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강연자 신연종
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.

첨부 '1'
  1. Universality of log-correlated fields

  2. <학부생을 위한 ɛ 강연> 양자상태의 기하학

  3. Class field theory for 3-dimensional foliated dynamical systems

  4. Satellite operators on knot concordance

  5. <정년퇴임 기념강연> 작용소대수와 양자정보이론

  6. Entropy of symplectic automorphisms

  7. Equations defining algebraic curves and their tangent and secant varieties

  8. Descent in derived algebraic geometry

  9. Toward bridging a connection between machine learning and applied mathematics

  10. Vlasov-Maxwell equations and the Dynamics of Plasmas

  11. Study stochastic biochemical systems via their underlying network structures

  12. <학부생을 위한 ɛ 강연> 복잡한 생명현상을 위한 21세기 현미경, 수학!

  13. Birational Geometry of varieties with effective anti-canonical divisors

  14. Contact instantons and entanglement of Legendrian links

  15. <학부생을 위한 ɛ 강연> Self-Supervised Learning in Computer Vision

  16. <학부생을 위한 강연> 수학과 보험산업

  17. Counting number fields and its applications

  18. 17Oct
    by 김수현
    in 수학강연회

    Towards Trustworthy Scientific Machine Learning: Theory, Algorithms, and Applications

  19. Elliptic equations with singular drifts in critical spaces

  20. Contact topology of singularities and symplectic fillings

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