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CHallenges in Preservation of Structure

Deliverables

Software 2

Publication of open source software

Workshops with industry

Workshop 7 where early stage researchers meet industry (task 8.3). Workshop 8 with SMEs (task 8.4).

Workshop 4

Workshop organized by La Trobe.

Talks 3

Presentations at the conference FoCM, 2017

Workshop 6

Workshop at Massey.

Talks at FoCM

Presentations at the FoCM meeting, 2017. Delivery month is tentative because the date of the FoCM conference is not known at the moment.

Software 3

Open source software package implementing the algorithms developed in tasks 7.1-7.4 and incorporating standard test cases.

SDEs

School on SDEs (see task 8.9).

Talks

Reports on tasks 3.1-3.2 at the SciCADE meeting, D 3.1-3.2, Bath, UK, 2017.

Workshop 5 and MaGIC

Workshop 5: The Abel symposium, August 16-19, 2016, Rosendal, Norway WP5 MaGIC Workshop WP8

Talks 2

Presentations at the SciCADE conference, Bath, UK, 2017.

Workshops organized by UCAM

Workshops at the Newton institute (Cambridge): -Workshop 1: Variational methods new optimization techniques and new fast numerical algorithms, (tasks 2.5, 2.6). -Workshop 2: Generative models, parameter learning and sparsity, (task 2.6). -Workshop 3: Flows, Mappings and Shapes, (task 2.7). Final CHiPS Workshop (event 12 table 3).

Software 1

Implementation of integrators in D 3.3-3.4 in open-spurce software.

School lecture

Science festival Gothenburg, school lecture.

Videos

Production of short instruction videos explaining the basics of Discrete Gradients, and corresponding methods. (WP 4) Production of short instructive videos giving the elementary background to elementary Geometric Mechanics targeted at new MSc and PhD students. (WP 3)

Report on the polarization

Report on the polarization technique generalizing Kahan’s method to higher degree polynomial vector fields.

Model Reduction/ Port-Hamiltonian

Report on structure-preserving model reduction and on port-Hamiltonian systems.

Reports Bayesian

Reports on geometric integrators for Bayesian inference (tasks 7.1-7.4)

Report on modified invariant measure

Report on modified invariant measure for new classes of completely integrable quadratic vector fields.

Symplectic

Reports on tasks 3.3-3.4

Case study/Convergence/Continuous model

Case study of the use of discrete gradient methods in image processing, report. Convergence of discrete gradients, report (task 2.2). Approximation of the continuous model, (task 2.4).

Reports HOsC

Publications in relevant journals on Structure preservation in partial differential equations with highly oscillatory solutions (delivered also on month 12)

Reports on algebraic combinatorics

Publications in algebraic combinatorics with applications

Publications

Symmetric and arbitrarily high-order Birkhoff–Hermite time integrators and their long-time behaviour for solving nonlinear Klein–Gordon equations

Author(s): Changying Liu, Arieh Iserles, Xinyuan Wu
Published in: Journal of Computational Physics, Issue 356, 2018, Page(s) 1-30, ISSN 0021-9991
DOI: 10.1016/j.jcp.2017.10.057

Discretization of polynomial vector fields by polarization

Author(s): Elena Celledoni, Robert I. McLachlan, David I. McLaren, Brynjulf Owren, G. R. W. Quispel
Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, Issue 471/2184, 2015, Page(s) 20150390, ISSN 1364-5021
DOI: 10.1098/rspa.2015.0390

Geometry of Discrete-Time Spin Systems

Author(s): Robert I. McLachlan, Klas Modin, Olivier Verdier
Published in: Journal of Nonlinear Science, Issue 26/5, 2016, Page(s) 1507-1523, ISSN 0938-8974
DOI: 10.1007/s00332-016-9311-z

Geometry of matrix decompositions seen through optimal transport and information geometry

Author(s): Klas Modin
Published in: Journal of Geometric Mechanics, Issue 9/3, 2017, Page(s) 335-390, ISSN 1941-4889
DOI: 10.3934/jgm.2017014

Geometric and integrability properties of Kahan's method

Author(s): Celledoni, Elena; McLaren, David; Owren, Brynjulf; Quispel, Reinout
Published in: Journal of Physics A, Issue 1, 2019, ISSN 1751-8113

Graph clustering, variational image segmentation methods and Hough transform scale detection for object measurement in images

Author(s): Calatroni, Luca; van Gennip, Yves; Schönlieb, Carola-Bibiane; Rowland, Hannah; Flenner, Arjuna
Published in: Journal of Mathematical Imaging and Vision, Issue 16, 2017, ISSN 0924-9907
DOI: 10.17863/CAM.31490

Bilevel Parameter Learning for Higher-Order Total Variation Regularisation Models

Author(s): De los Reyes, JC; Schonlieb, C-B; Valkonen, T
Published in: JOURNAL OF MATHEMATICAL IMAGING AND VISION, Issue 11, 2018, ISSN 0924-9907
DOI: 10.13039/501100000735

Two classes of quadratic vector fields for which the Kahan discretization is integrable

Author(s): Celledoni, Elena; McLachlan, Robert I.; McLaren, David I.; Owren, Brynjulf; Quispel, G. R. W.
Published in: Journal of Physics A, Issue 7, 2019, ISSN 1751-8113

Three classes of quadratic vector fields for which the Kahan discretization is the root of a generalised Manin transformation

Author(s): van der Kamp, Peter H.; Celledoni, Elena; McLachlan, Robert I.; McLaren, David I.; Owren, Brynjulf; Quispel, G. R. W.
Published in: Journal of Physics A, Issue 1, 2019, ISSN 1751-8113

The Joy and Pain of Skew Symmetry

Author(s): Arieh Iserles
Published in: Foundations of Computational Mathematics, Issue 16/6, 2016, Page(s) 1607-1630, ISSN 1615-3375
DOI: 10.1007/s10208-016-9321-0

Efficient methods for linear Schrödinger equation in the semiclassical regime with time-dependent potential

Author(s): Philipp Bader, Arieh Iserles, Karolina Kropielnicka, Pranav Singh
Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, Issue 472/2193, 2016, Page(s) 20150733, ISSN 1364-5021
DOI: 10.1098/rspa.2015.0733

Shape analysis on Lie groups with applications in computer animation

Author(s): Elena Celledoni, Markus Eslitzbichler, Alexander Schmeding
Published in: Journal of Geometric Mechanics, Issue 8/3, 2016, Page(s) 273-304, ISSN 1941-4889
DOI: 10.3934/jgm.2016008

A classification of volume preserving generating forms in $\mathbb{R}^3$

Author(s): Olivier Verdier, Huiyan Xue, Antonella Zanna
Published in: Discrete and Continuous Dynamical Systems, Issue 36/4, 2016, Page(s) 2285-2303, ISSN 1078-0947
DOI: 10.3934/dcds.2016.36.2285

High Order Semi-Lagrangian Methods for the Incompressible Navier–Stokes Equations

Author(s): Elena Celledoni, Bawfeh Kingsley Kometa, Olivier Verdier
Published in: Journal of Scientific Computing, Issue 66/1, 2016, Page(s) 91-115, ISSN 0885-7474
DOI: 10.1007/s10915-015-0015-6

The averaged Lagrangian method

Author(s): Elena Celledoni, Eirik Hoel Høiseth
Published in: Journal of Computational and Applied Mathematics, Issue 316, 2017, Page(s) 161-174, ISSN 0377-0427
DOI: 10.1016/j.cam.2016.09.047

Geometric integration of non-autonomous linear Hamiltonian problems

Author(s): Håkon Marthinsen, Brynjulf Owren
Published in: Advances in Computational Mathematics, Issue 42/2, 2016, Page(s) 313-332, ISSN 1019-7168
DOI: 10.1007/s10444-015-9425-0

Graph Clustering, Variational Image Segmentation Methods and Hough Transform Scale Detection for Object Measurement in Images

Author(s): Luca Calatroni, Yves van Gennip, Carola-Bibiane Schönlieb, Hannah M. Rowland, Arjuna Flenner
Published in: Journal of Mathematical Imaging and Vision, 2016, ISSN 0924-9907
DOI: 10.1007/s10851-016-0678-0

Bilevel Parameter Learning for Higher-Order Total Variation Regularisation Models

Author(s): J. C. De los Reyes, C.-B. Schönlieb, T. Valkonen
Published in: Journal of Mathematical Imaging and Vision, 2016, ISSN 0924-9907
DOI: 10.1007/s10851-016-0662-8

The structure of optimal parameters for image restoration problems

Author(s): J.C. De Los Reyes, C.-B. Schönlieb, T. Valkonen
Published in: Journal of Mathematical Analysis and Applications, Issue 434/1, 2016, Page(s) 464-500, ISSN 0022-247X
DOI: 10.1016/j.jmaa.2015.09.023

Individual Tree Species Classification From Airborne Multisensor Imagery Using Robust PCA

Author(s): Juheon Lee, Xiaohao Cai, Jan Lellmann, Michele Dalponte, Yadvinder Malhi, Nathalie Butt, Mike Morecroft, Carola-Bibiane Schonlieb, David A. Coomes
Published in: IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, Issue 9/6, 2016, Page(s) 2554-2567, ISSN 1939-1404
DOI: 10.1109/JSTARS.2016.2569408

Infimal Convolution Regularisation Functionals of BV and $$\varvec{\mathrm {L}}^{\varvec{p}}$$ L p Spaces

Author(s): Martin Burger, Konstantinos Papafitsoros, Evangelos Papoutsellis, Carola-Bibiane Schönlieb
Published in: Journal of Mathematical Imaging and Vision, Issue 55/3, 2016, Page(s) 343-369, ISSN 0924-9907
DOI: 10.1007/s10851-015-0624-6

Numerical Solution of Parabolic Problems Based on a Weak Space-Time Formulation

Author(s): Stig Larsson, Matteo Molteni
Published in: Computational Methods in Applied Mathematics, Issue 17/1, 2017, ISSN 1609-4840
DOI: 10.1515/cmam-2016-0027

Full Discretization of Semilinear Stochastic Wave Equations Driven by Multiplicative Noise

Author(s): Rikard Anton, David Cohen, Stig Larsson, Xiaojie Wang
Published in: SIAM Journal on Numerical Analysis, Issue 54/2, 2016, Page(s) 1093-1119, ISSN 0036-1429
DOI: 10.1137/15M101049X

Weak error analysis for semilinear stochastic Volterra equations with additive noise

Author(s): Adam Andersson, Mihály Kovács, Stig Larsson
Published in: Journal of Mathematical Analysis and Applications, Issue 437/2, 2016, Page(s) 1283-1304, ISSN 0022-247X
DOI: 10.1016/j.jmaa.2015.09.016

A Weak Space-Time Formulation for the Linear Stochastic Heat Equation

Author(s): Stig Larsson, Matteo Molteni
Published in: International Journal of Applied and Computational Mathematics, 2016, ISSN 2349-5103
DOI: 10.1007/s40819-016-0134-2

Weak convergence for a spatial approximation of the nonlinear stochastic heat equation

Author(s): Adam Andersson, Stig Larsson
Published in: Mathematics of Computation, Issue 85/299, 2016, Page(s) 1335-1358, ISSN 0025-5718
DOI: 10.1090/mcom/3016

Duality in refined Sobolev–Malliavin spaces and weak approximation of SPDE

Author(s): Adam Andersson, Raphael Kruse, Stig Larsson
Published in: Stochastics and Partial Differential Equations Analysis and Computations, Issue 4/1, 2016, Page(s) 113-149, ISSN 2194-0401
DOI: 10.1007/s40072-015-0065-7

Gradient flows: from theory to application

Author(s): Bertram Düring, Carola-Bibiane Schönlieb, Marie-Therese Wolfram
Published in: ESAIM: Proceedings and Surveys, Issue 54, 2016, Page(s) I-VIII, ISSN 2267-3059
DOI: 10.1051/proc/201654000

Discrete gradient methods for solving variational image regularisation models

Author(s): V Grimm, Robert I McLachlan, David I McLaren, G R W Quispel, C-B Schönlieb
Published in: Journal of Physics A: Mathematical and Theoretical, Issue 50/29, 2017, Page(s) 295201, ISSN 1751-8113
DOI: 10.1088/1751-8121/aa747c

8. Bilevel approaches for learning of variational imaging models

Author(s): Luca Calatroni, Chung Cao, Juan Carlos De los Reyes, Carola-Bibiane Schönlieb, Tuomo Valkonen
Published in: Variational Methods - In Imaging and Geometric Control, 2016
DOI: 10.1515/9783110430394-008

Learning Filter Functions in Regularisers by Minimising Quotients

Author(s): Martin Benning, Guy Gilboa, Joana Sarah Grah, Carola-Bibiane Schönlieb
Published in: cale Space and Variational Methods in Computer Vision: 6th International Conference, SSVM 2017, Kolding, Denmark, June 4-8, 2017, Proceedings, 2017, Page(s) 511-523
DOI: 10.1007/978-3-319-58771-4_41

Nonlinear Spectral Image Fusion

Author(s): Martin Benning, Michael Möller, Raz Z. Nossek, Martin Burger, Daniel Cremers, Guy Gilboa, Carola-Bibiane Schönlieb
Published in: Scale Space and Variational Methods in Computer Vision: 6th International Conference, SSVM 2017, Kolding, Denmark, June 4-8, 2017, Proceedings, 2017, Page(s) 41-53
DOI: 10.1007/978-3-319-58771-4_4