👨 Instructor: Misha Khodak (khodak@wisc.edu)
📍 Location: Morgridge Hall 2538
🕘 Time: Tuesdays & Thursdays 1:00–2:15
The final grade will be calculated based on:
There will be four types of lectures in this class: background lectures (by the instructor), research lectures (by the instructor or guests), paper presentations (by students), and project presentations (by students). During research lectures, paper presentations, and project presentations (but not background lectures), students will be expected to think of and submit questions to the speaker(s) via a Canvas quiz. Students do not need to ask these questions out loud if they do not wish to do so. All questions must be thought of independently. If someone else asks the same or similar question out loud before you can ask your own, you must submit the speaker's answer in addition to your own version of the question.
Questions can only be submitted to Canvas during class time. Each question will be assigned a binary grade based on relevance and significance (e.g. typo or basic clarification questions do not count). A third of the participation grade will be determined by taking the seven top-graded questions from across all research lectures, but only the first two questions during each lecture will be counted. The remaining thirds of the participation grade will be determined in the same manner based on the paper presentations and the project presentations, respectively. As there are expected to be more than four lectures of each type during the semester, this will allow flexibility in case a student is not able to attend some of the classes; this also means that requests to make up these points in some manner are extremely unlikely to be granted.
Students will be expected to give two presentations, each accounting for half of the presentation grade. The first presentations will be of an existing paper or a cohesive line of work; this will be given in groups of 1-3 and will be assessed based on clarity of presentation, understanding of the material, and analysis of the consequences of the research. Topics should be determined in consultation with the instructor but can draw upon the students' own research backgrounds. The second presentation will be a progress report on the final project; this will be given in groups of 1-4 and will be assessed based on clarity of presentation, assessment of research progress and roadblocks, and analysis of next steps. A tentative timeline of when the presentations will occur is in the course schedule below.
Students will complete a final project in groups of 1-4. Topics should be determined in consultation with the instructor but can draw upon the students' own research backgrounds, so long as they are sufficiently self-contained and relevant to the course topic. A two-page project proposal is due by midnight on March 27th; an eight-page project report is due by midnight on May 4th. Both may use unlimited room for references and appendices, should be typeset in LaTeX with 11pt font and 1-inch margins, and must be emailed to the instructor with all team members cc'd.
| Date | Lecture | Slides | Readings | |
|---|---|---|---|---|
| 20 January | Background lecture: Course overview & logistics | slides | ||
| 22 January | Background lecture: Machine learning basics | slides | ||
| 27 January | Background lecture: Advanced machine learning | slides | ||
| 29 January | Background lecture: Scientific computing basics | slides | ||
| 3 February | Background lecture: Neural operators | slides | ||
| 5 February | Background lecture: Physics-informed neural networks | slides | ||
| 10 February | Research lecture: Mariel Pettee Invisible Cities: Imagining the next era of AI-enabled fundamental physics research [+ abstract] |
slides | ||
| Abstract: Some of the most exciting fundamental physics discoveries in recent years emerged thanks to large-scale experimental collaborations that radically differed from conventional scientific practices a century ago. The recent success of large-scale AI models trained on highly diverse data sources begs the question: could our scientific conventions yet again be restricting our access to major discoveries? In this talk, I propose that broadening our analyses across datasets, detectors, and even scientific disciplines could be critical to finally answering the grand mysteries of our Universe that have thus far eluded our usual strategies. To achieve this vision, AI methods can help us publish detector-agnostic datasets, construct richer embeddings of our data, and highlight connections across varied domains -- but we also need to take care to ensure that we design these tools to uphold our highest priorities as scientists. | ||||
| 12 February | Background lecture: Symbolic regression | slides | ||
| 17 February | Research lecture: Qin Li PDE-Constrained Optimization in Kinetic Equations [+ abstract] |
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| Abstract: PDE-constrained optimization has become a powerful framework for addressing inverse and control problems in systems governed by partial differential equations (PDEs). Kinetic theory encompasses a broad class of equations that describe the non-equilibrium dynamics of interacting particles, and applying PDE-constrained optimization to these systems reveals a variety of unique and intriguing behaviors. In this talk, I will discuss two representative cases. In the first, we explore the use of PDE-constrained optimization for stabilizing plasma instabilities—a challenge central to achieving controlled fusion. Dispersion-relation-based linear analysis and landscape analysis are employed to identify optimal stabilization strategies. In the second case, we highlight an essential yet often overlooked adjustment required for gradient computation when PDEs are solved using particle methods. | ||||
| 19 February | Research lecture: Misha Khodak Efficiently Learning Linear System Solvers for Fast Numerical Simulation [+ abstract] |
slides | ||
| Abstract: Accelerating PDE solving is an important emerging AI application, but popular approaches that fully replace classical solvers using neural networks often struggle to compete due to insufficient data, optimization issues, low precision, and a lack of guarantees. We consider the alternative paradigm of integrating learning directly into solvers, focusing specifically on initial value PDEs, for which the main computational cost is often solving a sequence of linear systems. We introduce PCGBandit, a lightweight online learning algorithm that has performance guarantees under practically reasonable distributional assumptions on the linear systems' target vectors, and implement it in the popular open-source software OpenFOAM. In evaluations across six different settings, including two MHD simulations, PCGBandit yields significant wallclock reductions while inheriting the classical solvers' precision and correctness. Lastly, we highlight several future directions for analyzing scientific computing via the lens of learning theory/online algorithms and for further data-driven impact on numerical simulation. | ||||
| 24 February | Research lecture: Rogerio Jorge Relation Between Magnetic Geometry and Stellarator Confinement using Data-Driven Methods [+ abstract] |
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Abstract: Traditionally, stellarator design has been performed using numerical optimization that was informed mostly by physics goals. Recently, several databases of stellarator configurations have been created, using either near-axis expansions [1], coil sets [2], or MHD equilibria [3]. Such data can provide important insights to make informed decisions on the design of the next generation of fusion devices. In this work [4], we assess how databases can be used to inform new designs. Using a large number of confinement metrics such as loss fraction of ions, omnigenity, MHD stability, and the magnetic gradient scale length, we look at the relations between geometry and confinement metrics, as well as the pair-wise distributions between such metrics. Furthermore, we construct surrogate models such as supervised autoencoders to be used in optimization efforts. Finally, we determine Shapley values to assess the relative influence of different geometry coefficients in each metric. [1] P. Curvo, D. R. Ferreira, R. Jorge 2025. “Using deep learning to design high aspect ratio fusion devices.” Journal of Plasma Physics 91(1), E38 [2] A. Giuliani 2024. “Direct stellarator coil design using global optimization: application to a comprehensive exploration of quasi-axisymmetric devices.” Journal of Plasma Physics 90(3), 905900303 [3] M. Landreman, et al. “How does ion temperature gradient turbulence depend on magnetic geometry? Insights from data and machine learning.” arXiv:2502.11657 [4] R. Laia, R. Jorge, G. Abreu 2025. “Data-Driven Approach to Model the Influence of Magnetic Geometry in the Confinement of Fusion Devices.” arXiv:2507.03776 |
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| 26 February | Research lecture: Xuhui Huang & Zige Liu Understanding Dynamics – ML Models for Molecular Simulations [+ summary] |
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| Summary: An overview of the applications of ML models to study dynamics of chemical and biological systems. | ||||
| 3 March | Paper presentation | |||
| 5 March | Research lecture: Wenxiao Pan | |||
| 10 March | Paper presentation | |||
| 12 March | Paper presentation | |||
| 17 March | Paper presentation | |||
| 19 March | Paper presentation | |||
| 24 March | Paper presentation | |||
| 26 March | Paper presentation | |||
| 7 April | Paper presentation | |||
| 9 April | Paper presentation | |||
| 14 April | Project presentation | |||
| 16 April | Project presentation | |||
| 21 April | Project presentation | |||
| 23 April | Project presentation | |||
| 28 April | Project presentation | |||
| 30 April | Project presentation | |||