Pretrained partial differential equation (PDE) foundation models can generalize across different equations, but adapting them to unseen PDE systems typically requires dense solution data, which is often expensive or unavailable. To address this limitation, we propose an unsupervised PDE-based finetuning framework that eliminates the need for ground-truth solutions. We first pretrain a neighborhood attention Transformer on diverse time-dependent PDEs spanning varying spatial scales, yielding transferable representations across heterogeneous equations. In the adaptation stage, we construct a physics-based objective using the PDE residual and boundary conditions, and finetune the model on unseen equations via low-rank adaptation (LoRA). To address the uneven learning across physical quantities in standard LoRA, we introduce NSLoRA, a Newton-Schulz orthogonalized variant that rebalances adaptation. Our method achieves performance comparable to supervised LoRA finetuning without requiring any ground-truth solutions, while consistently outperforming competitive neural operator baselines and recent PDE foundation models across heterogeneous PDE benchmarks spanning multiple spatial dimensions.
Long-horizon web agents frequently fail without knowing where or why execution broke down. This issue is particularly pronounced in skill-based agentic web systems, where failures arise within composite skills whose internal decision processes are not directly traceable, making precise diagnosis and repair especially difficult over long horizons. We introduce SkillTracer, a framework that represents skills as attributed plan graphs structured by hierarchical nodes and verifiable edge transitions, enabling programmatic verification of execution progress. By decomposing skills into inspectable hierarchies, SkillTracer converts raw interaction traces into structural evidence, making execution breakdowns localizable to specific node-level decision points and attributable to failing components. This attribution signal facilitates targeted structural repair, allowing the agent to selectively revise failing components while preserving the integrity of valid substructures for partial reuse and adaptive recovery. Furthermore, SkillTracer synthesizes short-term traces with long-term historical evidence to construct a persistent skill graph, enabling failure patterns to drive continual refinement across episodes. Evaluated on challenging long-horizon benchmarks, SkillTracer achieves a 17.7% average improvement in success rate over strong baselines, with gains of up to 56.3% in cross-domain settings, demonstrating that structural attribution and skill repair are critical for reliable long-horizon web interaction. A project page is available at: https://liyuuuuy.github.io/SkillTracer/.
Yuyang Li, Yiran Dou, Jiejing Shao et al.· Proceedings of the 32nd ACM...· 5 citations
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