In this short course, we will introduce foundations of computational problem solving for models and datasets associated with equations describing real world problems. We start the course with an introduction to computational thinking along with an overview of Python as a programming language. Following that, we will provide an overview of machine learning fundamentals and showcase some of the powerful state-of-the-art machine learning algorithms with applications. Finally, we will build on the tools and techniques to introduce neural computing as a platform for artificial intelligence that takes advantage of the architecture of neural networks and the structure of the physical-laws governing the equations describing real-world problems to make data-driven intelligent decisions.
Prof. Padhu Seshaiyer* and Mr. Alonso G. Ogueda Oliva** Department of Mathematical Sciences College of Science, George Mason University, Fairfax, USA
- Introduction to Computational Thinking
- Introduction to Python Basics
- Overview of Machine Learning Fundamentals
- Machine Learning Algorithms and Applications
- Introduction to Neural Computing
- Data-driven Neural Computing
| Lesson | Notebook |
|---|---|
| Computational Thinking - Part 1 |  |
| Computational Thinking - Part 2 | |
| Machine Learning Overview | |
| Regression | |
| Classification | |
| Clustering | |
| Model Selection | |
| Neural Networks - Part 1 | |
| Neural Networks - Part 2 | |
| Physics-Informed Neural Networks | |
| Diseases-Informed Neural Networks | |
*Prof. Padhu Seshaiyer is a Full Professor of Mathematical Sciences and works in the broad areas of Computational Mathematics, Data science, Numerical methods for differential equations, Mathematical Biology, Computational Biomechanics, Design Thinking and STEM Education. In particular, his research includes the development of new analytical techniques and efficient computational algorithms to obtain numerical solutions to mathematical models describing multi-physics interactions with applications to real-world problems. During the last two decades, he has initiated and directed a variety of educational programs including faculty development, post-graduate, graduate and undergraduate research, K-12 outreach, teacher professional development, and enrichment programs to foster the interest of students and teachers at all levels to apply well-developed research concepts, to fundamental applications arising in STEM disciplines. Over the years, he has won several prestigious awards and honors for his contributions to research, teaching and service. In 2019, he was one of the Plenary Speakers for the VI WCDANM conference. More details can be found at https://math.gmu.edu/~pseshaiy/
**Mr. Alonso G. Ogueda Oliva is currently a graduate student pursuing his doctoral studies with Dr. Padhu Seshaiyer on applications of Physics Informed Neural Networks. He holds a Master’s degree in Mathematics from the Universidad Técnica Federico Santa María (2021) and a Mathematical Engineering degree from Universidad Técnica Federico Santa María (2019). He has worked on a variety of projects involving development of mathematical/statistical algorithms, data analysis, data science and engineering and cloud computing. More details can be found at https://aoguedao.github.io/cv/