Applied Mathematics Theses and Dissertations

Theses and Dissertations for the Applied Mathematics department.

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Description:: Hamilton-Jacobi partial differential equations (HJ PDEs) have deep connections to a wide range of scientific disciplines including optimal control, differential games, imaging sciences, and machine …
Year:: 2023
Contributor:: Chen, Paula (creator); Darbon, Jerome (Advisor); Shu, Chi-Wang (Reader); Hewer, Gary (Reader); Brown University. Department of Applied Mathematics (sponsor)
Genre:: theses
Subject:: Machine Learning; Field programmable gate arrays; Regression analysis; optimal control; Hamilton-Jacobi equations; Riccati equation
Collection:: Applied Mathematics; Theses and Dissertations

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Description:: In this thesis, we study optimization algorithms for evaluating solutions to certain high dimension (multi-time) Hamilton-Jacobi Partial Differential equations arising from optimal control. There are …
Year:: 2022
Contributor:: Kim, TaeWoo (creator); Darbon, Jerome (Advisor); Shu, Chi-Wang (Reader); Guzman, Johnny (Reader); Brown University. Department of Applied Mathematics (sponsor)
Genre:: theses
Subject:: Convex Optimization; optimal control; Hamilton-Jacobi equations; primal dual
Collection:: Applied Mathematics; Theses and Dissertations

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Description:: Hamilton-Jacobi PDEs and optimal control problems are widely used in many practical problems in control engineering, physics, financial mathematics, and machine learning. For instance, controlling …
Year:: 2022
Contributor:: Meng, Tingwei (creator); Darbon, Jerome (Advisor); Karniadakis, George (Reader); Shu, Chi-Wang (Reader); Brown University. Department of Applied Mathematics (sponsor)
Genre:: theses
Subject:: Optimizations; Neural networks (Computer science); optimal control; Hamilton-Jacobi equations
Collection:: Applied Mathematics; Theses and Dissertations

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