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.

本研究解决了基于短时间轨迹预测动态系统下一个状态的难题，鲸鱼标准变换器为这一任务提供了自然的黑箱解法，但数据中存在良好结构的演化算子提示了更有效的定制方法。我们提出的DISCO模型利用大型超网络处理短轨迹，生成更小算子网络的参数，从而通过时间积分预测下一个状态，实验证明此方法在多种物理数据集上实现了最先进的性能，并且在微调后在下游任务中保持竞争力。

DISCO：学习发现多物理无关预测的演化算子