Simon Fraser University
Engaging the World

Course Outlines

Fall 2026 - CMPT 419 D200

Special Topics in Artificial Intelligence (3)

Adv AI PDEs: Sim,Learn Formal Verification

Class Number: 4893

Delivery Method: In Person

Overview

  • Course Times + Location:

    Sep 9 – Dec 6, 2026: Mon, 10:30 a.m.–12:20 p.m.
    Burnaby

    Sep 9 – Dec 6, 2026: Wed, 10:30–11:20 a.m.
    Burnaby

Description

CALENDAR DESCRIPTION:

Current topics in artificial intelligence depending on faculty and student interest.

COURSE DETAILS:

Partial differential equations (PDEs) lie at the heart of physical simulation, of a rapidly growing body of scientific machine learning, and of an emerging effort to formally verify mathematics by computer. This course explores PDEs across all three perspectives. The first part introduces the foundations of PDE-based simulation: discretization techniques such as FEM and FVM, numerical schemes and linear solvers, and simulation models for a range of physical systems: Navier–Stokes flows, multiphase fluids, smoke, and turbulence, alongside mass-spring systems, rigid bodies, SPH, and hybrid methods such as MPM. The second part turns to learning, covering deep learning foundations, automatic differentiation, neural differential equations, differentiable physics and hybrid solvers, and generative models with uncertainty quantification. The final part introduces formal verification in Lean and Mathlib, building from dependent type theory and tactic-based proof toward the formalization of analysis and the current AI-for-mathematics frontier.
 
The course will be seminar-based and include both lectures and student presentations. It will be at an advanced undergraduate/beginner graduate level, and will assume familiarity with calculus and linear algebra.

COURSE-LEVEL EDUCATIONAL GOALS:

Topics

Simulation
    • PDE basics, methods, and analysis; boundary conditions
    • Advection, Laplace/Poisson, heat, wave, Navier–Stokes, multiphase (VOF)
    • Mass-spring systems, rigid bodies, continuum mechanics, FEM/FVM pipeline
    • Eulerian–Lagrangian, shallow water, SPH, hybrid methods (MPM), couplings
Learning
    • Deep learning basics, automatic differentiation / differentiable programming
    • Neural differential equations, differentiable physics & hybrid solvers
    • Generative models, uncertainty quantification
Formal Verification
    • Dependent type theory, Lean, logic and tactics
    • Mathlib, formalizing core mathematics
    • Analysis & topology, automated reasoning & the AI-for-math frontier

Grading

NOTES:

A detailed grading scheme will be discussed during the first week of class.

Department Undergraduate Notes:

The following are default policies in the School of Computing Science. Please check your course syllabus whether the instructor has chosen a different policy for your class, otherwise the following policies apply.

  • Students must attain an overall passing grade on the weighted average of exams in the course in order to get a D or higher.

 

  • All student requests for accommodations for their religious practices must be made in writing by the end of the first week of classes, or no later than one week after a student adds a course. After considering a request, an instructor may provide a concession or may decline to do so. Students requiring accommodations as a result of a disability can contact the Centre for Accessible Learning (caladmin@sfu.ca).

 

  • Use of AI tools by students for completing graded scholarly activities and course submissions that has not been explicitly authorized by the instructor  will be considered as plagiarism under SFU’s Code of Academic Policy (http://www.sfu.ca/policies/teaching/t10-02.htm).  Following this policy, instructors will report all instances of plagiarism to the academic integrity board.  

Registrar Notes:

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS

At SFU, you are expected to act honestly and responsibly in all your academic work. Cheating, plagiarism, or any other form of academic dishonesty harms your own learning, undermines the efforts of your classmates who pursue their studies honestly, and goes against the core values of the university.

To learn more about the academic disciplinary process and relevant academic supports, visit: 


RELIGIOUS ACCOMMODATION

Students with a faith background who may need accommodations during the term are encouraged to assess their needs as soon as possible and review the Multifaith religious accommodations website. The page outlines ways they begin working toward an accommodation and ensure solutions can be reached in a timely fashion.