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18.S096 - Applications of Scientific Machine Learning
| Date | Stars |
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| 2026-07-31 | 315 |
| 2026-08-03 | 315 |
| 2026-08-06 | 315 |
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# 18.S096 Special Subject in Mathematics: Applications of Scientific Machine Learning
## Lecturer: Dr. Christopher Rackauckas
Machine learning and scientific computing have previously lived in separate
worlds, with one focusing on training neural networks for applications like
image processing and the other solving partial differential equations defined
in climate models. However, a recently emerging discipline, called scientific
machine learning or physics-informed learning, has been bucking the trend by
integrating elements of machine learning into scientific computing workflows.
These recent advances enhance both the toolboxes of scientific computing and
machine learning practitioners by accelerating previous workflows and resulting
in data-efficient learning techniques ("machine learning with small data").
This course will be a project-based dive into scientific machine learning,
directly going to the computational tools to learn how the practical aspects of
"doing" scientific machine learning. Students will get hands-on experience
building programs which:
- Train data-efficient physics-informed neural networks
- Accelerate scientific models using surrogate methods like neural networks
- Solve hundred dimensional partial differential equations using recurrent neural networks
- Solve classical machine learning problems like image classification with neural ordinary differential equations
- Use machine learning and data-driven techniques to automatically discover physical models from data
The class will culminate with a project where students apply these techniques
to a scientific problem of their choosing. This project may be tied to one's
on-going research interest (this is recommended!).
#### Difference from 18.337
Note that the difference from the recent
[18.337: Parallel Computing and Scientific Machine Learning](https://github.com/mitmath/18337)
is that 18.337 focuses on the mathematical and computational underpinning of how
software frameworks train scientific machine learning algorithms. In contrast,
this course will focus on the applications of scientific machine learning,
looking at the current set of methodologies from the literature and learning
how to train these against scientific data using existing software frameworks.
Consult [18.337 Lecture 15](https://mitmath.github.io/18337/lecture15/diffeq_machine_learning)
as a sneak preview of the problems one will get experience solving.
Syllabus
--------
**Lectures**: Monday, Tuesday, Wednesday, and Thursday 1-3pm (2-139). Jan 6 - 31.
Note that there will be no lectures between 13-16.
**Office Hours**: There will be no formal office hours, however help can be found
at the Julia Lab 32-G785 during most working hours.
**Prerequisites**: While this course will be mixing ideas from machine learning
and numerical analysis, no one in the course is expected to have covered all of
these topics before. Understanding of calculus, linear algebra, and programming
is essential. While Julia will be used throughout the course, prior knowledge
of Julia is not necessary, but the ability to program is.
**Textbook & Other Reading**: There is no textbook for this course or the field
of scientific machine learning, so most of the materials will come from
primary literature. For a more detailed mathematical treatment of the ideas
presented in this course, consult the [18.337 course notes](https://github.com/mitmath/18337)
**Grading**: The course is based around the individual projects. 33% of the grade
is based on the writeup due on January 14th, 34% of the grade is based on the
project writeup, and 33% is based on the project presentation.
**Collaboration policy**: Make an effort to solve the problem on your own before
discussing with any classmates. When collaborating, write up the solution on
your own and acknowledge your collaborators.
## Individual Project
The goal of this course is to help the student get familiar with scientific
machine learning in a way that could Excerpt of 15,272 characters
Read on GitHubWould you bet a product on this? Bounded 0–100 and slow moving.
matched fp:83dac638b08486dd, llm:repository topics: differential-equations, neural-networks, neural-ode, partial-differential-equations, scientific-machine-learning, sciml; description/README: course on Applications of Scientific Machine Learning covering physics-informed neural nets, surrogate models, PDEs, neural ODEs, model discovery.
matched fp:83dac638b08486dd, llm:repository topics: differential-equations, neural-networks, neural-ode, partial-differential-equations, scientific-machine-learning, sciml; description/README: course on Applications of Scientific Machine Learning covering physics-informed neural nets, surrogate models, PDEs, neural ODEs, model discovery.
matched fp:83dac638b08486dd, llm:repository topics: differential-equations, neural-networks, neural-ode, partial-differential-equations, scientific-machine-learning, sciml; description/README: course on Applications of Scientific Machine Learning covering physics-informed neural nets, surrogate models, PDEs, neural ODEs, model discovery.