Extra Form
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. Entropy of symplectic automorphisms

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

  3. Descent in derived algebraic geometry

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

  5. Vlasov-Maxwell equations and the Dynamics of Plasmas

  6. Study stochastic biochemical systems via their underlying network structures

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

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

  9. Contact instantons and entanglement of Legendrian links

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

  11. <학부생을 위한 강연> 수학과 보험산업

  12. Counting number fields and its applications

  13. 17Oct
    by 김수현
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    Towards Trustworthy Scientific Machine Learning: Theory, Algorithms, and Applications

  14. Elliptic equations with singular drifts in critical spaces

  15. Contact topology of singularities and symplectic fillings

  16. Regularity theory for non-autonomous elliptic equations in divergence form

  17. <2020년도 젊은 과학자상 수상 기념강연> Metastability of stochastic systems

  18. Geometric Langlands theory: A bridge between number theory and physics

  19. Noise-induced phenomena in stochastic heat equations

  20. Mirror symmetry of pairings

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