DISCO: learning to DISCover an evolution Operator for multi-physics-agnostic prediction
This addresses the problem of efficient and accurate multi-physics prediction for researchers and practitioners, though it is incremental as it builds on existing transformer and hypernetwork ideas.
The paper tackles predicting the next state of dynamical systems governed by unknown PDEs using short trajectories, introducing DISCO, which uses a hypernetwork to generate parameters for a smaller operator network, achieving state-of-the-art performance with fewer epochs and good generalization.
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.