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강연자 신연종
소속 KAIST
date 2022-10-13

 

Machine learning (ML) has achieved unprecedented empirical success in diverse applications. It now has been applied to solve scientific problems, which has become an emerging field, Scientific Machine Learning (SciML). Many ML techniques, however, are very complex and sophisticated, commonly requiring many trial-and-error and tricks. These result in a lack of robustness and interpretability, which are critical factors for scientific applications. This talk centers around mathematical approaches for SciML, promoting trustworthiness. The first part is about how to embed physics into neural networks (NNs). I will present a general framework for designing NNs that obey the first and second laws of thermodynamics. The framework not only provides flexible ways of leveraging available physics information but also results in expressive NN architectures. The second part is about the training of NNs, one of the biggest challenges in ML. I will present an efficient training method for NNs - Active Neuron Least Squares (ANLS). ANLS is developed from the insight gained from the analysis of gradient descent training.

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List of Articles
카테고리 제목 소속 강연자
수학강연회 Trends to equilibrium in collisional rarefied gas theory file 포항공과대학교 이동현
수학강연회 Towards Trustworthy Scientific Machine Learning: Theory, Algorithms, and Applications file KAIST 신연종
수학강연회 Toward bridging a connection between machine learning and applied mathematics file 성균관대학교 홍영준
수학강연회 Topology of configuration spaces on graphs file KAIST 고기형
수학강연회 Topology and number theory file Univ. College London/포항공대 김민형
수학강연회 Topological surgery through singularity in mean curvature flow file 고등과학원 최경수
특별강연 Topological Mapping of Point Cloud Data file Stanford University Gunnar E. Carlsson
수학강연회 Topological aspects in the theory of aperiodic solids and tiling spaces file Georgia Institute of Technology, School of Mathematics and School of Physics Jean V. Bellissard
수학강연회 Theory and applications of partial differential equations file 서울대 변순식
수학강연회 The significance of dimensions in mathematics file Kyoto Univ./서울대학교 Heisuke Hironaka
수학강연회 The Shape of Data file Stanford University Gunnar E. Carlsson
수학강연회 The process of mathematical modelling for complex and stochastic biological systems file KAIST 김재경
수학강연회 The phase retrieval problem file Hong Kong University of Science and Technology Yang Wang
수학강연회 The Mathematics of the Bose Gas and its Condensation file KAIST 이지운
수학강연회 The Lagrange and Markov Spectra of Pythagorean triples file 동국대학교 김동한
수학강연회 The lace expansion in the past, present and future file Hokkaido University Akira Sakai
수학강연회 The classification of fusion categories and operator algebras file Kyoto University Masaki Izumi
수학강연회 Symplectic topology and mirror symmetry of partial flag manifolds file 부산대학교 수학과 김유식
수학강연회 Symplectic Geometry, Mirror symmetry and Holomorphic Curves file 연세대 수학과 홍한솔
수학강연회 Symmetry Breaking in Quasi-1D Coulomb Systems file 서강대학교 Paul Jung
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