Frozen-State Hierarchical Annealing

Abstract

There is significant interest in the synthesis of discrete-state random fields, particularly those possessing structure over a wide range of scales. However, given a model on some finest, pixellated scale, it is computationally very difficult to synthesize both large and small-scale structures, motivating research into hierarchical methods.This thesis proposes a frozen-state approach to hierarchical modelling, in which simulated annealing is performed on each scale, constrained by the state estimates at the parent scale. The approach leads significant advantages in both modelling flexibility and computational complexity. In particular, a complex structure can be realized with very simple, local, scale-dependent models, and by constraining the domain to be annealed at finer scales to only the uncertain portions of coarser scales, the approach leads to huge improvements in computational complexity. Results are shown for synthesis problems in porous media.v Acknowledgements There are many people without whom I never would have been able to complete this thesis. First and foremost, I would like to thank my supervisor, Prof. Paul Fieguth, for his patience, support, and guidance over the years. Recognition is also due to Simon Alexander, whose Ph.D. research in hierarchical annealing laid the foundation for the research presented here. Prof. Marios Ioannidis provided the porous media images, and was always a source of enthusiasm.

Fracture analysis of rock reconstruction models based on cooling–solidification annealing algorithms

“…Considering the limitation of the traditional hierarchical annealing algorithm, a novel cooling–solidification annealing algorithm is introduced, which greatly improves the computational and modeling ability of the traditional hierarchical annealing algorithm. Unlike the binary state of the traditional hierarchical annealing algorithm, an intermediate gray value is introduced into the reconstruction process as follows 28 : Similar to the traditional hierarchical annealing algorithm, an interpolation operator ρ is also used in the cooling–solidification annealing algorithm. Nevertheless, the annealing process of the cooling–solidification annealing algorithm is different from the annealing process of the traditional hierarchical annealing algorithm.…”

“…In the reconstruction process, the black (whose value is 1) and white (whose value is 0) elements on the coarser scale remain unchanged when the reconstruction moves on to the next finer scale. The elements and their subset must satisfy 28 : Then, the energy function can be defined as 29 The function f 1 s ( u n ) is the control function of the reference model, which is built by the CT image data for rocks, and f s ( u n ) and f ′ s ( u n ) are the actual values of the control function measured before and after the iteration step t , respectively.…”