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UPS: Towards Foundation Models for PDE Solving via Cross-Modal Adaptation
March 13, 2024, 4:41 a.m. | Junhong Shen, Tanya Marwah, Ameet Talwalkar
cs.LG updates on arXiv.org arxiv.org
Abstract: We introduce UPS (Unified PDE Solver), an effective and data-efficient approach to solve diverse spatiotemporal PDEs defined over various domains, dimensions, and resolutions. UPS unifies different PDEs into a consistent representation space and processes diverse collections of PDE data using a unified network architecture that combines LLMs with domain-specific neural operators. We train the network via a two-stage cross-modal adaptation process, leveraging ideas of modality alignment and multi-task learning. By adapting from pretrained LLMs and …
abstract architecture arxiv consistent cs.lg data dimensions diverse domains foundation modal network network architecture processes representation solve solver space type ups via
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