Spoken language from older adults often deviates from written norms due to omission, disordered syntax, constituent errors, and redundancy, limiting the usefulness of automatic transcripts in downstream tasks.We present COAS2W, a Chinese spoken-to-written corpus of 10,004 utterances from older adults, each paired with a written version, finegrained error labels, and four-sentence context.Fine-tuned lightweight open-source models on COAS2W outperform larger closed-source models.Context ablation shows the value of multi-sentence input, and normalization improves performance on downstream translation tasks.COAS2W supports the development of inclusive, context-aware language technologies for older speakers.Our annotation convention, data, and code are publicly available at https://github.com/Springrx/COAS2W.

Parameter-efficient fine-tuning (PEFT) powerful pre-trained models for complex downstream tasks has proven effective in vision and language processing, yet this paradigm remains unexplored in scientific machine learning, where the objective is to model complex physical systems. We conduct the first systematic study of PEFT for pre-trained Large Operator Models (LOMs) obtained by scaling variants of Fourier Neural Operator. We observe that the widely used Low-Rank Adaptation (LoRA) yields markedly poorer performance on LOMs than Adapter tuning. We further theoretically establish that stacked LoRA incurs a depth-amplified lower bound on approximation error within Fourier layers, whereas adapters retain universal approximation capacity and, by concentrating parameters on energy-dominant low-frequency modes, attain exponentially decaying error with bottleneck width in the Fourier domain. Motivated by the robust empirical gains of adapters and by our theoretical characterization of PDE solutions as spectrally sparse, we introduce Frequency-Adaptive Adapter (F-Adapter). F-Adapter allocates adapter capacity based on spectral complexity, assigning higher-dimension modules to low-frequency components and lower-dimension modules to high-frequency components. Our F-Adapters establish state-of-the-art results on multiple challenging 3D Navier–Stokes benchmarks, markedly enhancing both generalization and spectral fidelity over LoRA and other PEFT techniques commonly used in LLMs. To the best of our knowledge, this work is the first to explore PEFT for scientific machine-learning and establishes F-Adapter as an effective paradigm for this domain. The code will be made publicly available upon acceptance.