Phase change materials are substances that absorb and release thermal energy during the process of melting and freezing. This characteristic makes phase change material (PCM)  a favourite choice to integrate it in buildings. Stephan problem including melting and solidification in PMC materials is an practical problem in many engineering processes. The position of the moving boundary, its veloci...

In this paper, we propose an iterative procedure based on two dimensionalfuzzy block-pulse functions for solving nonlinear fuzzy Fredholm integralequations of the second kind. The error estimation and numerical stabilityof the proposed method are given in terms of supplementary Lipschitz condition.Finally, illustrative examples are included in order to demonstrate the accuracyand convergence of...

The error behavior of finite difference discretization schemes has been researched. Starting from the onedimensional case, where two particles of a fluidized bed were taken, the diffusion equation was numerically solved on a single grid as reference. Then the diffusion equation, a model equation for the real problem, was solved on a separated grids setup, where the grid spacing of the grid adja...

Building robust recognition systems requires a careful understanding of the eeects of error in sensed features. In model-based recognition, matches between model features and sensed image features typically are used to compute a model pose and then project the unmatched model features into the image. The error in the image features results in uncertainty in the projected model features. We rst ...

We perform an average case analysis of the generalization dynamics of large neural networks trained using gradient descent. We study the practically-relevant “high-dimensional” regime where the number of free parameters in the network is on the order of or even larger than the number of examples in the dataset. Using random matrix theory and exact solutions in linear models, we derive the gener...

Discontinuous velocity boundary data for the lid driven cavity flow has long been causing difficulties in both theoretical analysis and numerical simulations. In finite element methods, the variational form for the driven cavity flow is not valid since the velocity is not in H. Hence standard error estimates do not work. By using only W1,r (1 < r < 2) regularity and constructing a continuous ap...

In this paper, a semiparametric modeling approach is introduced as a paradigm for addressing model error arising from unresolved physical phenomena. Our approach compensates for model error by learning an ancillary dynamical model for the unknown parameters. Practically, the proposed approach consists of the following steps. Given a physics-based model and a noisy data set of historical observa...

Engineering problems commonly require functional outputs of computational fluid dynamics (CFD) simulations with specified accuracy. These simulations are performed with limited computational resources. Computable error estimates offer the possibility of quantifying accuracy on a given mesh and predicting a fine grid functional on a coarser mesh. Such an estimate can be computed by solving the f...