Legato group

IWR School 2019: “A Crash Course in Machine Learning with Applications in Natural- and Life Sciences (ML4Nature)”

Arnaud Mazier Legato group
IWR School 2019: “A Crash Course in Machine Learning with Applications in Natural- and Life Sciences (ML4Nature)”

We would like to bring to your attention our upcoming IWR School which will focus on machine
learning with applications from Natural Sciences and Life Sciences. The school will take place
from September 23 to 27, 2019, in Heidelberg, and addresses young researchers (PhD,
PostDoc, Master) from Natural and Life Sciences who want to learn more about machine
learning.
A background in Machine Learning is not required. Besides introducing the basic concepts we
teach selected topics in more depth, such as deep learning, metric learning, transfer learning,
Bayesian inverse problems, and causality. Experts from machine learning, Natural Science and
Life Science explain how these machine learning approaches are utilized to solve problems in
their respective fields of research.

IWR

Further information on the IWR School 2019 are available at:
www.iwr.uni-heidelberg.de/events/iwr-school-2019

Michael Ortiz “Model-Free Data-Driven Computing”

legato_admin Legato group

It was a pleasure to welcome Michael Ortiz from the California Institute of Technology to give a seminar on the topic of “Model-Free Data-Driven Computing” at the University of Luxembourg. You can watch the entire seminar below.

Abstract:

We develop a new computing paradigm, which we refer to as Data-Driven Computing, according to which calculations are carried out directly from experimental material data and pertinent kinematic constraints and conservation laws, such as compatibility and equilibrium, thus bypassing the empirical material modeling step of conventional computing altogether. Data-driven solvers seek to assign to each material point the state from a prespecified data set that is closest to satisfying the conservation laws. Equivalently, data-driven solvers aim to find the state satisfying the conservation laws that is closest to the data set. The resulting data-driven problem thus consists of the minimization of a distance function to the data set in phase space subject to constraints introduced by the conservation laws. We demonstrate the data-driven paradigm and investigate the performance of data-driven solvers by means of several examples of application, including statics and dynamics of nonlinear three-dimensional trusses, and linear and nonlinear elasticity. In these tests, the data-driven solvers exhibit good convergence properties both with respect to the number of data points and with regard to local data assignment, including noisy material data sets containing outliers. The variational structure of the data-driven problem also renders it amenable to analysis. We find that the classical solutions are recovered in the case of linear elasticity. We identify conditions for convergence of Data-Driven solutions corresponding to sequences of approximating material data sets. Specialization to constant material data set sequences in turn establishes an appropriate notion of relaxation. We find that relaxation within the Data-Driven framework is fundamentally different from the classical relaxation of energy functions. For instance, we show that in the Data-Driven framework the relaxation of a bistable material leads to effective material data sets that are not graphs. I will finish my presentation with highlights on work in progress, including closed-loop Data-Driven analysis and experiments, Data-Driven molecular dynamics, Data-Driven inelasticity and publicly-editable material data repositories and data management from a Data-Driven perspective.

Acoustic/Electromagnetic scattering

Acoustic/Electromagnetic scattering
WMtot
Electromagnetic field generated inside human brain

The purpose of this project is to reduce the errors associated with numerical solution of wave propagation problems and their computational costs. In high-frequency regimes, the solution of conventional FEM sufferers from pollution error which is due to dispersion and can be visualized as a phase shift of the numerical solution. To maintain a desired level of pollution error in conventional FEM, it is necessary to increase discretization density faster than the wave number which rapidly increase the computational cost. On the other hand, the geometrical accuracy of the scattering surfaces play an important role in accuracy of the solution. The possibility of representing man-made objects exactly in IGA even with very coarse meshes and the convenience of its refinement makes it a desirable platform to perform scattering analysis. The convergence graphs obtained for scattering problems performed in IGA platform approves the anticipated properties and makes it possible to increase the solution accuracy even for very high-frequency analysis. [http://mechanical907.rssing.com/browser.php?indx=25030677&last=1&item=1], [http://hdl.handle.net/10993/28982].

Sphere_real
Exterior acoustic scattering
p10_IGA
Exterior acoustic scattering problem – The evolution of L2 error with discretization density in IGA. High-order IGA yields low error with very coarse meshes.