7,903 research outputs found
On-the-fly adaptivity for nonlinear twoscale simulations using artificial neural networks and reduced order modeling
A multi-fidelity surrogate model for highly nonlinear multiscale problems is
proposed. It is based on the introduction of two different surrogate models and
an adaptive on-the-fly switching. The two concurrent surrogates are built
incrementally starting from a moderate set of evaluations of the full order
model. Therefore, a reduced order model (ROM) is generated. Using a hybrid
ROM-preconditioned FE solver, additional effective stress-strain data is
simulated while the number of samples is kept to a moderate level by using a
dedicated and physics-guided sampling technique. Machine learning (ML) is
subsequently used to build the second surrogate by means of artificial neural
networks (ANN). Different ANN architectures are explored and the features used
as inputs of the ANN are fine tuned in order to improve the overall quality of
the ML model. Additional ANN surrogates for the stress errors are generated.
Therefore, conservative design guidelines for error surrogates are presented by
adapting the loss functions of the ANN training in pure regression or pure
classification settings. The error surrogates can be used as quality indicators
in order to adaptively select the appropriate -- i.e. efficient yet accurate --
surrogate. Two strategies for the on-the-fly switching are investigated and a
practicable and robust algorithm is proposed that eliminates relevant technical
difficulties attributed to model switching. The provided algorithms and ANN
design guidelines can easily be adopted for different problem settings and,
thereby, they enable generalization of the used machine learning techniques for
a wide range of applications. The resulting hybrid surrogate is employed in
challenging multilevel FE simulations for a three-phase composite with
pseudo-plastic micro-constituents. Numerical examples highlight the performance
of the proposed approach
Variational Downscaling, Fusion and Assimilation of Hydrometeorological States via Regularized Estimation
Improved estimation of hydrometeorological states from down-sampled
observations and background model forecasts in a noisy environment, has been a
subject of growing research in the past decades. Here, we introduce a unified
framework that ties together the problems of downscaling, data fusion and data
assimilation as ill-posed inverse problems. This framework seeks solutions
beyond the classic least squares estimation paradigms by imposing proper
regularization, which are constraints consistent with the degree of smoothness
and probabilistic structure of the underlying state. We review relevant
regularization methods in derivative space and extend classic formulations of
the aforementioned problems with particular emphasis on hydrologic and
atmospheric applications. Informed by the statistical characteristics of the
state variable of interest, the central results of the paper suggest that
proper regularization can lead to a more accurate and stable recovery of the
true state and hence more skillful forecasts. In particular, using the Tikhonov
and Huber regularization in the derivative space, the promise of the proposed
framework is demonstrated in static downscaling and fusion of synthetic
multi-sensor precipitation data, while a data assimilation numerical experiment
is presented using the heat equation in a variational setting
Diffeomorphic density registration
In this book chapter we study the Riemannian Geometry of the density
registration problem: Given two densities (not necessarily probability
densities) defined on a smooth finite dimensional manifold find a
diffeomorphism which transforms one to the other. This problem is motivated by
the medical imaging application of tracking organ motion due to respiration in
Thoracic CT imaging where the fundamental physical property of conservation of
mass naturally leads to modeling CT attenuation as a density. We will study the
intimate link between the Riemannian metrics on the space of diffeomorphisms
and those on the space of densities. We finally develop novel computationally
efficient algorithms and demonstrate there applicability for registering RCCT
thoracic imaging.Comment: 23 pages, 6 Figures, Chapter for a Book on Medical Image Analysi
Numerical Fitting-based Likelihood Calculation to Speed up the Particle Filter
The likelihood calculation of a vast number of particles is the computational
bottleneck for the particle filter in applications where the observation
information is rich. For fast computing the likelihood of particles, a
numerical fitting approach is proposed to construct the Likelihood Probability
Density Function (Li-PDF) by using a comparably small number of so-called
fulcrums. The likelihood of particles is thereby analytically inferred,
explicitly or implicitly, based on the Li-PDF instead of directly computed by
utilizing the observation, which can significantly reduce the computation and
enables real time filtering. The proposed approach guarantees the estimation
quality when an appropriate fitting function and properly distributed fulcrums
are used. The details for construction of the fitting function and fulcrums are
addressed respectively in detail. In particular, to deal with multivariate
fitting, the nonparametric kernel density estimator is presented which is
flexible and convenient for implicit Li-PDF implementation. Simulation
comparison with a variety of existing approaches on a benchmark 1-dimensional
model and multi-dimensional robot localization and visual tracking demonstrate
the validity of our approach.Comment: 42 pages, 17 figures, 4 tables and 1 appendix. This paper is a
draft/preprint of one paper submitted to the IEEE Transaction
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