Topics in Digital Heritage

Numerical Methods for Digital Reconstruction

TR 05:30 PM - 7:00 PM / N25 #3229

Role	Name	Affiliation
Instructor	Jin Woo Lee	Assistant Professor, GSCT, KAIST

Course Description

Welcome to the “Numerical Methods for Digital Reconstruction” course! This class covers both the theory and practice of numerically digitizing real-world objects on a computer. By exploring how to transform real-world objects into forms that allow for audio and graphical interaction, we arrive at the question of what systems define our interactions with these objects in reality, and this course discusses how to understand these through the lens of physical principles and digital systems and recreate them by implementing them on a computer.

Whether your interests lie in cultural heritage preservation, virtual instruments, game engines, architectural acoustics, medical imaging, or immersive XR, the numerical intuition you cultivate in this course will prove valuable across all these fields.

Intended Learning Outcomes

By the end of this course, students will be able to…

Explain numerical methods and identify which method is most appropriate for a given digital reconstruction problem.
Implement the numerical algorithms and apply them to model physical phenomena relevant to graphics and/or audio domain.
Critically evaluate simulation results for accuracy, stability, and convergence, and articulate the trade-offs between different numerical approaches.

Syllabus

Download the course syllabus

Course Slides and Schedules

Both the schedules and the slides are subject to change.

Class	Date	Topic	Links	Note
1	09/01	Course Introduction	TBA	Online Lecture
2	09/03	Numerics and Error Analysis	TBA	Online Lecture
3	09/08	Linear Systems 1	TBA
4	09/10	Linear Systems 2	TBA
5	09/15	Eigenvectors	TBA
6	09/17	Singular Value Decomposition	TBA
7	09/22	Nonlinear Systems	TBA
8	09/24	Chuseok Holiday (No Class)
9	09/29	Iterative Linear Solvers	TBA
10	10/01	Specialized Optimization Methods	TBA
11	10/06	Interpolation	TBA
12	10/08	Numerical Integrations	TBA
13	10/13	Numerical Differentiation	TBA
14	10/15	Automatic Differentiation	TBA
15	10/20	Midterm Exam Week (No Class)
16	10/22	Midterm Exam Week (No Class)
17	10/27	Ordinary Differential Equations (ODEs) - I	TBA
18	10/29	Ordinary Differential Equations (ODEs) - II	TBA
19	11/03	Partial Differential Equations (PDEs) - I	TBA
20	11/05	Partial Differential Equations (PDEs) - II	TBA
21	11/10	Project Proposal Presentation
22	11/12	Wave Propagation	TBA
23	11/17	1D Wave Equation and Stability Analysis	TBA
24	11/19	Stringed Instruments	TBA
25	11/24	Wind Instruments	TBA
26	11/26	How to CAD - I	TBA
27	12/01	How to CAD - II	TBA
28	12/03	How to 3D Print	TBA
29	12/08	Open Office Hour Day (No Class)
30	12/10	Final Project Presentation
31	12/15	Final Exam Week (No Class)
32	12/17	Final Exam Week (No Class)

List of Assignments

Submit by Due Date 23:59 (KST) to the course portal. All assignments must be submitted in PDF format.

Pset #	Topic	Open Date	Due Date
Pset 0	Linear Algebra, Calculus, DSP	09/01	09/04
Pset 1	Linear Systems, Eigenvectors	09/17	09/24
Pset 2	SVD, Nonlinear Systems	09/22	10/01
Pset 3	Optimization	10/01	10/08
Pset 4	Interpolation and Integrations	10/08	10/15
Pset 5	Differentiation	10/15	10/22
Pset 6	ODEs	10/29	11/05
Pset 7	PDEs	11/05	11/12
Pset 8	Wave Equation	11/17	11/24
Final	Project Report		12/17

Grading Policy

Total of eight graded Psets will be assigned.
Pset 0 will not be graded.
All submissions except quizzes must be submitted to the portal in PDFs.
Late assignments are permitted up to twice per semester.
- You may use a ticket by completing this Google Form.
- Each ticket allows for three-days extension on a single assignment.
- Forms submitted after the due date will not be accepted.
- Assignments submitted after the due date without a ticket will be considered late and will receive only half of its original score.

Please find more details on the late submission policy from the course syllabus.