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英文字典中文字典相关资料:


  • Promising directions of machine learning for partial . . . - Nature
    Here, we examine several promising avenues of PDE research that are being advanced by machine learning, including (1) discovering new governing PDEs and coarse-grained approximations for
  • Tackling the curse of dimensionality with physics-informed . . .
    We develop a new method of scaling up physics-informed neural networks (PINNs) to solve arbitrary high-dimensional PDEs The new method, called Stochastic Dimension Gradient Descent (SDGD), decomposes a gradient of PDEs’ and PINNs’ residual into pieces corresponding to different dimensions and randomly samples a subset of these dimensional
  • [1707. 02568] Solving high-dimensional partial differential . . .
    This paper introduces a deep learning-based approach that can handle general high-dimensional parabolic PDEs To this end, the PDEs are reformulated using backward stochastic differential equations and the gradient of the unknown solution is approximated by neural networks, very much in the spirit of deep reinforcement learning with the
  • An extreme learning machine-based method for computational . . .
    We present two effective methods for solving high-dimensional partial differential equations (PDE) based on randomized neural networks Motivated by the universal approximation property of this type of networks, both methods extend the extreme learning machine (ELM) approach from low to high dimensions
  • High-Dimensional Partial Differential Equations - Deep PDE
    In recent years, tremendous progress has been made on numerical algorithms for solving partial differential equations in a very high dimension, using ideas from either nonlinear (multilevel) Monte Carlo or deep learning
  • Overcoming the curse of dimensionality: Solving high . . .
    Partial di erential equations (PDEs) are among the most ubiquitous tools used in modeling problems in nature Some of the most important ones are naturally formulated as PDEs in high dimensions Well-known examples include: The Schrodinger equation in quantum many-body problem





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