College of Computer Science and Mathematics

Discussion of Ph.D. Dissertation  in the College of Computer Science and Mathematics – Department of Mathematics Sciences entitled:

“ Solving Integro-Differential Equations Using the Approximate Methods and Deep Learning Methods “

It was discussed in the discussion room at the Faculty of Computer Science and Mathematics at the University of Mosul on Thursday, 13 -3-2025.

Ph.D. Dissertation by Student Oday Ahmed Jasim Mohammed

under the supervision of Prof. Dr. Abdulghafor Mohammed Ameen Khudhur

Deep learning is a subset of machine learning, where artificial neural networks with multiple layers are used to learn complex patterns from data.  Deep learning has revolutionized many fields in recent years, including image recognition, natural language processing, and scientific modelling. Deep learning has recently been used to solve partial differential equations using physics-based inputs. Physics-informed neural networks (PINNs) are a type of deep learning model that integrate physical laws and constraints into the learning process. This allows one to solve differential equations and model physical systems with high accuracy.  For the first time, physics-informed neural networks were used to create a deep neural network to solve second-order Volterra integro-differential equations using Python’s DeepXDE and IDRLnet libraries, after converting them into a differential equation, using the Gauss-Legendre quadrature numerical method to transform the integral part. After a thorough evaluation, we found that the DeepXDE library outperforms the IDRLnet library in many aspects. Neural networks that are based on physics are a promising way to solve differential integral equations because they are more accurate, faster, more efficient, and better than traditional methods.

The scientific committee included the following members:

• Dr. Omar Saber Qasim – Chairman
• Dr. Ekhlass Saadallah Ahmed – Member.
• Dr. Muhannad Ahmed Mahmud – Member.
• Prof. Dr. Waleed Mohammed Fathi – Member.
• Prof. Dr. Badran Jasim Salim – Member.
• Dr. Abdulghafor Mohammed Ameen Khudhur – Member and supervisor.