发表机构
The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对反应-扩散方程代理模型迁移需新模拟数据的问题，提出RD-JEPA自监督预训练架构，在五个系统预训练后适应三个保留系统，用少量轨迹即超越多种基线，实现数据高效迁移。
AI 中文摘要
学习时间相关偏微分方程的代理模型时，当控制算子发生变化，通常需要新的模拟语料库。我们引入了RD-JEPA，一种用于反应-扩散轨迹自监督预训练的联合嵌入预测架构。一个模型在五个参数化系统上进行预训练，然后适应于三个保留系统，这些系统的反应算子和轨迹不包含在预训练中。利用来自保留系统的一条、五条或十条完整轨迹，RD-JEPA在平均相对离散ℓ²场误差和平均绝对空间一阶差分误差上均低于五个监督代理基线、一个移除轨迹依赖预测潜在路径的独立训练控制，以及一个从头训练的架构匹配模型。在所评估的方程、输出分辨率、预测时域和适应轨迹选择范围内，结果表明预测未来状态表示可以支持跨相关反应-扩散系统的数据高效适应。
英文摘要
Learning surrogates for time-dependent partial differential equations often requires a new simulation corpus when the governing operator changes. We introduce RD-JEPA, a joint-embedding predictive architecture for self-supervised pretraining on reaction-diffusion trajectories. A single model is pretrained on five parameterized systems and then adapted to three held-out systems whose reaction operators and trajectories are excluded from pretraining. Using one, five, or ten complete trajectories from a held-out system, RD-JEPA achieves lower mean relative discrete $\ell^2$ field error and mean absolute spatial first-difference error than five supervised surrogate baselines, an independently trained control that removes the trajectory-dependent predictive latent pathway, and an architecture-matched model trained from scratch. Within the evaluated equations, output resolution, forecast horizons, and choices of adaptation trajectories, the results indicate that prediction of future-state representations can support data-efficient adaptation across related reaction-diffusion systems.
