2,006 research outputs found
Machine Learning for Fluid Mechanics
The field of fluid mechanics is rapidly advancing, driven by unprecedented
volumes of data from field measurements, experiments and large-scale
simulations at multiple spatiotemporal scales. Machine learning offers a wealth
of techniques to extract information from data that could be translated into
knowledge about the underlying fluid mechanics. Moreover, machine learning
algorithms can augment domain knowledge and automate tasks related to flow
control and optimization. This article presents an overview of past history,
current developments, and emerging opportunities of machine learning for fluid
mechanics. It outlines fundamental machine learning methodologies and discusses
their uses for understanding, modeling, optimizing, and controlling fluid
flows. The strengths and limitations of these methods are addressed from the
perspective of scientific inquiry that considers data as an inherent part of
modeling, experimentation, and simulation. Machine learning provides a powerful
information processing framework that can enrich, and possibly even transform,
current lines of fluid mechanics research and industrial applications.Comment: To appear in the Annual Reviews of Fluid Mechanics, 202
Data-driven modelling of biological multi-scale processes
Biological processes involve a variety of spatial and temporal scales. A
holistic understanding of many biological processes therefore requires
multi-scale models which capture the relevant properties on all these scales.
In this manuscript we review mathematical modelling approaches used to describe
the individual spatial scales and how they are integrated into holistic models.
We discuss the relation between spatial and temporal scales and the implication
of that on multi-scale modelling. Based upon this overview over
state-of-the-art modelling approaches, we formulate key challenges in
mathematical and computational modelling of biological multi-scale and
multi-physics processes. In particular, we considered the availability of
analysis tools for multi-scale models and model-based multi-scale data
integration. We provide a compact review of methods for model-based data
integration and model-based hypothesis testing. Furthermore, novel approaches
and recent trends are discussed, including computation time reduction using
reduced order and surrogate models, which contribute to the solution of
inference problems. We conclude the manuscript by providing a few ideas for the
development of tailored multi-scale inference methods.Comment: This manuscript will appear in the Journal of Coupled Systems and
Multiscale Dynamics (American Scientific Publishers
Multilevel Minimization for Deep Residual Networks
We present a new multilevel minimization framework for the training of deep
residual networks (ResNets), which has the potential to significantly reduce
training time and effort. Our framework is based on the dynamical system's
viewpoint, which formulates a ResNet as the discretization of an initial value
problem. The training process is then formulated as a time-dependent optimal
control problem, which we discretize using different time-discretization
parameters, eventually generating multilevel-hierarchy of auxiliary networks
with different resolutions. The training of the original ResNet is then
enhanced by training the auxiliary networks with reduced resolutions. By
design, our framework is conveniently independent of the choice of the training
strategy chosen on each level of the multilevel hierarchy. By means of
numerical examples, we analyze the convergence behavior of the proposed method
and demonstrate its robustness. For our examples we employ a multilevel
gradient-based methods. Comparisons with standard single level methods show a
speedup of more than factor three while achieving the same validation accuracy
Geometric Numerical Integration (hybrid meeting)
The topics of the workshop
included interactions between geometric numerical integration and numerical partial differential equations;
geometric aspects of stochastic differential equations;
interaction with optimisation and machine learning;
new applications of geometric integration in physics;
problems of discrete geometry, integrability, and algebraic aspects
Using Machine Learning for Model Physics: an Overview
In the overview, a generic mathematical object (mapping) is introduced, and
its relation to model physics parameterization is explained. Machine learning
(ML) tools that can be used to emulate and/or approximate mappings are
introduced. Applications of ML to emulate existing parameterizations, to
develop new parameterizations, to ensure physical constraints, and control the
accuracy of developed applications are described. Some ML approaches that allow
developers to go beyond the standard parameterization paradigm are discussed.Comment: 50 pages, 3 figures, 1 tabl
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