AI 中文总结
该研究针对时变PDE预测的条件不足问题，提出STCO架构，结合FAGL与DSFiLM设计通用接口，经12种骨干架构在CFD基准测试中验证，可显著降低预测误差。
AI 中文摘要
神经算子已成为由偏微分方程（PDE）描述的时变物理系统的高效替代模型，但它们的未来状态预测通常仅以观测状态和静态问题描述符为条件。然而，对于控制或优化任务，查询所需的刚体运动、流入量或作用力是预先规定的，并非仅由观测状态决定。我们提出用于规定条件算子学习（PCOL）的时空条件算子（STCO），这是一种通用接口，可为异构骨干架构提供规定的目标时间条件场，同时保留其架构特定的核心计算和上下文通路。其条件接口结合了流感知图叶（FAGL）与双位置特征线性调制（DSFiLM）。非学习型FAGL利用最后一帧观测到的涡度构造固定基数的自适应分区，随后将观测历史和目标时间条件场共置于其区域坐标处。DSFiLM通过当前特征驱动的槽和通道门，在算子计算前后注入独立的运动、流入和作用力通路。我们评估了12种匹配的骨干架构，这些架构具有不同的现有物理和时间输入。浸没边界计算流体动力学（CFD）基准涵盖规定运动、流入扰动、体力驱动和形态变化。在12种匹配的骨干架构、3种运行模式和2个领先范围中，STCO使相对L2场误差平均成对降低31.1%，归一化压力衍生载荷误差平均降低24.7%。它还降低了11种骨干架构的长领先场误差，而对单个条件组的干预会为所评估的每个组产生可测量的预测变化。
英文摘要
Neural operators have emerged as efficient surrogates for time-dependent physical systems governed by partial differential equations (PDEs), but their future-state predictions are often conditioned only on observed states and static problem descriptors. For control or optimization, however, body motion, inflow, or forcing are prescribed for the query without being determined solely by the observed state. We introduce the Spatiotemporal Conditional Operator (STCO) for prescribed-condition operator learning (PCOL), a common interface that supplies prescribed target-time condition fields to heterogeneous backbone architectures while retaining their architecture-specific core computation and context pathways. Its condition interface combines Flow-Aware Graph Leaf (FAGL) with Dual-Site Feature-wise Linear Modulation (DSFiLM). Non-learned FAGL uses vorticity from the final observed frame to construct a fixed-cardinality adaptive partition, then co-locates the observed history and target-time condition fields at its regional coordinates. DSFiLM injects separate motion, inflow, and force routes before and after operator computation through current-feature-driven slot- and channel-wise gates. We evaluate twelve matched backbone architectures with different existing physical and temporal inputs. The immersed-boundary computational fluid dynamics (CFD) benchmark spans prescribed motion, inflow disturbances, body-force actuation, and morphology. Across twelve matched backbones, three regimes, and two lead ranges, STCO yields mean paired reductions of 31.1% in relative-L2 field error and 24.7% in normalized pressure-derived load error. It also lowers longer-lead field error for 11 backbones, while interventions on individual condition groups produce measurable prediction changes for every group evaluated.
