发表机构
Massachusetts Institute of Technology; Zhejiang University（麻省理工学院; 浙江大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究如何从异构轨迹发现神经算子，提出因式分解潜在条件公式，联合学习神经算子与低维潜在表示，能捕获系统变化内在维度，实现零样本外推等泛化，为无显式监督的算子学习建立可解释范式。
AI 中文摘要
神经算子为动力学系统建模提供数据驱动映射。将其扩展到系统族通常需要诸如物理参数、几何形状或边界条件等显式条件变量。在许多实际场景中，这些量不可观测。本文将神经算子发现（NOD）表述为直接从异构轨迹学习共享解算子和系统特定变化的问题，无需访问标记的控制因素。引入了一种因式分解潜在条件公式，通过因式分解预测、轨迹解耦采样和维度选择联合学习神经算子和低维潜在表示。跨不同系统，学习到的潜在表示捕获系统变化的内在维度，并以与潜在控制因素对齐的平滑且近似可逆的潜在结构组织系统实例。这种组织实现了对以前未见系统实例的泛化，包括跨区域的零样本外推和稳定长期预测。这些结果为无显式因素监督下的算子学习建立了可解释范式。
英文摘要
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.
