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EP30.FSF1108 — Scientific Machine Learning | Chương trình đào tạo NEU

EP30.FSF1108 — Scientific Machine Learning

Credits
3
Self-study hours
90
Showing intake
K68-2026

Course description

Scientific Machine Learning (SciML) is an emerging interdisciplinary field that integrates machine learning techniques with scientific computing and physical modeling. The course focuses on combining data-driven methods with physical laws to model, simulate, and analyze complex systems arising in science and engineering.

This course emphasizes the synergy between classical scientific modeling and modern machine learning, with particular attention to physics-informed learning, operator learning, and reduced-order modeling. Students will gain both theoretical understanding and practical skills for applying SciML to real-world scientific problems.

The main topics of the course include data-driven scientific modeling, mathematical foundations for scientific machine learning, physics-informed learning, operator learning, reduced-order modeling, uncertainty quantification, and real-world scientific applications.

Course requirements

Requirements for Final Examination

Students are allowed to take the final/terminal exams (50%) if their attendance score (10%) is 5 or higher (on a 10-point scale).

See Appendix 2, Rubric 1 for attendance evaluation.

Requirements for Class Attendance

Students are responsible for attending all classes. In case of absence due to force majeure, students must provide sufficient and reasonable proof. For each absence, 1 point will be deducted from the attendance score. Students who miss more than 3 classes, with or without valid reasons, will be considered as failing to complete the course and must re-register.

Students will be awarded points for constructive comments. These points will be added to attendance and group assignment scores.

Groups that do not submit their group work will receive a score of 0. Late submissions will incur a deduction for each day they are late.

Requirements for In-class Behaviour

The course is conducted on the principle of mutual respect between learners and lecturers. Any behavior that disrupts the teaching and learning process is strictly prohibited.

Students must arrive on time for class. Those who are more than 10 minutes late will not be allowed to attend. Noise and other disturbances that affect the learning process are not permitted.

Laptops and tablets may only be used for taking notes and performing calculations related to lectures and exercises. Use for any other purpose is strictly prohibited.

Lecturers

  • Doan Trong Tuyen
  • Le Thi Anh
  • Phung Minh Duc
  • Bui Quoc Hoan

Teaching plan

Week 1

Lecture 1: Introduction to Scientific Machine Learning Motivation and scope SciML frameworks
References
[1] Chapter 1: Singular Value Decomposition (SVD) [2] Ch. 17: Image Recognition – Basics of Machine Learning (Sections 17.1–17.2)
Activities
Lecturer: Introduce course, SciML overview. Students: Read syllabus, chapter intros.
Assessment
Rubric 1

Week 2

Seminar 1: Modeling Concepts Discussion
References
[1] Chapter 1 (Sections 1.1–1.3) [2] Ch. 17.1–17.3: Basics of Machine Learning and MATLAB Implementation
Activities
Lecturer: Facilitate discussion. Students: Discuss modeling paradigms.
Assessment
Rubric 1

Week 3

Lecture 2: Mathematical Foundations Linear algebra for modeling Optimization
References
[1] Chapter 1.3–1.5 (Pseudo-inverse, least squares, PCA) Chapter 4.1–4.4 (Regression & optimization foundations) [2] Ch. 15: Linear Algebra and Singular Value Decomposition
Activities
Lecturer: Present fundamentals. Students: Study examples.

Learning resources

  • Data-Driven Science and Engineering — Brunton, S. L., & Kutz, J. N., Cambridge University Press, 2019
  • Data-driven Modelling and Scientific Machine Learning (Springer) — Krishna Garikipati, 2024
Assessment
Rubric 2

Week 4

Seminar 2: Exercises on Foundations
References
[1] Chapter 1.4–1.5 Chapter 4.2–4.4 [2] Ch. 15.1–15.6 (SVD, PCA, Robust PCA)
Activities
Lecturer: Provide exercises. Students: Solve problems.
Assessment
Rubric 2

Week 5

Lecture 3: Data-Driven Dynamical Systems Time-series modeling System identification
References
[1] Chapter 7 7.1 Overview 7.2 Dynamic Mode Decomposition (DMD) 7.3 SINDy [2] Ch. 20: Dynamic Mode Decomposition
Activities
Lecturer: Explain methods. Students: Analyze tasks.
Assessment
Rubric 2

Week 6

Seminar 3: Regression & Sparse Modeling
References
[1] Chapter 3: Sparsity and Compressed Sensing (3.1–3.6) Chapter 7.3 (SINDy – sparse dynamics) [2] Ch. 18: Basics of Compressed Sensing
Activities
Lecturer: Assign exercises. Students: Implement.
Assessment
Rubric 2

Week 7

Lecture 4: Machine Learning for Scientific Data Neural networks Approximation theory
References
[1] Chapter 4: Regression and Model Selection Chapter 5: Clustering and Classification [2] Ch. 17: Image Recognition – Machine Learning Foundations
Activities
Lecturer: Present theory. Students: Review.
Assessment
Rubric 2

Week 8

Seminar 4: Neural Network Implementation Midterm 1
References
[1] Chapter 6.1–6.4 (Single-layer, multi-layer NN, backprop, SGD) [2] Ch. 17.3: Implementing ML Models in MATLAB
Activities
Lecturer: Guide tasks. Students: Implement ML models.
Assessment
Rubric 2

Week 9

Lecture 5: Physics-Informed ML (PINNs) Governing laws as constraints
References
[1] Chapter 14 14.1 Mathematical Foundations 14.4 Learning Nonlinear Operators 14.5 Physics-Informed Neural Networks [2] Ch. 19: Dimensionality Reduction for Partial Differential Equations
Activities
Lecturer: Teach PINN concepts. Students: Study forms.
Assessment
Rubric 2

Week 10

Seminar 5: PINN examples & solvers
References
[1] Chapter 14.5–14.7 [2] Ch. 19.1–19.5 (POD, Symmetry, PDE dynamics)
Activities
Lecturer: Demonstrate solvers. Students: Implement examples.
Assessment
Rubric 2

Week 11

Lecture 6: Inverse Problems & Surrogate Models
References
[1] Chapter 9: Balanced Models & System Identification Chapter 12: Reduced-Order Models (ROMs) [2] Ch. 21: Data Assimilation Methods
Activities
Lecturer: Present inverse and surrogate modeling. Students: Review case studies.
Assessment
Rubric 2

Week 12

Seminar 6: Forward/Inverse Problem Practice
References
[1] Chapter 9 & 12 [2] Ch. 21.1–21.3 (Kalman Filtering, Data Assimilation Examples)
Activities
Lecturer: Guide practice. Students: Solve problems.
Assessment
Rubric 2

Week 13

Lecture 7: Neural Operators & Scale Bridging
References
[1] Chapter 14.4 (Learning Nonlinear Operators) Chapter 12.6–12.9 (NN-enhanced ROMs) [2] Ch. 22: Equation-Free Modeling
Activities
Lecturer: Teach advanced topics. Students: Review theory.
Assessment
Rubric 2

Week 14

Seminar 7: Operator Learning & Reduced-Order Models Midterm 2
References
[1] Chapter 12 Chapter 13 (Interpolation for parametric ROMs) [2] Ch. 22.1–22.3; Ch. 23 (Combining DR, CS & ML)
Activities
Lecturer: Discussion. Students: Implement tasks.
Assessment
Rubric 2

Week 15

Seminar 8: Project Presentations & Review
References
[1] Chapters 7, 12, 14 (review) [2] Ch. 23–25 (Applications of Data-Driven Modeling)
Activities
Lecturer: Review, evaluate. Students: Present.
Assessment
Rubric 3