Deep neural network for system of ordinary differential equations: Vectorized algorithm and simulation
Tamirat Temesgen Dufera
Abstract
This paper is aimed at applying deep artificial neural networks for solving system of ordinary differential equations. We developed a vectorized algorithm and implemented using python code. We conducted different experiments for selecting better neural architecture. For the learning of the neural network, we utilized the adaptive moment minimization method. Finally, we compare the method with one of the traditional numerical methods-Runge–Kutta order four. We have shown that, the artificial neural network could provide better accuracy for smaller numbers of grid points.
Topics & Concepts
Artificial neural networkOrdinary differential equationComputer scienceAlgorithmRunge–Kutta methodsPython (programming language)Deep learningGridCode (set theory)Automatic differentiationMinificationDifferential equationArtificial intelligenceMathematicsComputationGeometryMathematical analysisSet (abstract data type)Programming languageOperating systemModel Reduction and Neural NetworksNumerical methods for differential equationsNumerical Methods and Algorithms