About: Design of Loss Functions for Solving Inverse Problems Using Deep Learning

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An Entity of Type : schema:ScholarlyArticle, within Data Space : wasabi.inria.fr associated with source document(s)

Attributes	Values
type	Academic Article research paper schema:ScholarlyArticle
isDefinedBy	Covid-on-the-Web dataset
has title	Design of Loss Functions for Solving Inverse Problems Using Deep Learning
Creator	Pardo, David Alberdi, Elisabete Rivera, Jon
Source	PMC
abstract	Solving inverse problems is a crucial task in several applications that strongly affect our daily lives, including multiple engineering fields, military operations, and/or energy production. There exist different methods for solving inverse problems, including gradient based methods, statistics based methods, and Deep Learning (DL) methods. In this work, we focus on the latest. Specifically, we study the design of proper loss functions for dealing with inverse problems using DL. To do this, we introduce a simple benchmark problem with known analytical solution. Then, we propose multiple loss functions and compare their performance when applied to our benchmark example problem. In addition, we analyze how to improve the approximation of the forward function by: (a) considering a Hermite-type interpolation loss function, and (b) reducing the number of samples for the forward training in the Encoder-Decoder method. Results indicate that a correct design of the loss function is crucial to obtain accurate inversion results.
has issue date	2020-05-22(xsd:dateTime)
bibo:doi	10.1007/978-3-030-50420-5_12
has license	no-cc
sha1sum (hex)	ec225b77b1d34cc80512d24287893339e43a72cb
schema:url	https://doi.org/10.1007/978-3-030-50420-5_12
resource representing a document's title	Design of Loss Functions for Solving Inverse Problems Using Deep Learning
has PubMed Central identifier	PMC7304019
schema:publication	Computational Science - ICCS 2020
resource representing a document's body	covid:ec225b77b1d34cc80512d24287893339e43a72cb#body_text
is schema:about of	named entity 'benchmark' named entity 'benchmark' named entity 'compare' named entity 'loss function' named entity 'Solving' named entity 'Results' named entity 'loss functions' named entity 'simple' named entity 'energy' named entity 'Deep Learning' named entity 'statistics' named entity 'introduce' named entity 'study' named entity 'inverse problems' named entity 'loss functions' named entity 'inverse problems' named entity 'loss function' named entity 'Inverse Problems' named entity 'Hermite interpolation' named entity 'benchmark problem' named entity 'probability' named entity 'NNs' named entity 'loss function' named entity 'loss function' named entity 'database' named entity 'loss function' named entity 'Partial Differential Equation' named entity 'PDEs' named entity 'PDE' named entity 'PDEs' named entity 'loss function' named entity 'function approximation' named entity 'inverse operator' named entity 'Hermite interpolation' named entity 'loss function' named entity 'two-steps' named entity 'ReLU' named entity 'activation function' named entity 'inverse problems' named entity 'ReLU' named entity 'function approximation' named entity 'gradient' named entity 'loss function' named entity 'inverse problem' named entity 'Training data' named entity 'blue line' named entity 'identity mapping' named entity 'change of coordinates' named entity 'loss function' named entity 'inverse problems' named entity 'loss function' named entity 'Total Loss' named entity 'injective function' named entity 'pseudo-inverse' named entity 'NNs' named entity 'database' named entity 'computational cost' named entity 'inverse operator' named entity 'loss functions' named entity 'loss function' named entity 'sampling' named entity 'inverse problem' named entity 'Deep Learning' named entity 'adjoint operator' named entity 'loss function' named entity 'inverse operator' named entity 'inverse problems' named entity 'inverse function' named entity 'analytical solution' named entity 'training dataset' named entity 'benchmark problem' named entity 'regularization' named entity 'inverse problems' named entity 'loss function' named entity 'loss function' named entity 'loss functions' named entity 'evolution' named entity 'PDE' named entity 'Hermite interpolation' named entity 'regularization' named entity 'inverse function'

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