting Context into Flux Neural Operators via Recurrent Vision Transformers
- 用循环ViT编码动态，生成条件化神经算子参数。
- 无需方程或系数，可稳定求解多种守恒系统。
- 适合需要泛化能力的物理模拟场景。
我们提出一种增强型架构，将基于视觉变压器的上下文注入机制融入流函数神经算子（Flux NO），该算子结合了经典有限体积法（FVM）与神经算子。模型以超网络形式构建：提取有限时间窗口内的解动力学，通过循环视觉变压器编码，并生成条件化神经算子的参数。此设计使模型在未显式提供控制方程或偏微分方程系数的情况下，仍能推断并求解守恒律。实验表明，该方法在标准神经算子基础上保持了良好的鲁棒性、泛化能力及长期预测优势，且在涵盖此前未见通量的多种保守系统中均能输出可靠数值解。代码已开源：https://github.com/xx257xx/CONTEXT_FLUX_NO。
原文摘要 · Abstract (English)
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.
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