Course Description

CSC2539 is a graduate seminar on neural representations and physics-informed machine learning. We will study how continuous neural fields, differential equations, neural operators, and generative models can be used to represent, simulate, and reason about physical systems, with an emphasis on inverse problems and scientific applications.

The course combines student-led paper presentations and discussions, one integrative interactive lab, and an open-ended research project. Students will compare methods across related papers, build intuition through visual and interactive explanations, and develop a research proposal leading to a final project. Modern AI tools will be used throughout for research and coding, with students remaining responsible for verification, attribution, and scientific judgment.

Recommended preparation: A foundation in machine learning and familiarity with deep networks and optimization. Prior exposure to computer vision, graphics, scientific computing, numerical simulation, or a related area is helpful but not required.

Instructor

Teaching Assistant

Course Logistics

Meetings: Wednesdays, 13:00–15:00 in BF214.

Instructor office hours: Scheduled in coordination with the instructor.

Announcements & Materials: Posted on Quercus.

GitHub Repository:
https://github.com/uoft-csc2539-seminar/csc2539-2026-fall

Communication:
All teamwork, lab coordination, and informal discussions will take place via Discord (invite link provided on Quercus). Use GitHub Issues and PR comments for structured collaboration and technical Q&A.

AI-Assisted Research and Coding

Modern AI tools may be used throughout the course to support literature exploration, concept development, coding, debugging, and the creation of visual explanations. Week 2 will provide a hands-on introduction to agent-based research and coding workflows.

These tools should extend—not replace—your own scientific reasoning. You remain responsible for:

The quality of your work will be assessed through its scientific insight, clarity, correctness, and evidence—not through whether AI tools were used.

Coursework & Grading

Paper Presentation and Discussion Participation — 25%

Paper presentation: 20%. Teams will present two related papers and lead the subsequent class discussion. Presentations should build intuition, connect the papers, and use effective visual explanations rather than simply reproducing their contents.

Discussion participation: 5%. Non-presenting students will sign up for papers and work in small groups during the first 10 minutes of class. Groups will record their observations and questions, then selected group leads will contribute to the discussion after the presentation.

Interactive Lab — 25%

Teams of two or three will develop three connected notebooks exploring a course topic: a toy example, a paper-based investigation, and an extension. During class, another group will explore the notebooks and then deliver a short reverse pitch presenting the lab's key ideas, results, and what they learned through interacting with it.

Project Proposal Pitch — 10%

Students may work individually or in pairs. The pitch should define the research goal, position it relative to prior work, summarize relevant methods, and present an initial plan or, optionally, preliminary results.

Final Project Report — 40%

The final project is an open-ended physics-informed machine-learning investigation. The report should follow the CVPR format and be 6–8 pages, including references, with an absolute maximum of 8 pages.

Schedule (Fall 2026)

On student-presentation weeks, Group A leads the first hour and Group B leads the second. See the full schedule and reading list for paper links, background readings, and discussion materials.

Week Date Topic Format and readings
1 Sep 9 Course overview and introduction Instructor-led
2 Sep 16 Hands-on agent-based research and coding seminar Led by Rohan Dahale
3 Sep 23 Neural Fields Across Astronomical Scales Instructor research presentation
4 Sep 30 Neural fields: representations and inverse problems Group A: Representing high-frequency signals
Group B: Neural fields in inverse problems
Lab topic declaration: pitch your lab idea and submit the initial README by the end of Week 4.
5 Oct 7 Conditioned neural fields: shape families, topology, and discontinuities Group A: Representing families of shapes
Group B: Topology and discontinuities through lifting
6 Oct 14 Physics-informed learning: solving and discovering equations Group A: Known physics, hidden solutions
Group B: Unknown physics and hidden coordinates
7 Oct 21 Neural differential equations and structured dynamics Group A: Neural ordinary differential equations
Group B: Learning mechanics with physical structure
Oct 28 Reading Week — no class No class
8 Nov 4 Integrative interactive lab Notebook exploration and reverse pitches
Lab due Nov 3, 23:59
9 Nov 11 Neural operators and parametric solution maps Group A: Foundational neural operators
Group B: Continuous fields and changing geometry
10 Nov 18 Diffusion models for scientific inverse problems Group A: From pixel-space to latent diffusion
Group B: Generative priors without complete observations
11 Nov 25 Project proposal presentations I Individual students or pairs
12 Dec 2 Project proposal presentations II Final class
Dec 8 End of term Final project due Dec 15

Policies

Academic Integrity and Attribution

Submitted work must reflect your own understanding and scientific judgment. Cite papers, software, datasets, code, figures, and other sources appropriately, and acknowledge substantial assistance from AI tools. You are responsible for verifying every claim, result, and piece of code included in your work.

Collaboration

Discussion and exchange of ideas are encouraged. For team assignments, all members should understand the complete submission and contribute meaningfully. Work submitted for an individual component must be your own unless collaboration is explicitly permitted.

Deadlines and Accommodations

Assignment deadlines are listed in the course GitHub repository. If illness, accessibility needs, or other circumstances may affect your work, contact the instructor or teaching assistant as early as possible so that appropriate arrangements can be discussed.

Communication and Announcements

Discord is the main channel for coordination and informal discussion; the invitation is available on Quercus. Official announcements, course materials, and grading information will also be posted on Quercus.