Machine Learning and Dynamical Systems

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Project Description

The student will work on machine learning techniques applied to the study of dynamical systems. Specifically, the student will use different Neural Network architectures to approximate the equations governing a given system's evolution. This evolution may be intrinsically random, or we may add randomness to contemplate the possibility of approximating a large dimensional system by a low dimensional one. He will also test this methodology in several applications and report his results to get familiar with the problem and its input data.
Program - Applied Mathematics and Computer Science
Division - Computer, Electrical and Mathematical Sciences and Engineering
Field of Study - Computational and Applied Mathematics

About the
Researcher

Raul F. Tempone

Professor, Applied Mathematics and Computational Science

Raul F. Tempone
Raul Tempone's research interests are in the mathematical foundation of computational science and engineering. More specifically, he has focused on a posteriori error approximation and related adaptive algorithms for numerical solutions of various differential equations, including ordinary differential equations, partial differential equations, and stochastic differential equations.

He is also interested in the development and analysis of efficient numerical methods for optimal control, uncertainty quantification and bayesian model calibration, validation and optimal experimental design. The areas of application he considers include, among others, engineering, chemistry, biology, physics as well as social science and computational finance.

Desired Project Deliverables

As the main project deliverable, we expect a scientific report describing the methodology developed in the internship and its numerical use in various applications. The working environment the student will use should include a GIT repository for all project-related materials to facilitate proper verification and feedback processes. These materials include, among others, the codes and the saved input-outputs corresponding to all tested cases

RECOMMENDED STUDENT ACADEMIC & RESEARCH BACKGROUND

Education in applied & computational mathematics
Education in applied & computational mathematics
Education and possibly experience in machine learning and/or stochastic numerics
Education and possibly experience in machine learning and/or stochastic numerics
Experience with code development and software engineering skills, such as C++ and/or python
Experience with code development and software engineering skills, such as C++ and/or python