Transcription of On Neural Di erential Equations
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On Neural Di erential Equations
On Neural Differential EquationsPatrick KidgerMathematical InstituteUniversity of OxfordA thesis submitted for the degree ofDoctor of PhilosophyTrinity 2021 [ ] 4 Feb 2022 AbstractThe conjoining of dynamical systems and deep learning has become atopic of great interest. In particular, Neural differential Equations (NDEs)demonstrate that Neural networks and differential equation are two sidesof the same coin. Traditional parameterised differential Equations are aspecial case. Many popular Neural network architectures, such as residualnetworks and recurrent networks, are are suitable for tackling generative problems, dynamical systems,and time series (particularly in physics, finance, .. ) and are thus ofinterest to both modern machine learning and traditional mathematicalmodelling. NDEs offer high-capacity function approximation, strong pri-ors on model space, the ability to handle irregular data, memory efficiency,and a wealth of available theory on both doctoral thesis provides an in-depth survey of the include: neuralordinarydifferential Equations ( for hybridneural/mechanistic modelling of physical systems); neuralcontrolleddif-ferential Equations ( for learning functions of irregular time series);and neuralstochasticdifferential equatio
modelling. NDEs o er high-capacity function approximation, strong pri-ors on model space, the ability to handle irregular data, memory e ciency, and a wealth of available theory on both sides. This doctoral thesis provides an in-depth survey of the eld. Topics include: neural ordinary di erential equations (e.g. for hybrid
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