3 Credit Hours

MM

Mehran Mirramezani

Asst Professor

mmirram@ncsu.edu

Scientific Machine Learning (SciML) is an interdisciplinary field that integrates the governing physical laws of a system such as equations from physics or engineering with modern data-driven machine learning methodologies. By embedding domain knowledge into the learning process, SciML enables the design of models that are both physically consistent and data-efficient. This course provides a rigorous introduction to SciML, emphasizing the formulation, analysis, and implementation of machine learning techniques for systems governed by ordinary and partial differential equations. Bridging numerical analysis, scientific computing, and deep learning, SciML offers novel computational paradigms for challenges where traditional methods face limitations, such as high-dimensional problems, inverse problems, and systems with incomplete physical knowledge.

Prerequisites

Graduate standing.

Course Learning Outcomes

At the end of the course, the student will be able to:

• Apply core mathematical concepts required for machine learning algorithm development.
• Implement fundamental supervised and unsupervised learning methods for engineering data.
• Articulate neural network models, including advanced deep learning architectures.
• Integrate mechanistic/physics-based models with machine learning into various SciML pipelines.
• Use modern open-source ML libraries (e.g., JAX, PyTorch, scikit-learn) to build computational tools.
• Critically analyze and communicate findings from current SciML research through presentations and scholarly discussion.
• Develop and validate original SciML solutions through a hands-on final project addressing a real- world engineering problem.

Course Requirements

Textbook

The readings and materials are optional. However, the three main references are freely available online.

Textbook:

• M. P. Deisenroth, A. A. Faisal, C. S. Ong. Mathematics for Machine Learning. Cambridge University Press.
• C. Bishop. Deep Learning: Foundations and Concepts. Springer.
• Brunton, N. Kutz. Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control. Cambridge Press – 2nd edition.

Standard references for classical machine learning:
1- G. James et al., An Introduction to Statistical Learning, 2023 Python version, Springer
2- C. Bishop., Pattern Recognition and Machine Learning, Springer.
3- Bishop, Deep Learning – Foundations and Concepts, Springer

Mathematical background for machine learning:
1- C. Aggarwal, Linear Algebra and Optimization for Machine Learning, Springer.
2- G. Strang, Linear Algebra and Learning from Data, Cambridge

Created: 04/17/2026.