PDE And Deep Learning

Another Perspective And New Application Of Deep Learning

Author: © 2prime


Dynamic Perspective Of Deep Learning

  • Weinan E.A Proposal on Machine Learning via Dynamical Systems link

    First one use the forward dynamic to discribe the residual network.

  • Bo Chang, Lili Meng, Eldad Haber, Lars Ruthotto, David Begert, Elliot Holtham. Reversible Architectures for Arbitrarily Deep Residual Neural Networks arXiv

    Using Hamilton ODE to approach linearize stable. Approach better result when the number of label data is small.

  • Sho Sonoda, Noboru Murata. Double Continuum Limit of Deep Neural Networks arXiv
  • Zhen Li ,Zuoqiang Shi. Deep Residual Learning and PDEs on Manifold arXiv

    The ODE which is the continuum limit of the residual net is the characteristics of a transport equation.

  • Yiping Lu, Aoxiao Zhong, Quanzheng Li, Bin Dong. Beyond Finite Layer Neural Network:Bridging Deep Architects and Numerical Differential Equations
  • Bo Chang, Lili Meng, Eldad Haber, Lars Ruthotto, David Begert, Elliot Holtham. MULTI-LEVEL RESIDUAL NETWORKS FROM DYNAMICAL SYSTEMS VIEW
  • Qianxiao Li, Long Chen, Cheng Tai, E Weinan Maximum Principle Based Algorithms for Deep Learning arXiv

Deep Learning In Numerical PDE

  • Jonathan Tompson, Kristofer Schlachter, Pablo Sprechmann, Ken PerlinACCELERATING EULERIAN FLUID SIMULATION WITH CONVOLUTIONAL NETWORKS

    ICLR2017 workshop version:link

    ICML2017 Version

  • Jiequn Han, Weinan E.Deep Learning Approximation for Stochastic Control Problems arxiv

    Hoping approximation by neural network can overcome the curse of dimensionality to solve PDE in high dimensional space.

  • Jiequn Han, Arnulf Jentzen, Weinan E.Overcoming the curse of dimensionality: Solving high-dimensional partial differential equations using deep learning arxiv

    longer version.

  • J.Nagoor Kani, Ahmed H. Elsheikh.DR-RNN: A deep residual recurrent neural network for model reduction arXiv

    Designed a physic based RNN with residual connection to do model reduction.(Reduce the dimension for a dynamic.)

  • Weinan E, Bing YuThe Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems. arXiv:1710.00211
  • Christian Beck, Weinan E, Arnulf Jentzen Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations.
  • Masaaki Fujii, Akihiko Takahashi, Masayuki Takahashi.Asymptotic Expansion as Prior Knowledge in Deep Learning Method for high dimensional BSDEs
  • Zichao long, Yiping Lu, Xianzhong Ma, Bin Dong. PDE-Net:Learning PDEs From Data
  • Jens Berg, Kaj NyströmA unified deep artificial neural network approach to partial differential equations in complex geometries

    arXiv

  • Emmanuel de Bezenac, Arthur Pajot, Patrick Gallinari Deep Learning for Physical Processes: Incorporating Prior Scientific Knowledge

    arXiv

  • Ronan Fablet, Said Ouala, Cedric Herzet Bilinear residual Neural Network for the identification and forecasting of dynamical systems arXiv
  • Y. Khoo, J. Lu, and L. Ying. Solving parametric PDE problems with artificial neural networks. pdf
  • Linfeng Zhang, Han Wang, Weinan E Reinforced dynamics for enhanced sampling in large atomic and molecular systems. I. Basic MethodologyarXiv
  • Maziar Raissi, Paris Perdikaris, George Em Karniadakis Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations arXiv2 arXiv(part2)


© Yiping Lu | Last updated: 28/10/2017

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