用短轨迹学习生成物理系统演化算子，提升多物理场景预测效率
DISCO: learning to DISCover an evolution Operator for multi-physics-agnostic prediction
- 通过超网络从短轨迹中学习演化算子参数，实现动态建模与预测解耦
- 在多个物理数据集上预训练后，仅需少量训练轮次即达顶尖性能
- 适用于多物理场景泛化，适合需要快速适配新任务的科研与工程应用
我们研究了仅用短轨迹预测由未知时间偏微分方程（PDE）控制的动力系统下一状态的问题。尽管标准Transformer可作为黑箱解决方案，但数据中蕴含的结构化演化算子提示更定制化的高效方法。当PDE完全已知时，经典数值求解器仅需少量参数即可准确演化状态。受此启发，我们提出DISCO模型：利用大型超网络处理短轨迹，生成一个小型算子网络的参数，再通过时间积分预测下一状态。该框架将动力学估计（从短轨迹中发现演化算子）与状态预测（演化算子）解耦。实验表明，在多样物理数据集上预训练后，模型达到当前最优性能，且所需训练轮次显著减少；同时具备良好泛化能力，微调后在下游任务中仍保持竞争力。
原文摘要 · Abstract (English)
We address the problem of predicting the next state of a dynamical system governed by unknown temporal partial differential equations (PDEs) using only a short trajectory. While standard transformers provide a natural black-box solution to this task, the presence of a well-structured evolution operator in the data suggests a more tailored and efficient approach. Specifically, when the PDE is fully known, classical numerical solvers can evolve the state accurately with only a few parameters. Building on this observation, we introduce DISCO, a model that uses a large hypernetwork to process a short trajectory and generate the parameters of a much smaller operator network, which then predicts the next state through time integration. Our framework decouples dynamics estimation (i.e., DISCovering an evolution operator from a short trajectory) from state prediction (i.e., evolving this operator). Experiments show that pretraining our model on diverse physics datasets achieves state-of-the-art performance while requiring significantly fewer epochs. Moreover, it generalizes well and remains competitive when fine-tuned on downstream tasks.
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