Embargoed until 2021-05-25
- Doctoral Thesis
Parameter estimation for differential equations is an important and challenging problem in many areas of science and engineering. In practical applications one often encounters partially observable systems, where only combinations of variables can be measured or the differential equations contain even unobserved variables. Then both parameters and unobserved states have to be inferred from data. In order to solve these problems for a restricted but highly relevant class of differential equations, we propose a scalable probabilistic inference approach for inferring states and parameters in deterministic and stochastic dynamical systems. Extensive experimental validation across examples from multiple disciplines demonstrates significant improvements in accuracy, runtime and required training samples while being robust to model misspecification. In the absence of observations with given parameters and initial conditions for a deterministic dynamical system i.e. state rather than parameter estimation, the concept of an ODE Oracle is introduced, to infer state dynamics without numerical integration. Without any observations and without explicitly solving the ODEs, competitive results to established ODE solvers are achieved even for a large-scale system. We argue that the proposed inference approach is more expert aware, since placing a prior on the functional form of the state variables is often easier than obtaining good priors for parameters. The contributions hopefully open the door for practical applications, which so far have been too high dimensional to be analyzed with current state-of-the-art methods. Show more
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Organisational unit03659 - Buhmann, Joachim M. / Buhmann, Joachim M.
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