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

Rudy Morel, Jiequn Han, Edouard Oyallon
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:44750-44774, 2025.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-morel25a, title = {{DISCO}: learning to {DISC}over an evolution Operator for multi-physics-agnostic prediction}, author = {Morel, Rudy and Han, Jiequn and Oyallon, Edouard}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {44750--44774}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/morel25a/morel25a.pdf}, url = {https://proceedings.mlr.press/v267/morel25a.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T DISCO: learning to DISCover an evolution Operator for multi-physics-agnostic prediction %A Rudy Morel %A Jiequn Han %A Edouard Oyallon %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-morel25a %I PMLR %P 44750--44774 %U https://proceedings.mlr.press/v267/morel25a.html %V 267 %X 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.
APA
Morel, R., Han, J. & Oyallon, E.. (2025). DISCO: learning to DISCover an evolution Operator for multi-physics-agnostic prediction. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:44750-44774 Available from https://proceedings.mlr.press/v267/morel25a.html.

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