49,465 research outputs found
Parameter Estimation via Conditional Expectation --- A Bayesian Inversion
When a mathematical or computational model is used to analyse some system, it
is usual that some parameters resp.\ functions or fields in the model are not
known, and hence uncertain. These parametric quantities are then identified by
actual observations of the response of the real system. In a probabilistic
setting, Bayes's theory is the proper mathematical background for this
identification process. The possibility of being able to compute a conditional
expectation turns out to be crucial for this purpose. We show how this
theoretical background can be used in an actual numerical procedure, and
shortly discuss various numerical approximations
Learning deep dynamical models from image pixels
Modeling dynamical systems is important in many disciplines, e.g., control,
robotics, or neurotechnology. Commonly the state of these systems is not
directly observed, but only available through noisy and potentially
high-dimensional observations. In these cases, system identification, i.e.,
finding the measurement mapping and the transition mapping (system dynamics) in
latent space can be challenging. For linear system dynamics and measurement
mappings efficient solutions for system identification are available. However,
in practical applications, the linearity assumptions does not hold, requiring
non-linear system identification techniques. If additionally the observations
are high-dimensional (e.g., images), non-linear system identification is
inherently hard. To address the problem of non-linear system identification
from high-dimensional observations, we combine recent advances in deep learning
and system identification. In particular, we jointly learn a low-dimensional
embedding of the observation by means of deep auto-encoders and a predictive
transition model in this low-dimensional space. We demonstrate that our model
enables learning good predictive models of dynamical systems from pixel
information only.Comment: 10 pages, 11 figure
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