DISCO: learning to DISCover an evolution Operator for multi-physics-agnostic prediction

We address the problem of predicting the next states of a dynamical system governed by unknown temporal partial differential equations (PDEs) using only a short trajectory. While standard transformers provide a natural blackbox solution to this task, the presence of a wellstructured 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 states 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 to unseen initial conditions and remains competitive when fine-tuned on downstream tasks. The code will be made publicly available upon publication at https: //github.com/RudyMorel/DISCO.