학술행사
- 발표자 이승규 교수(고려대학교)
- 개최일시 2024-01-17 14:00-16:00
- 장소 국가수리과학연구소 산업수학혁신센터(판교)
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일시: 2024년 1월 17일(수), 14:00 - 16:00
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장소: 판교 테크노밸리 산업수학혁신센터 세미나실
- 경기 성남시 수정구 대왕판교로 815, 기업지원허브 231호 국가수리과학연구소
- 무료주차는 2시간 지원됩니다.
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발표자: 이승규 교수(고려대학교)
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주요내용: Gradient flows and its numerical method
In this talk, I will present several mathematical modeling instances employing gradient flows and associated numerical schemes for its fundamental equations. A gradient flow is a curve that follows the steepest descent direction of a function within a metric space. It has been a valuable tool in the analysis of ODEs and PDEs. Recently, gradient flows under various distances have also been emerged for potential use in machine learning or generative modelling. Given that the solution of gradient flows can be expressed as the minimization of an energy functional that is lower semi-continuous and bounded below, the development of a numerical method ensuring energy dissapation or energy non-increasing, commonly referred to as an unconditionally (energy) gradient stable scheme, becomes a critical consideration. For a practical demenstration of the numerical method, the Allen-Cahn and Cahn-Hilliard equations will be employed as examples.
*유튜브 스트리밍 예정입니다.
-
일시: 2024년 1월 17일(수), 14:00 - 16:00
-
장소: 판교 테크노밸리 산업수학혁신센터 세미나실
- 경기 성남시 수정구 대왕판교로 815, 기업지원허브 231호 국가수리과학연구소
- 무료주차는 2시간 지원됩니다.
-
발표자: 이승규 교수(고려대학교)
-
주요내용: Gradient flows and its numerical method
In this talk, I will present several mathematical modeling instances employing gradient flows and associated numerical schemes for its fundamental equations. A gradient flow is a curve that follows the steepest descent direction of a function within a metric space. It has been a valuable tool in the analysis of ODEs and PDEs. Recently, gradient flows under various distances have also been emerged for potential use in machine learning or generative modelling. Given that the solution of gradient flows can be expressed as the minimization of an energy functional that is lower semi-continuous and bounded below, the development of a numerical method ensuring energy dissapation or energy non-increasing, commonly referred to as an unconditionally (energy) gradient stable scheme, becomes a critical consideration. For a practical demenstration of the numerical method, the Allen-Cahn and Cahn-Hilliard equations will be employed as examples.
