Abstract:We introduce Tadpole, a novel foundation model for three-dimensional partial differential equations (PDEs) that addresses key challenges in transferability, scalability to high dimensionality, and multi-functionality. Tadpole is pre-trained as an autoencoder on synthetic 3D PDE data generated by an efficient online data-generation framework. This enables large-scale, diverse training without storage or I/O overhead, demonstrated by scaling to an equivalent of hundreds of terabytes of training data. By autoencoding single-channel spatial crops, Tadpole learns rich and transferable representations across heterogeneous physical systems with varying numbers of state variables and spatial resolutions. Although pre-trained solely as an autoencoder, Tadpole can be efficiently applied for multiple downstream tasks beyond reconstruction, including dynamics learning and generative modeling. For dynamics learning, we propose a novel parameter-efficient fine-tuning strategy that integrates low-rank adaptation, latent-space transformations, and reintroduced skip connections, achieving accurate temporal modeling with a minimal number of trainable parameters. Tadpole demonstrates strong fine-tuning performance across various downstream tasks, highlighting its versatility and effectiveness as a foundation model for 3D PDE learning. Source code and pre-trained weights of Tadpole are available at this https URL
| Subjects: | Machine Learning (cs.LG) |
| MSC classes: | 68T07 |
| Cite as: | arXiv:2605.15284 [cs.LG] |
| (or arXiv:2605.15284v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.15284 arXiv-issued DOI via DataCite (pending registration) |
From: Qiang Liu [view email]
[v1]
Thu, 14 May 2026 18:00:58 UTC (23,654 KB)
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