提出STCO模型，让神经算子能精准预测受外部条件控制的物理系统演化。
STCO: Conditional Neural Operators for Time-Dependent PDEs
- 引入时空条件算子，通过流感知图与双位特征调制融合预设条件输入
- 在流体模拟中平均降低31.1%的场误差和24.7%的载荷误差
- 适用于需外力、运动或边界条件控制的物理系统建模，如流体控制
神经算子作为时变偏微分方程（PDE）系统的高效代理模型已崭露头角，但其未来状态预测通常仅依赖观测状态和静态问题描述符。然而，在控制或优化场景中，物体运动、流入或驱动力是预设的，而非仅由观测状态决定。本文提出时空条件算子（STCO），用于预设条件算子学习（PCOL），为异构骨干架构提供统一接口，注入目标时间的预设条件场，同时保留其架构特有核心计算与上下文路径。其条件接口结合非学习的流感知图叶（FAGL）与双位特征逐路线性调制（DSFiLM）。FAGL利用末帧涡度构建固定基数自适应分区，并将历史观测与目标条件场共置于此区域坐标；DSFiLM通过当前特征驱动的通道与槽门，在算子计算前后分别注入运动、流入和力的独立路径。我们在十二种匹配骨干架构上评估了不同物理与时间输入。浸入边界计算流体力学（CFD）基准涵盖预设运动、流入扰动、体力驱动及形态变化。在十二种骨干、三种工况与两个预测范围下，STCO实现相对L2场误差均值降低31.1%，归一化压力载荷误差降低24.7%。对十一个骨干模型，其长预测步误差亦下降；对每类条件组干预均引发可测量预测变化。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。