Hidden physics models: Machine learning of nonlinear partial differential equations
TLDR
In this article, a new paradigm of learning partial differential equations from small data is presented, which is essentially data-efficient learning machines capable of leveraging the underlying laws of physics, expressed by time dependent and nonlinear partial differential equation, to extract patterns from high-dimensional data generated from experiments.Citations
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Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
TL;DR: In this article, the authors introduce physics-informed neural networks, which are trained to solve supervised learning tasks while respecting any given laws of physics described by general nonlinear partial differential equations.
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Machine Learning for Fluid Mechanics
TL;DR: An overview of machine learning for fluid mechanics can be found in this article, where the strengths and limitations of these methods are addressed from the perspective of scientific inquiry that considers data as an inherent part of modeling, experimentation, and simulation.
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Neural Ordinary Differential Equations
TL;DR: In this paper, the authors introduce a new family of deep neural network models called continuous normalizing flows, which parameterize the derivative of the hidden state using a neural network, and the output of the network is computed using a black-box differential equation solver.
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An overview of deep learning in medical imaging focusing on MRI
Alexander Lundervold,Alexander Lundervold,Arvid Lundervold,Arvid Lundervold,Arvid Lundervold +4 more
TL;DR: In this article, the authors provide a short overview of recent advances and some associated challenges in machine learning applied to medical image processing and image analysis, and provide a starting point for people interested in experimenting and perhaps contributing to the field of machine learning for medical imaging.
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An overview of deep learning in medical imaging focusing on MRI
Alexander Lundervold,Alexander Lundervold,Arvid Lundervold,Arvid Lundervold,Arvid Lundervold +4 more
TL;DR: This paper indicates how deep learning has been applied to the entire MRI processing chain, from acquisition to image retrieval, from segmentation to disease prediction, and provides a starting point for people interested in experimenting and contributing to the field of deep learning for medical imaging.
References
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Regression Shrinkage and Selection via the Lasso
TL;DR: A new method for estimation in linear models called the lasso, which minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant, is proposed.
Book
The Nature of Statistical Learning Theory
TL;DR: Setting of the learning problem consistency of learning processes bounds on the rate of convergence ofLearning processes controlling the generalization ability of learning process constructing learning algorithms what is important in learning theory?
Book
Gaussian Processes for Machine Learning
TL;DR: The treatment is comprehensive and self-contained, targeted at researchers and students in machine learning and applied statistics, and deals with the supervised learning problem for both regression and classification.
Book
Machine Learning : A Probabilistic Perspective
TL;DR: This textbook offers a comprehensive and self-contained introduction to the field of machine learning, based on a unified, probabilistic approach, and is suitable for upper-level undergraduates with an introductory-level college math background and beginning graduate students.