학술행사
- 발표자 최준호 박사(성균관대학교)
- 개최일시 2022-12-08 14:00-16:00
- 장소 국가수리과학연구소 산업수학혁신센터(광교)
1. 일시: 2022년 12월 8일(목), 14:00-16:00
2. 장소: 산업수학혁신센터 세미나실
- 경기 성남시 수정구 대왕판교로 815, 기업지원허브 231호 국가수리과학연구소
- 무료주차 2시간 등록 가능
3. 발표자: 최준호 박사(성균관대학교)
4. 주요내용: Unsupervised Legendre-Galerkin Neural Network for Stiff Partial Differential Equations
In this talk, I will introduce an machine learning method called unsupervised Legendre-Galerkin Neural Network(ULGNet) to solve various partial differential equations(PDEs). In recent works, many neural network approaches without using solution datasets of PDEs have been successfully developed, such as physics informed neural networks(PINN), deep Ritz method(DRM), and deep Galerkin method(DGM). While these methods are optimized to solve a single PDE, it will be presented how ULGNet is able to solve multiple PDEs. In addition, because the methods depend on auto-gradient to compute residuals of PDEs in a loss function, they have suffered with handling stiff slopes of solutions, for example, stiff boundary layers. Hence, I will introduce how ULGNet employs Legendre-Galerkin method to deal with not only the general 1D and 2D PDEs, Dirichlet and Neumann boundary condition, but also singular perturbed PEDs which have stiff boundary layers.
1. 일시: 2022년 12월 8일(목), 14:00-16:00
2. 장소: 산업수학혁신센터 세미나실
- 경기 성남시 수정구 대왕판교로 815, 기업지원허브 231호 국가수리과학연구소
- 무료주차 2시간 등록 가능
3. 발표자: 최준호 박사(성균관대학교)
4. 주요내용: Unsupervised Legendre-Galerkin Neural Network for Stiff Partial Differential Equations
In this talk, I will introduce an machine learning method called unsupervised Legendre-Galerkin Neural Network(ULGNet) to solve various partial differential equations(PDEs). In recent works, many neural network approaches without using solution datasets of PDEs have been successfully developed, such as physics informed neural networks(PINN), deep Ritz method(DRM), and deep Galerkin method(DGM). While these methods are optimized to solve a single PDE, it will be presented how ULGNet is able to solve multiple PDEs. In addition, because the methods depend on auto-gradient to compute residuals of PDEs in a loss function, they have suffered with handling stiff slopes of solutions, for example, stiff boundary layers. Hence, I will introduce how ULGNet employs Legendre-Galerkin method to deal with not only the general 1D and 2D PDEs, Dirichlet and Neumann boundary condition, but also singular perturbed PEDs which have stiff boundary layers.
