Home /  Principled Scientific Discovery with Formal Methods (IBM, Yorktown)

Summer Graduate School

Principled Scientific Discovery with Formal Methods (IBM, Yorktown) July 07, 2025 - July 18, 2025
Parent Program: --
Location: IBM T. J. Watson Research Center, Yorktown Heights, New York
Organizers Kenneth Clarkson (IBM Research Division), Cristina Cornelio (Samsung AI), Claudia D Ambrosio (Centre National de la Recherche Scientifique (CNRS); École Polytechnique), Sanjeeb Dash (IBM Thomas J. Watson Research Center), Lior Horesh (IBM Thomas J. Watson Research Center)
Speaker(s)

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Description
Sci method
<p>The traditional scientific method cycle, with Francis Bacon and Rene Descartes, its concievers in the center, alongside formal and statistical AI machinary, as a propsective evolution of the method.&nbsp;<br />&nbsp;</p>

The summer school aims to expose participants to formal methods that can facilitate principled scientific discovery. The school will cover some of the basic automated statistical inference (in the form of machine learning techniques) and reasoning methods that are commonly used in scientific discovery, as well as novel techniques developed to tackle open questions and issues. This summer school will address novel computational methods for scientific discovery and focus on fusing axiomatic knowledge and experimental data to enable principled derivations of models of natural phenomena along with certificates of the consistency of these models with background knowledge specified as axioms.

School Structure

The school will consist of lectures, tutorials, a lab visit, a hands-on experimental session, an invited lecture seminars, and problem session. The tutorial will be more interactive than the lectures and will show students how to use important software tools. The purpose of the problem sessions is to reinforce students’ understanding of the material from the lectures by working on problems and reviewing prerequisites. Activities may include presentation of solutions to problems based on lectures, student and TA presentation of material relevant to lectures. In addition, students will learn to use and analyze relevant software packages and implementations.

Prerequisites

The minimum requirement for students to beneficially participate in this summer school are the basics of probability, algorithms, linear algebra, and discrete mathematics. See the first book (and chapters listed) for linear algebra, and the second book for discrete mathematics and probability. 

  1. S. Boyd, L. Vandenberghe, Linear Algebra – Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares, 2018, Cambridge University Press, Cambridge, UK.  Chapters 1-3, 5-8, 10-14. 
  2. CPSC 202a, Mathematical Tools for Computer Science lecture notes, Yale University. Chapters 2,10,12 (backup)
  3. 3. J. Erickson, Algorithms, 2019.

Application Procedure

SLMath is only able to support a limited number of students to attend this school.  Therefore, it is likely that only one student per institution will be funded by SLMath.

For eligibility and how to apply, see the Summer Graduate Schools homepage.

Venue

The location of the summer school is the IBM T. J. Watson Research Center in Yorktown Heights, NY.
The Yorktown lab houses industry-leading facilities for advancing science and technology including an IBM Q lab where researchers are pioneering quantum computing, and the original THINKLab, where IBM researchers and clients collaborate on innovative solutions to complex industry challenges

Keywords and Mathematics Subject Classification (MSC)
Tags/Keywords
  • Derivable discovery

  • Symbolic Regression

  • Automated Theorem Proving

  • Polynomial Optimization

  • Mixed-integer nonlinear optimization

  • Hypothesis generation and testing

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Schedule, Notes/Handouts & Videos
Show Schedule, Notes/Handouts & Videos
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Jul 07, 2025
Monday
09:30 AM - 10:45 AM
  Welcome to IBM Research; Background and Motivation
10:45 AM - 11:00 AM
  Break
11:00 AM - 12:15 PM
  Preliminaries
12:15 PM - 01:30 PM
  Lunch
12:15 PM - 12:30 PM
  Welcome with SLMath Director
01:30 PM - 02:45 PM
  Data Driven Discovery I
02:45 PM - 03:00 PM
  Break
03:00 PM - 04:30 PM
  Working Groups
Jul 08, 2025
Tuesday
09:30 AM - 10:45 AM
  Data Driven Discovery II
10:45 AM - 11:00 AM
  Break
11:00 AM - 12:15 PM
  Data Driven Discovery III
12:15 PM - 01:30 PM
  Lunch
01:30 PM - 02:45 PM
  Data Driven Discovery Tutorial
02:45 PM - 03:00 PM
  Break
03:00 PM - 04:30 PM
  Working Groups
Jul 09, 2025
Wednesday
09:30 AM - 10:45 AM
  Knowledge Based Discovery I
10:45 AM - 11:00 AM
  Break
11:00 AM - 12:15 PM
  Knowledge Based Discovery II
12:15 PM - 01:30 PM
  Lunch
01:30 PM - 02:45 PM
  Knowledge Based Discovery III
02:45 PM - 03:00 PM
  Break
03:00 PM - 04:30 PM
  Tutorial
Jul 10, 2025
Thursday
09:30 AM - 10:45 AM
  Knowledge Based Discovery IV
10:45 AM - 11:00 AM
  Break
11:00 AM - 12:15 PM
  Knowledge Based Discovery V
12:15 PM - 01:30 PM
  Lunch
01:30 PM - 02:45 PM
  Knowledge Based Discovery Applications
02:45 PM - 03:00 PM
  Break
03:00 PM - 04:30 PM
  Tutorial
Jul 11, 2025
Friday
09:30 AM - 10:45 AM
  Integrated Discovery I
10:45 AM - 11:00 AM
  Break
11:00 AM - 12:15 PM
  Integrated Discovery II
12:15 PM - 01:30 PM
  Lunch
01:30 PM - 02:45 PM
  Student Presentations
02:45 PM - 03:00 PM
  Break
03:00 PM - 04:30 PM
  Working Groups
Jul 14, 2025
Monday
09:30 AM - 10:45 AM
  Integrated Discovery III
10:45 AM - 11:00 AM
  Break
11:00 AM - 12:15 PM
  Integrated Discover Applications
12:15 PM - 01:30 PM
  Lunch
01:30 PM - 02:45 PM
  Integrated Discovery Tutorial
02:45 PM - 03:00 PM
  Break
03:00 PM - 04:30 PM
  Working Groups
Jul 15, 2025
Tuesday
09:30 AM - 10:45 AM
  Visiting Lecturer
10:45 AM - 11:00 AM
  Break
11:00 AM - 12:15 PM
  Hands-on Interactive Lab Experimentation
12:15 PM - 01:30 PM
  Lunch
01:30 PM - 02:45 PM
  Yorktown Lab Tour
02:45 PM - 03:00 PM
  Break
03:00 PM - 04:30 PM
  Working Groups
Jul 16, 2025
Wednesday
09:30 AM - 10:45 AM
  Beyond Hypotheses Generation I
10:45 AM - 11:00 AM
  Break
11:00 AM - 12:15 PM
  Beyond Hypotheses Generation II
12:15 PM - 01:30 PM
  Yorktown BBQ
01:30 PM - 02:45 PM
  Beyond Hypotheses Generation Tutorial
02:45 PM - 03:00 PM
  Break
03:00 PM - 04:30 PM
  Working Groups
Jul 17, 2025
Thursday
09:30 AM - 10:45 AM
  Beyond Hypotheses Generation III
10:45 AM - 11:00 AM
  Break
11:00 AM - 12:15 PM
  Beyond Hypotheses Generation IV
12:15 PM - 01:30 PM
  Lunch
01:30 PM - 02:45 PM
  Student Presentations
02:45 PM - 03:00 PM
  Break
03:00 PM - 04:30 PM
  MOC Reception
Jul 18, 2025
Friday
09:30 AM - 10:45 AM
  Beyond Hypotheses Generation Applications
10:45 AM - 11:00 AM
  Break
11:00 AM - 12:15 PM
  Student Presentations
12:15 PM - 01:30 PM
  Lunch
01:30 PM - 02:45 PM
  Student Presentations
02:45 PM - 03:00 PM
  Break
03:00 PM - 04:30 PM
  Summary