Advances in PDE-Based Models, Artificial Intelligence and Deep Learning

Dear Colleagues,

Partial differential equations (PDE), which have long been used to formulate dynamical phenomena, have been applied successfully in various digital image processing and analysis and computer vision fields, such as image filtering, inpainting, segmentation, compression, decomposition, registration, and optical flow estimation, in the last 35 years. They have also been applied in artificial intelligence, where PDE-based models have been used to generate artificial neural network architectures.

An important sub-domain of artificial intelligence, deep learning, also represents an application area of partial differential equations. Deep learning represents a family of advanced machine learning techniques based on artificial neural networks with representation learning, such as deep belief networks, deep reinforcement learning, recurrent neural networks, and convolutional neural networks. Deep neural networks, which have been applied successfully to all image processing and analysis and computer vision fields, have many connections to PDE models. Thus, neural partial differential equations (NPDE) can be used to describe AI systems and the architectures of some deep networks that can be interpreted as nonlinear PDEs, such as recurrent neural networks (RNN). Further, evolution PDEs can be learned from given datasets using deep neural networks, which also predict their dynamical behavior. Convolutional neural networks (CNN) have been increasingly used to numerically solve PDE-based models, providing fast and effective numerical approximations for them. Finally, PDE and deep-learning-based models can be combined successfully to provide more effective image and video processing and computer vision solutions. 

This proposed Special Issue deals with all these mentioned connections between PDE models, AI systems, and deep learning, especially those related to image analysis and computer vision, the main purpose being the dissemination of advanced and original research in these scientific domains and bringing together of researchers working in partial differential equations, image processing and analysis, computer vision, artificial intelligence, and deep learning, so as to extend the existing knowledge in these important fields.

We thus encourage you to send high-quality papers that disseminate new research achievements for this issue.

Prof. Dr. Tudor Barbu
Guest Editor

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