Course Syllabus
18-647: Computational Problem Solving
Spring 2023

Location: HH-1107
Class Lecture: Tuesday and Thursday, 9:30am–10:50am
Recitation: Friday, 10:00am–10:50am
Number of Units: 12
Recommended pre-requisites: 18-213/613, 18-645/646, 18-202 or equivalent

Overview:

Computing platforms used in engineering span an incredible dynamic range from embedded and wearable processors through handhelds/laptops to high performance computing servers and the cloud. Similar engineering and AI/ML problems need to be solved across the entire dynamic range. When developing algorithms or solving R&D problems, one usually starts with Matlab and Python using frameworks like Torch, Spark, and TensorFlow, and only resorts to C/C++ only when needed. This course covers how to solve AI/ML and engineering research and development problems across the entire range of machines in a productive and performant way. It discusses how to scale problems from the initial concept stage usually executed on a laptop to more powerful computing systems like enterprise or HPC servers, GPU accelerated systems, and cloud computing platforms.

This course addresses a wide range of computational and informatics problem families from traditional numerical simulation and symbolic data processing to AI and machine learning problems. It covers the most important scalable parallel algorithms used in engineering computing, and discusses frameworks providing problem-specific and general implementation templates. It covers algorithm analysis from the numerical and complexity perspective, parallelization approaches and scalability, algorithm optimization, evaluation and analysis of results.

Students in this course learn to productively solve AI/ML and engineering research and development problems on advanced computer systems across the dynamic range of computing systems. Further, they learn to carry algorithms from the concept stage to efficient-enough scaled-up implementations necessary to solve large scale problem instances, or squeeze them into the small footprint of embedded and wearable devices. Students will solve assigned homeworks and do a final blog post about lessons learned.

Brief List of Topics Covered:

• Parallel algorithms, scalability, and numerical analysis of these algorithms
• Software stack and hardware for computational engineering and AI/ML problems
• Hardware and software available to CMU students (on-site, cloud, NSF XSEDE)
• Frameworks and execution environments for quick problem solving
• How to scale from initial concepts to large-scale problems
• Next steps: How to transition to C/C++ with CUDA/OpenCL, OpenMP, MPI etc.

Download the syllabus here.

Tentative Course Calendar

Homework and Blog Post Logistics and Requirements

Machines

In this course we will use a large variety of machines in the homeworks and projects:

• Large Linux servers with direct ssh access. The machines we will access are the ECE number cluster and the data science cloud.
• Large number of small Linux machines in high throughput mode via ECE's HTCondor.
• HPC multicore nodes and multi-node configurations with and without GPUs via a batch system at PSC and CMU/MechE.
• Hadoop/Spark/Tensorflow with and without GPUs at PSC.
• Special hardware at PSC: Bridges AI multi-GPU resources (HPE Apollo and DGX-2) and large memory machines.
• AWS instances with or without multicore and GPU support.

Software Platforms

In the course we will try out a number of high-level languages and libraries in these languages:

• Python with NumPy, SciPy, and matplotlib
• R with CRAN packages
• Matlab
• Mathematica
• Haskell
• Frameworks: Torch, Theano, OpenCV
• High-end engineering software
• C/C++ with HPC math/ML libraries

Algorithms

We will use algorithms covered in the lecture as simple examples to experiment across the machines and software platforms. Students either implement the algorithms themselves or find implementations online, and then run them on the target machines to perform scalability studies. Algorithm groups targeted in the homeworks are as following:

• Dense numerical linear algebra, CNNs/DNNs/FFTs
• Graph algorithms and sparse numerical linear algebra
• ODE and PDE solvers, stencils, filters, discretization
• Discrete and continuous optimization, ML training
• Informatics, symbolic computing, higher level AI algorithms
• Statistics: Monte Carlo, MCMC, statistical machine learning
• Deep Learning, Big Data Analytics

MS Homework 1—5 Deliverables

Homework 1 to 5 will have as deliverables examples that run the specified/chosen algorithms on the specified/chosen machines for a range of problem sizes. The homework submission consists of the following:

• The source code for the algorithm, with source attribution as applicable
• The necessary data files
• All necessary scripts and make files
• The captured output of the submission runs
• Measurements in CSV files and performance plot

Blog post—Deliverables

As final project students submit a blog post addressing the following aspects of one of the homework problems:

• Problem specification: explain what problem you are addressing and where it is used.
• Algorithm: describe the algorithm you used.
• Hardware and software: describe the hardware platform and software infrastructure you used.
• Outcome: describe the result you obtained and how larger computing resources were necessary.
• Scalability and complexity: describe the algorithm's complexity, how the algorithm scales with problem size, and how it scales number of processors/cores in strong and weak scaling sense.
• Quality of the result: assess the numerical or approximation quality of your result.
• Performance anyalysis: measure the runtime behavior, model fit it to the theoretical growth behavior, and assess the efficiency of the implementation.
• Suggested performance optimization: Assume a limited engineering budget but the need for a faster solution. Suggest which parts of the algorithm one would optimize and what optimization approach and target hardware should be used.