From Uniform to Adaptive: General Skip-Block Mechanisms for Efficient PDE Neural Operators

Recent advancements in Neural Operators have significantly increased their popularity as a method for solving Partial Differential Equations (F2). These operators are widely used due to their ability to model complex physical phenomena (F1). However, their application in large-scale engineering tasks faces challenges, primarily due to high computational costs (F3). One key issue is the mismatch between uniform computational demands and the varying complexities present in physical fields, which leads to inefficiencies (F4). This computational mismatch limits the scalability and practicality of Neural Operators in real-world scenarios. Addressing these challenges is crucial for enhancing the efficiency and adaptability of Neural Operators in engineering applications. The development of more adaptive mechanisms could potentially bridge this gap and optimize computational resources.