4 papers
Disentangled Representation Learning for Parametric Partial Differential Equations
Ning Liu, Lu Zhang, Tian Gao +1
Neural operators (NOs) excel at learning mappings between function spaces, serving as efficient forward solution approximators for PDE-governed systems. However, as black-box solve…
Neural Interpretable PDEs: Harmonizing Fourier Insights with Attention for Scalable and Interpretable Physics Discovery
Ning Liu, Yue Yu
Attention mechanisms have emerged as transformative tools in core AI domains such as natural language processing and computer vision. Yet, their largely untapped potential for mode…
Nonlocal Attention Operator: Materializing Hidden Knowledge Towards Interpretable Physics Discovery
Yue Yu, Ning Liu, Fei Lu +3
Despite the recent popularity of attention-based neural architectures in core AI fields like natural language processing (NLP) and computer vision (CV), their potential in modeling…
Harnessing the Power of Neural Operators with Automatically Encoded Conservation Laws
Ning Liu, Yiming Fan, Xianyi Zeng +3
Neural operators (NOs) have emerged as effective tools for modeling complex physical systems in scientific machine learning. In NOs, a central characteristic is to learn the govern…