
DataDriven Deep Learning of Partial Differential Equations in Modal Space
We present a framework for recovering/approximating unknown timedepende...
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Learning Partial Differential Equations from Data Using Neural Networks
We develop a framework for estimating unknown partial differential equat...
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Differential radial basis function network for sequence modelling
We propose a differential radial basis function (RBF) network termed RBF...
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Error analysis for probabilities of rare events with approximate models
The estimation of the probability of rare events is an important task in...
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Asymptotic Theory of ℓ_1Regularized PDE Identification from a Single Noisy Trajectory
We prove the support recovery for a general class of linear and nonlinea...
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Analysis of PDEbased binarization model for degraded document images
This report presents the results of a PDEbased binarization model for d...
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Disentangling Physical Dynamics from Unknown Factors for Unsupervised Video Prediction
Leveraging physical knowledge described by partial differential equation...
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Error bounds for PDEregularized learning
In this work we consider the regularization of a supervised learning problem by partial differential equations (PDEs) and derive error bounds for the obtained approximation in terms of a PDE error term and a data error term. Assuming that the target function satisfies an unknown PDE, the PDE error term quantifies how well this PDE is approximated by the auxiliary PDE used for regularization. It is shown that this error term decreases if more data is provided. The data error term quantifies the accuracy of the given data. Furthermore, the PDEregularized learning problem is discretized by generalized Galerkin discretizations solving the associated minimization problem in subsets of the infinite dimensional functions space, which are not necessarily subspaces. For such discretizations an error bound in terms of the PDE error, the data error, and a best approximation error is derived.
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