Exame de Qualificação: Embedding Prior Knowledge Into Loss Function of Neural Networks

Orientadores:
Gilson Antônio Giraldi - Laboratório Nacional de Computação Científica - LNCC

Banca Examinadora:
Pablo Javier Blanco - Laboratório Nacional de Computação Científica - LNCC (presidente)
Antônio Tadeu Azevedo Gomes - Laboratório Nacional de Computação Científica - LNCC
José Manoel Seixas - Universidade Federal do Rio de Janeiro - UFRJ

Suplentes:
Marcio Rentes Borges - Laboratório Nacional de Computação Científica - LNCC

Resumo:

The increase of available data and technological advances led to he adoption of machine learning techniques, which enable the model to extract information from training data. Deep Learning methodologies have revolutionized the field of computational modeling, achieving impressive results in areas like computer vision and solution of differential equations. Nevertheless, deep learning models need sufficient data for training and suffer from issues related to the incorporation of prior knowledge, which require regularization or specific reprocessing steps to improve training performance. For instance, in natural science applications, the phenomena are governed by conservation laws. Moreover, in computer vision, tasks involving pattern recognition may be invariant under some groups of transformations. The former motivates a new type of machine learning method named Physical Informed Neural Networks (PINNs) that has opened up new possibilities for addressing computational modeling tasks, like solving partial differential equations (PDEs). Regarding computer vision applications, the usual procedure is to argument the training data with samples generated considering the desired tranformations, like rigid motion in point clouds classification. One important aspect of PINN s is the composition of the loss function that includes terms derived from the governing equations. Such point steers our research towards its main claim: address computer vision problems by transferring knowledge through the incorporation of new mathematical terms into the loss function.
Such claim involves the combination of classical and deep learning methodologies having the potencial to lead to more powerful methodologies as verified in the computacional experiments shown in this proposal for point cloud classification and magnetic resonance image (MRI) denoising. Also, taking in mind that PINNs were first developed to solve differential equations with or without the auxiliary of real/simulated data, this proposal explores PINNs model to aproximate the solution of a differential equation without a known analytical or numerical solution.