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

• URL: http://arxiv.org/abs/2504.19496v1
• Date: Mon, 28 Apr 2025 05:36:52 GMT
• Title: DISCO: learning to DISCover an evolution Operator for multi-physics-agnostic prediction
• Authors: Rudy Morel, Jiequn Han, Edouard Oyallon,
• Abstract summary: 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.<n>Our framework decouples dynamics estimation (i.e., DISCovering an evolution operator from a short trajectory) from state prediction (i.e., evolving this operator)
• Score: 11.041893960136164
• License: http://creativecommons.org/licenses/by/4.0/
• 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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