수학과

안녕하세요. 수학과입니다.
 
9/26 (목)에 예정된 수학과 colloquium에 대해 안내 드립니다.

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일시: 9월 26일(목) 16:30~17:30
장소: 팔달관 621호
연사: 고승찬 교수님(인하대학교 수학)
제목: Mathematical Theory of Neural Network Approximation and its Application to Scientific Machine Learning 
초록:
 In recent years, modern machine learning techniques using deep neural networks have achieved tremendous success in various fields. From a mathematical point of view, deep learning essentially involves approximating a target function, relying on the approximation power of deep neural networks. Therefore, it is important to understand the approximation and generalization properties of neural networks in high dimensions. The primary objective of this talk is to mathematically analyze the approximation of neural networks within the classical numerical analysis framework. We will explore the proper regularity of target functions which is suitable for the neural network approximation, and investigate how these properties are reflected in the approximation and learning complexity of neural networks. Next, I will apply these theories to my recent work on the operator learning method for solving parametric PDEs. I will analyze the intrinsic structure of the proposed method through the theory described above, deriving some useful results both theoretically and practically. Furthermore, I will demonstrate some relevant numerical experiments, confirming that these theory-guided strategies can be utilized to significantly improve the performance of the method. 

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