
A Discussion on Solving Partial Differential Equations using Neural Networks
Can neural networks learn to solve partial differential equations (PDEs)...
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ODEN: A Framework to Solve Ordinary Differential Equations using Artificial Neural Networks
We explore in detail a method to solve ordinary differential equations u...
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Deep Neural Networks motivated by Partial Differential Equations
Partial differential equations (PDEs) are indispensable for modeling man...
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Solving highdimensional eigenvalue problems using deep neural networks: A diffusion Monte Carlo like approach
We propose a new method to solve eigenvalue problems for linear and semi...
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DNN or kNN: That is the Generalize vs. Memorize Question
This paper studies the relationship between the classification performed...
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Correspondence Analysis Using Neural Networks
Correspondence analysis (CA) is a multivariate statistical tool used to ...
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Solving the functional EigenProblem using Neural Networks
In this work, we explore the ability of NN (Neural Networks) to serve as a tool for finding eigenpairs of ordinary differential equations. The question we aime to address is whether, given a selfadjoint operator, we can learn what are the eigenfunctions, and their matching eigenvalues. The topic of solving the eigenproblem is widely discussed in Image Processing, as many image processing algorithms can be thought of as such operators. We suggest an alternative to numeric methods of finding eigenpairs, which may potentially be more robust and have the ability to solve more complex problems. In this work, we focus on simple problems for which the analytical solution is known. This way, we are able to make initial steps in discovering the capabilities and shortcomings of DNN (Deep Neural Networks) in the given setting.
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