Yue Yu

Ning Liu, Siavash Jafarzadeh, Yue Yu

Fourier neural operators (FNOs) can learn highly nonlinear mappings between function spaces, and have recently become a popular tool for learning responses of complex physical systems. However, to achieve good accuracy and efficiency, FNOs rely on the Fast Fourier transform (FFT), which is restricted to modeling problems on rectangular domains. To lift such a restriction and permit FFT on irregular geometries as well as topology changes, we introduce domain agnostic Fourier neural operator (DAFNO), a novel neural operator architecture for learning surrogates with irregular geometries and evolving domains. The key idea is to incorporate a smoothed characteristic function in the integral layer architecture of FNOs, and leverage FFT to achieve rapid computations, in such a way that the geometric information is explicitly encoded in the architecture. In our empirical evaluation, DAFNO has achieved state-of-the-art accuracy as compared to baseline neural operator models on two benchmark datasets of material modeling and airfoil simulation. To further demonstrate the capability and generalizability of DAFNO in handling complex domains with topology changes, we consider a brittle material fracture evolution problem. With only one training crack simulation sample, DAFNO has achieved generalizability to unseen loading scenarios and substantially different crack patterns from the trained scenario. Our code and data accompanying this paper are available at https://github.com/ningliu-iga/DAFNO.

Ran Xu, Yuchen Zhuang, Yue Yu et al. · gatech

Retrieval-augmented generation (RAG) enhances large language models (LLMs) by integrating external knowledge retrieved at inference time. While RAG demonstrates strong performance on benchmarks largely derived from general-domain corpora like Wikipedia, its effectiveness under realistic, diverse retrieval scenarios remains underexplored. We evaluated RAG systems using MassiveDS, a large-scale datastore with mixture of knowledge, and identified critical limitations: retrieval mainly benefits smaller models, rerankers add minimal value, and no single retrieval source consistently excels. Moreover, current LLMs struggle to route queries across heterogeneous knowledge sources. These findings highlight the need for adaptive retrieval strategies before deploying RAG in real-world settings. Our code and data can be found at https://github.com/ritaranx/RAG_in_the_Wild.