Structure-Preserving Model Reduction of Physical Network Systems

This paper considers physical network systems where the energy storage is naturally associated to the nodes of the graph, while the edges of the graph correspond to static couplings. The first sections deal with the linear case, covering examples such as mass-damper and hydraulic systems, which have a structure that is similar to symmetric consensus dynamics. The last section is concerned with a specific class of nonlinear physical network systems; namely detailed-balanced chemical reaction networks governed by mass action kinetics. In both cases, linear and nonlinear, the structure of the dynamics is similar, and is based on a weighted Laplacian matrix, together with an energy function capturing the energy storage at the nodes. We discuss two methods for structure-preserving model reduction. The first one is clustering; aggregating the nodes of the underlying graph to obtain a reduced graph. The second approach is based on neglecting the energy storage at some of the nodes, and subsequently eliminating those nodes (called Kron reduction).</p

Model-data fusion in digital twins of large scale dynamical systems

Digital twins (DTs) are virtual entities that serve as the real-time digital counterparts of actual physical systems across their life-cycle. In a typical application of DTs, the physical system provides sensor measurements and the DT should incorporate the incoming data and run different simulations to assess various scenarios and situations. As a result, an informed decision can be made to alter the physical system or at least take necessary precautions, and the process is repeated along the system's life-cycle. Thus, the effective deployment of DTs requires fulfilling multi-queries while communicating with the physical system in real-time. Nonetheless, DTs of large-scale dynamical systems, as in fluid flows, come with three grand challenges that we address in this dissertation.First, the high dimensionality makes full order modeling (FOM) methodologies unfeasible due to the associated computational time and memory costs. In this regard, reduced order models (ROMs) can potentially accelerate the forward simulations by orders of magnitude, especially for systems with recurrent spatial structures. However, traditional ROMs yield inaccurate and unstable results for turbulent and convective flows. Therefore, we propose a hybrid variational multi-scale framework that benefits from the locality of modal interactions to deliver accurate ROMs. Furthermore, we adopt a novel physics guided machine learning technique to provide on-the-fly corrections and elevate the trustworthiness of the resulting ROM in the sparse data and incomplete governing equations regimes.Second, complex natural or engineered systems are characterized by multi-scale, multi-physics, and multi-component nature. The efficient simulation of such systems requires quick communication and information sharing between several heterogeneous computing units. In order to address this challenge, we pioneer an interface learning (IL) paradigm to ensure the seamless integration of hierarchical solvers with different scales, physics, abstractions, and geometries without compromising the integrity of the computational setup. We demonstrate the IL paradigm for non-iterative domain decomposition and the FOM-ROM coupling in multi-fidelity computations.Third, fluid flow systems are continuously evolving and thus the validity of the DT should be warranted across varying operating conditions and flow regimes. To do so, we embed data assimilation (DA) techniques to enable the DT to self-adapt based on in-situ observational data and efficiently replicate the physical system. In addition, we combine DA algorithms with machine learning models to build a robust framework that collectively addresses the model closure problem, the error in prior information, and the measurement noise

Kontextsensitive Modellhierarchien für Quantifizierung der höherdimensionalen Unsicherheit

We formulate four novel context-aware algorithms based on model hierarchies aimed to enable an efficient quantification of uncertainty in complex, computationally expensive problems, such as fluid-structure interaction and plasma microinstability simulations. Our results show that our algorithms are more efficient than standard approaches and that they are able to cope with the challenges of quantifying uncertainty in higher-dimensional, complex problems.Wir formulieren vier kontextsensitive Algorithmen auf der Grundlage von Modellhierarchien um eine effiziente Quantifizierung der Unsicherheit bei komplexen, rechenintensiven Problemen zu ermöglichen, wie Fluid-Struktur-Wechselwirkungs- und Plasma-Mikroinstabilitätssimulationen. Unsere Ergebnisse zeigen, dass unsere Algorithmen effizienter als Standardansätze sind und die Herausforderungen der Quantifizierung der Unsicherheit in höherdimensionalen, komplexen Problemen bewältigen können

Model Order Reduction

An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This three-volume handbook covers methods as well as applications. This third volume focuses on applications in engineering, biomedical engineering, computational physics and computer science

Computer Science Research Institute 2004 annual report of activities.

This report summarizes the activities of the Computer Science Research Institute (CSRI) at Sandia National Laboratories during the period January 1, 2004 to December 31, 2004. During this period the CSRI hosted 166 visitors representing 81 universities, companies and laboratories. Of these 65 were summer students or faculty. The CSRI partially sponsored 2 workshops and also organized and was the primary host for 4 workshops. These 4 CSRI sponsored workshops had 140 participants--74 from universities, companies and laboratories, and 66 from Sandia. Finally, the CSRI sponsored 14 long-term collaborative research projects and 5 Sabbaticals

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described