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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.19496 |
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| _version_ | 1866918001928830976 |
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| author | Morel, Rudy Han, Jiequn Oyallon, Edouard |
| author_facet | Morel, Rudy Han, Jiequn Oyallon, Edouard |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19496 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | DISCO: learning to DISCover an evolution Operator for multi-physics-agnostic prediction Morel, Rudy Han, Jiequn Oyallon, Edouard Machine Learning Artificial Intelligence 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. |
| title | DISCO: learning to DISCover an evolution Operator for multi-physics-agnostic prediction |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2504.19496 |