Related papers: Some Technical Thoughts on Modeling
Formally capturing the transition from a continuous model to a discrete model is investigated using model based refinement techniques. A very simple model for stopping (eg. of a train) is developed in both the continuous and discrete…
We describe a new framework for fitting jump models to a sequence of data. The key idea is to alternate between minimizing a loss function to fit multiple model parameters, and minimizing a discrete loss function to determine which set of…
Functional aspects as well as the influence of integration technology on the system behavior have to be considered in the 3D integration design process of micro systems. Therefore, information from different physical domains has to be…
In software applications, user models can be used to specify the profile of the typical users of the application, including personality traits, preferences, skills, etc. In theory, this would enable an adaptive application behavior that…
Overfitting is a common problem in machine learning, which means the model too closely fits the training data while performing poorly in the test data. Among various methods of coping with overfitting, dropout is one of the representative…
Differential equations (DEs) are commonly used to describe dynamic systems evolving in one (ordinary differential equations or ODEs) or in more than one dimensions (partial differential equations or PDEs). In real data applications the…
In this work, we propose a multi-stage training strategy for the development of deep learning algorithms applied to problems with multiscale features. Each stage of the pro-posed strategy shares an (almost) identical network structure and…
Preprocessing data is an important step before any data analysis. In this paper, we focus on one particular aspect, namely scaling or normalization. We analyze various scaling methods in common use and study their effects on different…
This paper discusses a model-based approach to testing as a vital part of software development. It argues that an approach using models as central development artifact needs to be added to the portfolio of software engineering techniques,…
Model-based experimental design is attracting increasing attention in chemical process engineering. Typically, an iterative procedure is pursued: an approximate model is devised, prescribed experiments are then performed and the resulting…
There is a growing need for better development methods and tools to keep up with the increasing complexity of new software systems. New types of user interfaces, the need for intelligent components, sustainability concerns, ... bring new…
Constructing a conceptual model as an abstract representation of a portion of the real world involves capturing the (1) static (things/objects and trajectories of flow), (2) the dynamic (event identification), and (3) the behavior (e.g.,…
In this article, we describe a function fitting method that has potential applications in machine learning and also prove relevant theorems. The described function fitting method is a convex minimization problem and can be solved using a…
Degradation models play a critical role in quality engineering by enabling the assessment and prediction of system reliability based on data. The objective of this paper is to provide an accessible introduction to degradation models. We…
A face model is a mathematical representation of the distinct features of a human face. Traditionally, face models were built using a set of fiducial points or landmarks, each point ideally located on a facial feature, i.e., corner of the…
Decision making algorithms are used in a multitude of different applications. Conventional approaches for designing decision algorithms employ principled and simplified modelling, based on which one can determine decisions via tractable…
Neural networks are one tool for approximating non-linear differential equations used in scientific computing tasks such as surrogate modeling, real-time predictions, and optimal control. PDE foundation models utilize neural networks to…
This work introduces a general multi-level model for self-adaptive systems. A self-adaptive system is seen as composed by two levels: the lower level describing the actual behaviour of the system and the upper level accounting for the…
Partial differential equations (PDEs) are used, with huge success, to model phenomena arising across all scientific and engineering disciplines. However, across an equally wide swath, there exist situations in which PDE models fail to…
Two-step predictor/corrector methods are provided to solve three classes of problems that present themselves as systems of ordinary differential equations (ODEs). In the first class, velocities are given from which displacements are to be…