Deep learning as optimal control problems
Martin Benning, Elena Celledoni, Matthias J. Ehrhardt, Brynjulf Owren, Carola‐Bibiane Schönlieb
Abstract
We briefly review recent work where deep learning neural networks have been interpreted as discretisations of an optimal control problem subject to an ordinary differential equation constraint. We report here new preliminary experiments with implicit symplectic Runge-Kutta methods. In this paper, we discuss ongoing and future research in this area.
Topics & Concepts
Constraint (computer-aided design)Computer scienceOrdinary differential equationSymplectic geometryOptimal controlDeep learningRunge–Kutta methodsArtificial intelligenceControl (management)Artificial neural networkDeep neural networksSubject (documents)Work (physics)Differential equationMathematical optimizationMachine learningMathematicsEngineeringMathematical analysisLibrary scienceMechanical engineeringGeometryModel Reduction and Neural NetworksAdvanced Numerical Methods in Computational MathematicsAdvanced Numerical Analysis Techniques