Solving Problems with Uncertainties (SPU) Session 1

Time and Date: 16:30 - 18:10 on 13th June 2019

Room: 0.6

Chair: Vassil Alexandrov

14 Path-Finding with a Full-Vectorized GPU Implementation of Evolutionary Algorithms in an Online Crowd Model Simulation Framework [abstract]
Abstract: This article introduces a path-finding method based on evolutionary algorithms. It makes an extension of the current work on this problem providing a path-finding algorithm and a parallel computing implementation (GPU-based) of it. The article describes both the GPU implementation of full-vectorized genetic algorithms and a path-finding method for large maps based on dynamic tiling. The approach is able to serve a large number of agents due its performance and can handle dynamic obstacles in maps of arbitrary size. The experiments show the proposed approach outperforms other traditional path-finding algorithms, like breadth-first search, Dijkstra’s algorithm, and A*. The conclusions present further improvement possibilities to the proposed approach like the application of multi-objective algorithms to represent full crowd models. Also, further improvement of the presented approach is discussed.
Anton Aguilar-Rivera
44 Analysing the trade-off between computational performance and representation richness in ontology-based systems [abstract]
Abstract: As the result of the intense research activity of the past decade, Semantic Web technology has achieved a notable popularity and maturity. This technology is leading the evolution of the Web via interoperability by providing structured metadata. Because of the adoption of rich data models on a large scale to support the representation of complex relationships among concepts and automatic reasoning, the computational performance of ontology-based systems can significantly vary. In the evaluation of such a performance, a number of critical factors should be considered. Within this paper, we provide an empirical framework that yields an extensive analysis of the computational performance of ontology-based systems. The analysis can be seen as a decision tool in managing the constraints of representational requirements versus reasoning performance. Our approach adopts synthetic ontologies characterised by an increasing level of complexity up to OWL 2 DL. The benefits and the limitations of this approach are discussed in the paper.
Salvatore Flavio Pileggi, Fabian Peña, Maria Del Pilar Villamil and Ghassan Beydoun
92 Assessing uncertainties of unrepresented heterogeneity in soil hydrology using data assimilation [abstract]
Abstract: Soil hydrology is a discipline of environmental physics exhibiting considerable model errors in all its processes. Soil water movement is a key ecosystem process, with a crucial role in services like water buffering, fresh water retention, and climate regulation. The soil hydraulic properties as well as the multi-scale soil architecture are hardly ever known with sufficient accuracy. In interplay with a highly non-linear process described by the Richards equation, this yields significant prediction uncertainties. Data assimilation is a recent approach to cope with the challenges of quantitative soil hydrology. The ensemble Kalman filter (EnKF) is a method which allows to handle model errors for non-linear processes. This enables estimation of system state and trajectory, soil hydraulic parameters, and small-scale soil heterogeneities at measurement locations. Uncertainties in all estimated compartments can be incorporated and quantified. However, as measurements are typically scarce, estimations of high-resolution heterogeneity fields remain challenging. Relevant spatial scales for soil water movement range from less than a meter to kilometers. Accurately representing soil heterogeneities in models at all scales is exceptionally difficult. We investigate this issue on the small scale, where we model a two-dimensional domain with prescribed heterogeneity and conduct synthetic observations in typical measurement configurations. The EnKF is applied to estimate a one-dimensional soil profile including heterogeneities. We assess the capability of the method to cope with the effects of unrepresented heterogeneity by analyzing the discrepancy between synthetic 2D and estimated 1D representation.
Lukas Riedel, Hannes Helmut Bauser and Kurt Roth
119 A Framework for Distributed Approximation of Moments with Higher-Order Derivatives through Automatic Differentiation [abstract]
Abstract: We present a framework for the distributed approximation of moments, enabling an online evaluation of the uncertainty in a dynamical system. The first and second moment, mean, and variance are computed with up to third-order Taylor series expansion. The required derivatives for the expansion are generated automatically by automatic differentiation and propagated through an implicit time stepper. The computational kernels are the accumulation of the derivatives (Jacobian, Hessian, tensor) and the covariance matrix. We apply distributed parallelism to the Hessian or third-order tensor, and the user merely has to provide a function for the differential equation, thus achieving similar ease of use as Monte Carlo-based methods. We demonstrate our approach using with benchmarks on Theta, a KNL-based system at the Argonne Leadership Computing Facility.
Michel Schanen, Daniel Adrian Maldonado and Mihai Anitescu
191 IPIES for Uncertainly Dened Shape of Boundary, Boundary Conditions and Other Parameters in Elasticity Problems [abstract]
Abstract: The main purpose of this paper is modelling and solving boundary value problems considering simultaneously uncertainty of all of input data. These are such data as: shape of boundary, boundary conditions and other parameters. The strategy is presented on problems described by Navier-Lamé equations. Therefore, the uncertainty of parameters here, means the uncertainty of the Poisson ratio and Young's modulus. For solving uncertainly defined problems we use interval parametric integral equations system method (IPIES). In this method we propose modification of directed interval arithmetic for modeling and solving uncertainly defined problems. We consider an examples of uncertainly defined, 2D elasticity problems. We present boundary value problems with linear and as well curvelinear (modelled using NURBS curves) shape of boundary. We verify obtained interval solutions with compare to precisely defined (without uncertainty) analytical solutions. Additionally, to obtain errors of such solutions, we decided to use the total differential method. We also analyze influence of input data uncertainty on interval solutions.
Marta Kapturczak and Eugeniusz Zieniuk