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 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 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.

Imagine dropping ink into a still glass of water -- the way it spreads and twists is governed by complex physical laws. But what if we don’t know these laws exactly, or they change from one situation to another? Can a computer still predict how the system will move?Our model, called DISCO, tackles this challenge. It looks at a short sequence showing how the system evolves -- like the first few moments of ink dispersing -- and learns to uncover the hidden rules behind it. Then it uses these rules to forecast what happens next.This two-step process is both more efficient and more accurate than existing black-box models. Trained on a wide variety of physical systems, DISCO generalizes well and could become a useful tool to model real-world phenomena when equations are unknown or measurements are limited.