Research Mentor Information
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Primary Research Mentor Name: Mark Sussman
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Contact Email (FSU Email if affiliated): sussman@math.fsu.edu
Position Title: Faculty
FSU College (if applicable): Arts and Sciences
FSU Department or Non-FSU Organization Affiliation: mathematics
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Additional Research Mentor(s)
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Research Assistant Supervisor (if different from above): {Empty}
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Overall Project Details
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Title of the Project: Comparing classical methods for solving partial differential equations to machine learning methods.
Project Keywords: differential equations, data science, numerical analysis
Are you currently looking for research assistants?: Yes
Number of Research Assistants Needed : 2
Relevant Research Assistant Major(s):
open to all majors

Project Location:: On FSU Main Campus
If the project location is off campus, does the research assistant(s) need to provide their own transportation?: {Empty}
Please select the choice that most accurately describes your expectations for the research assistant(s):: In-person
Approximately how many hours a week would the research assistant(s) need to work?: 10 hours
Roughly what time frame do you expect research assistant(s) to work?: Flexible schedule (Combination of business and outside of business. TBD between student and research mentor.)
Overall Research Project Description:
There have recently been many new developments in solving differential equations using data science techniques.  See for example the "PINN" ("Physics Informed Neural Networks") method developed by Prof. Karniadakis at Brown University.  Are these methods better than classical methods (finite element, finite difference, finite volume, or Runge Kutta methods) for solving differential equations?  It could be that the new ``data science motivated'' methods are a transformative development since the methods are "embarrassingly vectorizable" (for GPU processing) and have anecdotally been shown to represent solutions using a minimum number of degrees of freedom.  There are many test problems to try  and compare classical methods to data science techniques, all ranging in level of difficulty.  

Research Tasks:
Research tasks:
1. develop a classical numerical method (your choice) for solving an ODE or PDE.  Computer language is flexible.
2. develop a data science numerical method for solving the same ODE or PDE as in step 1.
3. Compare (1) to (2) in terms of (i) ease of implementation, (ii) accuracy, and (iii) efficiency.

Skills that research assistant(s) may need::
required:
basic programming skills.  Calculus II or higher.

Mentoring Philosophy:
We should meet about once per week in which we go over outstanding problems and questions.  This is "directed independent research."  So it is up to the student to seek out resources (e.g. existing code that is available) that will help in answering the research question.

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UROP Program Elements
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Mentor Handbook, FAQs, and Communication: Yes
UROP Performance Evaluation: Yes
Materials Grant: Yes
UROP Poster Presentation: Yes

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Year: 2024
update url: https://cre.fsu.edu/urop-research-mentor-project-submission-portal?token=RSqXh2VL0AhJPXoVdJt_ksM3V0OC0ULP8aPczHmQzD0