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Centre for Frontier AI Research

Academic institutionasia · sg
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Representative Papers

Unsupervised Adaptation of PDE Foundation Models

Aug 07, 2026

This work addresses the challenge that pre-trained PDE foundation models typically require dense solution data—often unavailable—for effective transfer to unseen systems. To overcome this limitation, the authors propose an unsupervised fine-tuning framework that leverages PDE residuals and boundary conditions to construct a physics-informed objective, enabling efficient adaptation without ground-truth solutions. A key innovation is the introduction of NSLoRA, which incorporates Newton–Schulz orthogonalization into low-rank adaptation (LoRA) to mitigate imbalanced learning of physical quantities inherent in standard LoRA. Experimental results demonstrate that the proposed method achieves performance on par with supervised LoRA fine-tuning across diverse, heterogeneous multidimensional PDE benchmarks, significantly outperforming existing neural operators and PDE foundation models.

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Latest Papers

Unsupervised Adaptation of PDE Foundation Models

Aug 07, 2026

This work addresses the challenge that pre-trained PDE foundation models typically require dense solution data—often unavailable—for effective transfer to unseen systems. To overcome this limitation, the authors propose an unsupervised fine-tuning framework that leverages PDE residuals and boundary conditions to construct a physics-informed objective, enabling efficient adaptation without ground-truth solutions. A key innovation is the introduction of NSLoRA, which incorporates Newton–Schulz orthogonalization into low-rank adaptation (LoRA) to mitigate imbalanced learning of physical quantities inherent in standard LoRA. Experimental results demonstrate that the proposed method achieves performance on par with supervised LoRA fine-tuning across diverse, heterogeneous multidimensional PDE benchmarks, significantly outperforming existing neural operators and PDE foundation models.

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