arXiv AI August 24, 2026 By Xingxin Yang, Zhan Zhang, Juan Li

STCO: Conditional Neural Operators for Time-Dependent PDEs

The paper introduces the Spatiotemporal Conditional Operator (STCO), a framework for learning neural operators that can incorporate prescribed target‑time condition fields—such as body motion, inflow disturbances, or body‑force actuation—into time‑dependent PDE simulations. STCO combines a Flow‑Aware Graph Leaf (FAGL) partitioning scheme with Dual‑Site Feature‑wise Linear Modulation (DSFiLM) to inject these conditions before and after the core operator computation. Evaluated on twelve backbone architectures across an immersed‑boundary CFD benchmark, STCO achieves significant reductions in relative‑L2 field error (31.1%) and pressure‑derived load error (24.7%) while improving long‑lead predictions for most backbones.

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