Prediction and Data Assimilation for Nonlocal Diffusions

Organizer:	Michal Branicki	(University of Edinburgh)
	m.branicki (at) ed.ac.uk

Organizing Committee:	Michal Branicki	(University of Edinburgh)
	Heiko Gimperlein	(Heriot-Watt University)
	Kody Law	(University of Manchester)

Speakers:	Ali Aydogdu	(NERSC, Norway)
	Wietse Boon	(University of Stuttgart)
	Alberto Carrassi	(NERSC, Norway)
	Ahmed El Sheikh	(Heriot-Watt University)
	Heiko Gimperlein	(Heriot-Watt University)
	Daniel Goldberg	(University of Edinburgh)
	Denny Kirwan	(University of Delaware)
	Kody Law	(University of Manchester)
	James Maddison	(University of Edinburgh)
	Erdogan Madenci	(University of Arizona)
	Erkan Oterkus	(University of Strathclyde)
	Roland Potthast	(Deutscher Wetter Dienst and University of Reading)
	Abner Salgado	(University of Tennessee, Knoxville)
	Christian Sampson	(SAMSI, University of North Carolina)
	Jana de Wiljes	(University of Potsdam)
	Sergiy Zhuk	(IBM Research)

Flyer	Abstracts	Logistics

The aim of the workshop is to gather researchers interested in the recent developments in variational analysis and data assimilation for nonlocal diffusion problems given by linear integro-differential equations on bounded domains. The nonlocal operators associated with such problems arise in many applications ranging from continuum mechanics to graph theory; a topical application area is crack nucleation and propagation which is increasingly important for understanding and modelling the large-scale dynamics of sea ice in the Arctic. The workshop will focus on a set of intertwined issues ranging from the numerical modelling of integro-differential systems under uncertainty, to well-posedness of local and nonlocal operators with random parameters, to (Lagrangian-type) data assimilation on the nodes time-dependent random graphs. In the presence of model uncertainties a number of important problems need to be addressed: (i) Appropriate (stochastic) parameterisation the underlying integral operators.
(ii) Choice of the necessary data-adapted discretisation for approximating time-dependent models for crack propagation and their capture.
(iii) Aiding the procedures in (i)-(ii) via Bayesian data assimilation and appropriate Markov Chain Monte Carlo (MCMC), and Multi Level Sequential Monte Carlo sampling (MLSMC).
(iv) Derivation of criteria for stability, accuracy and quantification of uncertainty due to the parameterisation and/or the necessary discretisation of nonlocal problems. It is expected that this workshop will serve as a nucleus for developing new research directions and collaborations in the area of modelling and prediction of non-local dynamical problems which fall into the large class of anomalous diffusion problems driven by dynamic streams of data.
Information about travel to Edinburgh can be found here.

Monday	(room 2.12, Appleton Tower)
9.15	Registration and coffee
9.30	opening remarks
9.40	Ali Aydogdu	Some aspects of ensemble prediction and data
	and Alberto Carrassi	assimilation using a Lagrangian model of sea-ice
10.20	Christian Sampson	Toward a metric for evaluating sea ice fracture forecast
11.00	coffee break
11.30	Daniel Goldberg	Ice shelf rifting: Constitutive modelling, satellite data assimilation, and connections to fracture mechanics
12.00	Ahmed El Sheikh	Generation of stochastic fields using generative adversarial networks with applications to geological modelling
12.30	Denny Kirwan	Prediction and Data Assimilation: Ocean vs. Arctic Sea Ice
13.00	lunch break
14.20	Abner Salgado	Optimization with respect to order in a fractional diffusion model: analysis and approximation
15.00	Heiko Gimperlein	Adaptive finite element methods for nonlocal problems
15.40	coffee break
16.10	Erdogan Madenci	Peridynamics for paradigm shift in computational methods
16.50	James Maddison	PDE constrained Hessian action information for time dependent finite element models
19.45	conference dinner	Howies (10-14 Victoria St, Edinburgh EH1 2HG)

Tuesday	(room 2.12, Appleton Tower)
9.40	Roland Potthast	Data Assimilation and Kernel Reconstruction for Nonlocal Field Dynamics
10.20	Jana de Wiljes	Linear ensemble transform filters and smoothers
11.00	coffee break
11.30	Kody Law	Strategies for multilevel Monte Carlo
12.10	Sergiy Zhuk	Geometry of data assimilation for non-linear differential equations
12.50	lunch break
13.50	Wietse Boon	Flow and Mechanics in Fractured Media as Mixed-Dimensional PDEs
14.30	Erkan Oterkus	Peridynamics for Modelling Ice Fracture
15.10	discussions

We are grateful for the support from the Office of Naval Research and ICMS.