Carnegie Mellon University · Fall 2026

10-749 AI for Scientific Computing

Emerging techniques at the intersection of AI, machine learning, and applied mathematics for solving computational problems in the sciences.

  • Meeting time MWF · 11:00–12:20
  • Location MM A14

About the course

Course Outline

AI for Scientific Computing introduces emerging techniques at the intersection of AI, machine learning, and applied mathematics for solving computational problems in the sciences. The course is technical in nature and covers the mathematical foundations of these methods, practical engineering details, benchmarking of current approaches, and obstacles to deployment in real-world scientific and industry settings.

Key Topics

  1. Physics-informed neural networks (PINNs)
  2. PDE solvers and surrogate models, including neural operators
  3. Applications of learned PDE solvers in computational fluid dynamics
  4. Diffusion models for forecasting turbulent systems and climate
  5. Learned samplers and rare-event sampling in computational chemistry
  6. Mathematical foundations, engineering practice, benchmarking, and deployment

Course Relevance

Modern scientific workflows increasingly combine numerical methods with learned models. This course connects machine learning, applied mathematics, and domain applications so that students can evaluate when AI-based methods improve scientific computing—and when they do not.

Course Goals

Students should gain enough mathematical and practical knowledge to understand, implement, and benchmark contemporary AI methods for scientific computing; diagnose their failure modes; and engage critically with specialized technical literature and real-world deployment constraints.

Course information

Logistics

Time and Location
MWF, 11:00am–12:20pm in MM A14.
Contact
Course communication details will be shared with enrolled students. For longer discussions with the teaching team and in-person help, students are encouraged to attend office hours.
Office Hours
Office hours will be posted on the course calendar.
Education Associate
There is no Education Associate for this course.

Teaching Assistants

Prerequisites

Students entering the class are expected to have a pre-existing working knowledge of the following:

  • Introductory machine learning.
  • Proficiency programming in Python or a comparable scientific-computing environment.
  • Mathematical maturity, including probability, multivariable calculus, and linear algebra.
  • Prior exposure to numerical methods, differential equations, or scientific computing is helpful but not required.

Course Materials

Slides, readings, assignments, and other course materials will be linked from the course schedule as they become available.

Coursework

Assignments and Grading

Homeworks

There will be three assignments combining written mathematical problems and coding components. A tentative schedule of release and due dates will be added to the course schedule shortly.

Depending on the final size of the class, a short one-on-one discussion with the instructor or a TA may also be included.

Project

Students will work in groups of two or three. Projects may be applied—centered on machine-learning methodology or a specific application area—or theoretical/foundational, such as controlled experiments designed to understand a phenomenon or work proving a new theoretical result.

Deliverables: Each group will submit a final report and give an oral presentation. Depending on the final size of the class, presentations will take the form of talks or a poster show.

Evaluation

Grading

Assignments
24%
Project
73%
Class attendance
3%

Expectations and support

Course Policies

General Policies

Late Work and Extensions

The detailed late-work policy will be announced before the semester begins. Students experiencing medical, family, personal, or university-approved circumstances should contact the instructor as early as practical and use the appropriate university support channels.

  • Medical circumstances: Contact University Health Services and, for extended circumstances, your Student Liaison or Academic Advisor.
  • Family or personal emergencies: Contact your academic advisor or Counseling and Psychological Services (CaPS) for support.
  • University-approved absences: Notify the instructor and provide confirmation from the event organizer.

Requests about extensions should be directed to the instructor rather than the TAs.

Audit and Pass/Fail Options

Audit and pass/fail enrollment are subject to university and program rules. Contact the instructor when course-level permission is required.

Accommodations for Students with Disabilities

If you have a disability and have an accommodation letter from the Disability Resources office, I encourage you to discuss your accommodations and needs with the instructor as early in the semester as possible. We will work with you to ensure that accommodations are provided as appropriate. If you suspect that you may have a disability and would benefit from accommodations but are not yet registered with the Office of Disability Resources, I encourage you to contact them at access@andrew.cmu.edu.

Academic Integrity Policies

Read this carefully.

(Adapted from Roni Rosenfeld’s 10-601 Spring 2016 Course Policies.)

Collaboration among Students

  • The purpose of student collaboration is to facilitate learning, not to circumvent it. Studying the material in groups is strongly encouraged. It is also allowed to seek help from other students in understanding the material needed to solve a particular homework problem, provided no written notes (including code) are shared, or are taken at that time, and provided learning is facilitated, not circumvented. The actual solution must be done by each student alone.
  • The presence or absence of any form of help or collaboration, whether given or received, must be explicitly stated and disclosed in full by all involved. Specifically, each assignment solution must answer the following questions:
    1. Did you receive any help whatsoever from anyone in solving this assignment? Yes / No.
      • If you answered “yes,” give full details.
      • For example: “Jane Doe explained to me what is asked in Question 3.4.”
    2. Did you give any help whatsoever to anyone in solving this assignment? Yes / No.
      • If you answered “yes,” give full details.
      • For example: “I pointed Joe Smith to section 2.3 since he didn’t know how to proceed with Question 2.”
    3. Did you find or come across code that implements any part of this assignment? Yes / No.
      • If you answered “yes,” give full details, including the book and page or the URL and location within the page.
  • If you gave help after turning in your own assignment and/or after answering the questions above, you must update your answers before the assignment’s deadline, if necessary by emailing the course staff.
  • Collaboration without full disclosure will be handled severely, in compliance with CMU’s Policy on Academic Integrity.

Previously Used Assignments

Some of the homework assignments used in this class may have been used in prior versions of this class, or in classes at other institutions, or elsewhere. Solutions to them may be, or may have been, available online, or from other people or sources. It is explicitly forbidden to use any such sources, or to consult people who have solved these problems before. It is explicitly forbidden to search for these problems or their solutions on the internet. You must solve the homework assignments completely on your own. We will be actively monitoring your compliance. Collaboration with other students who are currently taking the class is allowed, but only under the conditions stated above.

Policy Regarding “Found Code”

You are encouraged to read books and other instructional materials, both online and offline, to help you understand the concepts and algorithms taught in class. These materials may contain example code or pseudo code, which may help you better understand an algorithm or an implementation detail. However, when you implement your own solution to an assignment, you must put all materials aside, and write your code completely on your own, starting “from scratch.” Specifically, you may not use any code you found or came across. If you find or come across code that implements any part of your assignment, you must disclose this fact in your collaboration statement.

Duty to Protect One’s Work

Students are responsible for pro-actively protecting their work from copying and misuse by other students. If a student’s work is copied by another student, the original author is also considered to be at fault and in gross violation of the course policies. It does not matter whether the author allowed the work to be copied or was merely negligent in preventing it from being copied. When overlapping work is submitted by different students, both students will be punished.

To protect future students, do not post your solutions publicly, neither during the course nor afterwards.

Penalties for Violations of Course Policies

Violations of course and university academic-integrity policies will be reported and handled under Carnegie Mellon procedures and may carry significant academic penalties.

Support

Take care of yourself. Do your best to maintain a healthy lifestyle this semester by eating well, exercising, avoiding drugs and alcohol, getting enough sleep and taking some time to relax. This will help you achieve your goals and cope with stress.

All of us benefit from support during times of struggle. You are not alone. There are many helpful resources available on campus and an important part of the college experience is learning how to ask for help. Asking for support sooner rather than later is often helpful.

If you or anyone you know experiences any academic stress, difficult life events, or feelings like anxiety or depression, we strongly encourage you to seek support. Counseling and Psychological Services (CaPS) is here to help: call 412-268-2922 and visit the CaPS website. Consider reaching out to a friend, faculty or family member you trust for help getting connected to the support that can help.

If you or someone you know is feeling suicidal or in danger of self-harm, call someone immediately, day or night:

  • CaPS: 412-268-2922
  • Re:solve Crisis Network: 888-796-8226
  • If the situation is life threatening, call the police:
    • On campus: CMU Police, 412-268-2323
    • Off campus: 911

If you have questions about this or your coursework, please let the instructor know.

Contact Information

aristesk@andrew.cmu.edu