从无标签轨迹中自动发现系统共性与差异，实现零样本外推。
Neural operator discovery from heterogeneous trajectories
- 通过因子化潜在条件建模，联合学习解算子与低维隐变量表示。
- 在多种系统上实现对未见实例的零样本外推和长时程稳定预测。
- 适合缺乏物理参数标注的真实场景，如复杂流体、生物系统建模。
神经算子可数据驱动地建模动力系统。传统方法需显式提供物理参数、几何或边界条件等调节变量，但在真实场景中这些量常不可观测。本文将神经算子发现（NOD）定义为：仅从异构轨迹中同时学习共享解算子与系统特异性变化，无需标注控制因素。提出因子化潜在条件框架，通过因子化预测、轨迹解耦采样与维度选择，联合学习神经算子与低维隐表示。在多类系统上，所学隐表示捕捉了系统变化的本质维度，组织系统实例形成平滑且近似可逆的潜在结构，与底层控制因素对齐。该结构支持对未见系统实例的泛化，包括跨区域的零样本外推与稳定长时程预测。结果建立了一种无显式因子监督下的可解释算子学习范式。
原文摘要 · Abstract (English)
Neural operators provide data-driven mappings for modeling dynamical systems. Extending them to families of systems typically requires explicit conditioning variables such as physical parameters, geometries, or boundary conditions. In many real-world settings, these quantities are unobserved. Here, we formulate neural operator discovery (NOD) as the problem of learning both shared solution operators and system-specific variation directly from heterogeneous trajectories without access to labeled governing factors. We introduce a factorized latent-conditioning formulation that jointly learns a neural operator and a low-dimensional latent representation through factorized prediction, trajectory-decoupled sampling, and dimension selection. Across diverse systems, the learned latent representation captures the intrinsic dimensionality of system variation and organizes system instances in a smooth and approximately invertible latent structure aligned with the underlying governing factors. This organization enables generalization to previously unseen system instances, including zero-shot extrapolation across regimes and stable long-horizon prediction. These results establish an interpretable paradigm for operator learning in the absence of explicit factor supervision.
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