알림마당

  • 공지사항
  • 수학과소식
  • 세미나/심포지엄
  • 취업게시판
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  • 역대 콜로퀴움
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세미나/심포지엄

세미나/심포지엄 게시글의 상세 화면
2022-2학기 제1회 수학과 colloquium 안내 [9/2 금]
작성자 수학과 등록일 2022-08-31 조회수 85
안녕하세요. 수학과입니다.
 
09/02 (금)에 열리는 수학과 colloquium에 대해 안내드립니다.
 
많은 관심과 참여 요청드립니다.
 
 
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1. 연사: 신동욱 (아주대학교)
2. 일시: 9월 2일(금) 오후 5~6시
3. 장소: 팔달관 621호
4. 제목: Numerical methods and neural networks for PDEs
5. 초록: Various natural and physical phenomena can be described by partial differential equations (PDEs).  In order to solve these equations, a number of numerical methods have been introduced and developed. In this talk, we consider various numerical methods for PDEs. The finite difference and finite element methods are popular and work very well for the  boundary value problems. These methods are simple and easy to implement, but the mass conservation property does not hold. On the other hands, nonstandard methods such as mixed finite element, Discontinuous Galerkin (DG), hybrid DG and hybrid difference methods are locally conservative and important for certain class of problems, e.g., Darcy flows in porous media and convection diffusion equations.  These methods allow to achieve high-order accuracy with high-order approximations. However, convergence rates are influenced by smoothness of the solutions. An adaptive algorithm aims to overcome slow convergence for non-smooth solutions. Here, we introduce two types of reliable, efficient, and fully computable a posteriori error estimators and show their numerical results.
Recently, deep learning models have been received large attention and applied to a wide range of fields. Most deep learning models are data-driven approaches. In these approaches, it is difficult to predict correctly outside the data domain. Physics informed neural networks (PINNs) overcome this issue by using the knowledge of any physical laws that govern a given data-set. Here, we consider a simple example of PINNs.
 
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세미나/심포지엄 게시판의 이전글 다음글
이전 2022-2학기 제2회 수학과 colloquium 안내 [9/16 금]
다음 2022-1학기 학부생을 위한 날개달린 수학 강연회 안내 [5/12 목]
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