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arXiv · 2504.19496

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

Rudy Morel·Jiequn Han·Edouard Oyallon
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Abstract

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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Rudy Morel, Jiequn Han, Edouard Oyallon. 2025-04-28. DISCO: learning to DISCover an evolution Operator for multi-physics-agnostic prediction. https://arxiv.org/abs/2504.19496

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