PREDICTION AND DATA ASSIMILATION FOR NON-LOCAL DIFFUSIONS. FROM CRACK PROPAGATION AND ANOMALOUS DIFFUSION TO RANDOM GRAPHS AND THE ARTIC SEA ICE
Abstract
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 integral 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 largescale dynamics of sea ice in the Arctic. The workshop will focus on a set of intertwined issues ranging from the numerical modelling of integro-differen"tial systems under uncertainty, to well-posedness of nonlocal operators with random parameters, to (Lagrangian-type) data assimilati"on 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 nonlocal integral operators.(ii) Choice of the necessary data-a"dapted discretisation for approximating nonlocal, time-dependent models and crack capture.(iii) Aiding the procedures in (i)-(ii) v""ia Bayesian data assimilation and appropriate Markov Chain Monte Carlo (MCMC), and Multi Level Sequential Monte Carlo sampling (MLSM""C).(iv) Derivation of criteria for well-posedness, stability, accuracy and quantification of uncertainty due to theparameterisatio"n 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.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Sep 01, 2017
- Source ID
- N000141712765
Entities
People
- Michal Branicki
Organizations
- Office of Naval Research
- United States Navy
- University of Edinburgh