Supermesh Analysis Solved Problems Pdf Download
Stephanie Dejoode
Let me know if I have clarified what is meant by mesh and supermesh analysis, and I will return to this in a short while when I have time to show what I mean with a solution to the problem using mesh analysis.
As we seen in the example 2, it contains current source in one of its branches. And before the application of the mesh analysis to that circuit, we assumed the unknown voltage across the current source and then mesh analysis is applied. This is a quite difficult approach and this can be overcome by applying supermesh technique.
(Joint work with Coralia Cartis) The problem of finding the most extreme value of a function, also known as global optimization, is a challenging task. The difficulty is associated with the exponential increase in the computational time for a linear increase in the dimension. This is known as the ``curse of dimensionality''. In this talk, we demonstrate that such challenges can be overcome for functions with low effective dimensionality --- functions which are constant along certain linear subspaces. Such functions can often be found in applications, for example, in hyper-parameter optimization for neural networks, heuristic algorithms for combinatorial optimization problems and complex engineering simulations.
We propose the use of random subspace embeddings within a(ny) global minimisation algorithm, extending the approach in Wang et al. (2013). We introduce a new framework, called REGO (Random Embeddings for GO), which transforms the high-dimensional optimization problem into a low-dimensional one. In REGO, a new low-dimensional problem is formulated with bound constraints in the reduced space and solved with any GO solver. Using random matrix theory, we provide probabilistic bounds for the success of REGO, which indicate that this is dependent upon the dimension of the embedded subspace and the intrinsic dimension of the function, but independent of the ambient dimension. Numerical results demonstrate that high success rates can be achieved with only one embedding and that rates are for the most part invariant with respect to the ambient dimension of the problem.
Structure from Motion (SfM) is a problem which asks: given photos of an object from different angles, can we reconstruct the object in 3D? This problem is important in computer vision, with applications including urban planning and autonomous navigation. A key part of SfM is bundle adjustment, where initial estimates of 3D points and camera locations are refined to match the images. This results in a high-dimensional nonlinear least-squares problem, which is typically solved using the Gauss-Newton method. In this talk, I will discuss how dimensionality reduction methods such as block coordinates and randomised sketching can be used to improve the scalability of Gauss-Newton for bundle adjustment problems.