Zakariya Abugrin Author

ic_202501 Author

I am delighted to have this space to share my research and engage with the community. Much of my work is conducted within the framework of my PhD in applied mathematics at FAU.

My research is focused on merging AI with scientific computing to solve partial differential equations (PDEs) using different techniques including: analytical solutions, numerical solutions, and neurical solutions (i.e. solutions based on artificial neural networks). For neurical solutions, I am investigating physics-informed neural networks (PINNs) and their advanced variants. To demonstrate the applicability of these approaches, I am tackling partial differential equations (PDEs) related to fluid flow problems (i.e. which is why I developed reservoirflow), aiming to enhance the understanding and resolution of complex physical processes.

The outcomes of this study are expected to contribute significantly to the development of the next generation of AI models, which will be more efficient and robust in handling complex systems. By refining the integration of AI with scientific computing, these advanced models could offer improved predictive accuracy and adaptability across diverse fields.

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