Enquiry for Course Details
ASAI4012 High-performance computing: algorithms and applications (6 credits) Academic Year 2025
Offering Department Mathematics Quota
Course Co-ordinator Dr Z Zhang, Mathematics < zhangzw@hku.hk >
Teachers Involved (Dr Z Zhang,Mathematics)
Course Objectives The development of High-Performance Computing (HPC) systems has been largely driven by the needs of computational scientists conducting large-scale numerical simulations in fields such as global weather forecasting, computational biology, materials science, data analysis, and artificial intelligence (AI). This course aims to provide a comprehensive understanding of the mathematical foundations and essential concepts involved in designing fast and efficient algorithms for HPC and deep learning (DL) applications. Students will delve into the fundamental numerical methods and computational patterns used in HPC and explore their various practical applications, including data analysis, DL, and AI.
Course Contents & Topics The course will cover:
- Basic introductions to numerical methods, floating-point representation, error analysis, and computational complexity.
- Dense linear algebra, algorithms, and applications in designing deep neural networks.  
- Sparse linear algebra and data compression.
- Simple differential equations on structured grids, and deep learning-based methods for solving differential equations.  
- Spectral methods, fast Fourier transforms (FFTs), and divide-and-conquer algorithms.
- N-body problems and fast multipole methods.
- Monte Carlo methods in sampling high-dimensional distributions and stochastic gradient descent methods in training and optimizing deep learning models.
Course Learning Outcomes
On successful completion of this course, students should be able to:

CLO 1 gain a solid understanding of the fundamental numerical methods, including stability, error analysis, and computational complexities
CLO 2 apply numerical methods for solving dense and sparse linear equation systems, design the architectures of the deep neural networks, and analyze their complexities
CLO 3 compute low-rank approximation of matrices and carry out data compression and data analysis
CLO 4 solve simple ordinary differential equations and partial differential equations that arise from real-world applications on structured grids. Implement the Physics Informed Neural Networks (PINNs) method and the Deep Ritz method to solve differential equations
CLO 5 understand the basic ideas of the divide-and-conquer method and fast multipole method in designing fast algorithms
CLO 6 apply Monte Carlo methods to sample high-dimensional probability distributions and to solve high-dimensional problems arising from DL and AI. Understand the stochastic gradient descent for training and optimizing deep learning models
CLO 7 use software packages such as MATLAB or Python for large-scale scientific simulations, data analysis, and AI
Pre-requisites
(and Co-requisites and
Impermissible combinations)		 (Passed in SDST2601) and (Pass or already enrolled in MATH3904)
For BASc(AppliedAI) students only.
Only for students admitted in 2025 and thereafter.
Course Status with Related Major/Minor /Professional Core 2U000C00 Course not offered under any Major/Minor/Professional core
2025 Bachelor of Arts and Sciences in Applied Artificial Intelligence ( Disciplinary Elective )
Course to PLO Mapping 2025 Bachelor of Arts and Sciences in Applied Artificial Intelligence < PLO 2,3,5 >
Offer in 2025 - 2026 Y        1st sem    Examination Dec     
Offer in 2026 - 2027 Y
Course Grade A+ to F
Grade Descriptors
A Demonstrate thorough mastery at an advanced level of extensive knowledge and skills required for attaining all the course learning outcomes. Show strong analytical and critical abilities and logical thinking, with evidence of original thought, and ability to apply knowledge to a wide range of complex, familiar and unfamiliar situations. Apply highly effective organizational and presentational skills.
B Demonstrate substantial command of a broad range of knowledge and skills required for attaining at least most of the course learning outcomes. Show evidence of analytical and critical abilities and logical thinking, and ability to apply knowledge to familiar and some unfamiliar situations. Apply effective organizational and presentational skills.
C Demonstrate general but incomplete command of knowledge and skills required for attaining most of the course learning outcomes. Show evidence of some analytical and critical abilities and logical thinking, and ability to apply knowledge to most familiar situations. Apply moderately effective organizational and presentational skills.
D Demonstrate partial but limited command of knowledge and skills required for attaining some of the course learning outcomes. Show evidence of some coherent and logical thinking, but with limited analytical and critical abilities. Show limited ability to apply knowledge to solve problems. Apply limited or barely effective organizational and presentational skills.
Fail Demonstrate little or no evidence of command of knowledge and skills required for attaining the course learning outcomes. Lack of analytical and critical abilities, logical and coherent thinking. Show very little or no ability to apply knowledge to solve problems. Organization and presentational skills are minimally effective or ineffective.
Communication-intensive Course N
Course Type Lecture-based course
Course Teaching
& Learning Activities
Activities Details No. of Hours
Lectures 36.0
Tutorials 12.0
Reading / Self study 100.0
Assessment Methods
and Weighting
Methods Details Weighting in final
course grade (%)		 Assessment Methods
to CLO Mapping
Assignments 50.0 1,2,3,4,5,6,7
Examination 50.0 1,2,3,4,5,6,7
Required/recommended reading
and online materials		 Instructor's Lecture Notes and Learning materials.
Course Website http://moodle.hku.hk
Additional Course Information