Differentiable Boundary Value Problem Solver

Abstract

This thesis proposes a differentiable architecture for solving boundary value problems. That framework is then verified on several problems, including problems related to autonomous vehicle control. It is then shown that the proposed architecture can have greatly reduced convergence times by two methods of priming the solver. Then a method for optimizing among solutions to a boundary value problem for a loss function is proposed. This optimization method is then used to optimize the solution to an autonomous vehicle boundary value problem to maximize passenger comfort. The proposed optimization method is also shown to benefit from the priming effect.