TY - GEN
AB - In backward error analysis, an approximate solution to an equation is
compared to the exact solution to a nearby "modified" equation. In numerical
ordinary differential equations, the two agree up to any power of the step
size. If the differential equation has a geometric property then the modified
equation may share it. In this way, known properties of differential equations
can be applied to the approximation. But for partial differential equations,
the known modified equations are of higher order, limiting applicability of the
theory. Therefore, we study symmetric solutions of discretized partial
differential equations that arise from a discrete variational principle. These
symmetric solutions obey infinite-dimensional functional equations. We show
that these equations admit second-order modified equations which are
Hamiltonian and also possess first-order Lagrangians in modified coordinates.
The modified equation and its associated structures are computed explicitly for
the case of rotating travelling waves in the nonlinear wave equation.
AU - McLachlan, Robert I
AU - Offen, Christian
ID - 19941
T2 - arXiv:2006.14172
TI - Backward error analysis for variational discretisations of partial differential equations
ER -
TY - JOUR
AU - Kreusser, Lisa Maria
AU - McLachlan, Robert I
AU - Offen, Christian
ID - 19939
IS - 5
JF - Nonlinearity
SN - 0951-7715
TI - Detection of high codimensional bifurcations in variational PDEs
VL - 33
ER -
TY - CONF
AB - Current GNN architectures use a vertex neighborhood aggregation scheme, which limits their discriminative power to that of the 1-dimensional Weisfeiler-Lehman (WL) graph isomorphism test. Here, we propose a novel graph convolution operator that is based on the 2-dimensional WL test. We formally show that the resulting 2-WL-GNN architecture is more discriminative than existing GNN approaches. This theoretical result is complemented by experimental studies using synthetic and real data. On multiple common graph classification benchmarks, we demonstrate that the proposed model is competitive with state-of-the-art graph kernels and GNNs.
AU - Damke, Clemens
AU - Melnikov, Vitalik
AU - Hüllermeier, Eyke
ED - Jialin Pan, Sinno
ED - Sugiyama, Masashi
ID - 19953
KW - graph neural networks
KW - Weisfeiler-Lehman test
KW - cycle detection
T2 - Proceedings of The 12th Asian Conference on Machine Learning
TI - A Novel Higher-order Weisfeiler-Lehman Graph Convolution
VL - 129
ER -
TY - CONF
AU - Grabo, Matti
AU - Acar, Emre
AU - Kenig, Eugeny
ID - 19965
TI - Modeling of a Latent Heat Storage System Consisting of Encapsulated PCM- Elements
ER -
TY - CONF
AU - Müller, Michelle
AU - Neumann, Jürgen
AU - Gutt, Dominik
AU - Kundisch, Dennis
ID - 19782
T2 - Proceedings of the 41th International Conference on Information Systems (ICIS)
TI - Toss a Coin to your Host - How Guests End up Paying for the Cost of Regulatory Policies
ER -
TY - GEN
AU - Kramer, Paul
ID - 18638
TI - Comparison of Zero-Knowledge Range Proofs
ER -
TY - THES
AU - Heinzel, Joachim
ID - 15824
TI - Essays on the Theory of Industrial Organization: Credence Goods, Vertical Relations and Product Bundling
ER -
TY - THES
AU - Setzer, Alexander
ID - 18520
TI - Local Graph Transformation Primitives For Some Basic Problems In Overlay Networks
ER -
TY - GEN
ED - Troschitz, Juliane
ED - Vorderbrüggen, Julian
ED - Kupfer, Robert
ED - Gude, Maik
ED - Meschut, Gerson
ID - 20119
T2 - Applied Sciences
TI - Joining of Thermoplastic Composites with Metals Using Resistance ElementWelding
ER -
TY - JOUR
AB - Multi-objective optimization is an active field of research that has many applications. Owing to its success and because decision-making processes are becoming more and more complex, there is a recent trend for incorporating many objectives into such problems. The challenge with such problems, however, is that the dimensions of the solution sets—the so-called Pareto sets and fronts—grow with the number of objectives. It is thus no longer possible to compute or to approximate the entire solution set of a given problem that contains many (e.g. more than three) objectives. On the other hand, the computation of single solutions (e.g. via scalarization methods) leads to unsatisfying results in many cases, even if user preferences are incorporated. In this article, the Pareto Explorer tool is presented—a global/local exploration tool for the treatment of many-objective optimization problems (MaOPs). In the first step, a solution of the problem is computed via a global search algorithm that ideally already includes user preferences. In the second step, a local search along the Pareto set/front of the given MaOP is performed in user specified directions. For this, several continuation-like procedures are proposed that can incorporate preferences defined in decision, objective, or in weight space. The applicability and usefulness of Pareto Explorer is demonstrated on benchmark problems as well as on an application from industrial laundry design.
AU - Schütze, Oliver
AU - Cuate, Oliver
AU - Martín, Adanay
AU - Peitz, Sebastian
AU - Dellnitz, Michael
ID - 10596
IS - 5
JF - Engineering Optimization
SN - 0305-215X
TI - Pareto Explorer: a global/local exploration tool for many-objective optimization problems
VL - 52
ER -
TY - JOUR
AB - The three-dimensional (3D) crystal structures of the GAF3 domain of cyanobacteriochrome Slr1393 (Synechocystis PCC6803) carrying a phycocyanobilin chromophore could be solved in both 15-Z dark-adapted state, Pr, λmax = 649 nm, and 15-E photoproduct, Pg, λmax = 536 nm (resolution, 1.6 and 1.86 Å, respectively). The structural data allowed identifying the large spectral shift of the Pr-to-Pg conversion as resulting from an out-of-plane rotation of the chromophore’s peripheral rings and an outward movement of a short helix formed from a formerly unstructured loop. In addition, a third structure (2.1-Å resolution) starting from the photoproduct crystals allowed identification of elements that regulate the absorption maxima. In this peculiar form, generated during X-ray exposition, protein and chromophore conformation still resemble the photoproduct state, except for the D-ring already in 15-Z configuration and tilted out of plane akin the dark state. Due to its formation from the photoproduct, it might be considered an early conformational change initiating the parental state-recovering photocycle. The high quality and the distinct features of the three forms allowed for applying quantum-chemical calculations in the framework of multiscale modeling to rationalize the absorption maxima changes. A systematic analysis of the PCB chromophore in the presence and absence of the protein environment showed that the direct electrostatic effect is negligible on the spectral tuning. However, the protein forces the outer pyrrole rings of the chromophore to deviate from coplanarity, which is identified as the dominating factor for the color regulation.
AU - Xu, Xiuling
AU - Port, Astrid
AU - Wiebeler, Christian
AU - Zhao, Kai-Hong
AU - Schapiro, Igor
AU - Gärtner, Wolfgang
ID - 15628
JF - Proceedings of the National Academy of Sciences
SN - 0027-8424
TI - Structural Elements Regulating the Photochromicity in a Cyanobacteriochrome
ER -
TY - JOUR
AU - Pelster, Matthias
ID - 15306
JF - Economics Letters
SN - 0165-1765
TI - The gambler’s and hot-hand fallacies: Empirical evidence from trading data
VL - 187
ER -
TY - JOUR
AU - Schryen, Guido
ID - 15414
JF - {Communications of the ACM}
TI - Integrating Management Science into the HPC Research Ecosystem
VL - forthcoming
ER -
TY - CONF
AU - Sadeghi-Kohan, Somayeh
AU - Hellebrand, Sybille
ID - 15419
T2 - Proceedings IEEE VLSI Test Symposium
TI - Dynamic Multi-Frequency Test Method for Hidden Interconnect Defects
ER -
TY - JOUR
AU - Schryen, Guido
AU - Kliewer, Natalia
AU - Fink, Andreas
ID - 14985
JF - Business & Information Systems Engineering
TI - High Performance Business Computing
ER -
TY - JOUR
AU - Schryen, Guido
ID - 15022
JF - European Journal of Operational Research
TI - Parallel computational optimization in operations research: A new integrative framework, literature review and research directions
VL - forthcoming
ER -
TY - CHAP
AU - Yigitbas, Enes
AU - Jovanovikj, Ivan
AU - Sauer, Stefan
AU - Engels, Gregor
ID - 15267
T2 - Handling Security, Usability, User Experience and Reliability in User-Centered Development Processes - IFIP WG 13.2/13.5
TI - On the Development of Context-aware Augmented Reality Applications (to appear)
ER -
TY - CHAP
AB - In the development of model predictive controllers for PDE-constrained problems, the use of reduced order models is essential to enable real-time applicability. Besides local linearization approaches, proper orthogonal decomposition (POD) has been most widely used in the past in order to derive such models. Due to the huge advances concerning both theory as well as the numerical approximation, a very promising alternative based on the Koopman operator has recently emerged. In this chapter, we present two control strategies for model predictive control of nonlinear PDEs using data-efficient approximations of the Koopman operator. In the first one, the dynamic control system is replaced by a small number of autonomous systems with different yet constant inputs. The control problem is consequently transformed into a switching problem. In the second approach, a bilinear surrogate model is obtained via a convex combination of these autonomous systems. Using a recent convergence result for extended dynamic mode decomposition (EDMD), convergence of the reduced objective function can be shown. We study the properties of these two strategies with respect to solution quality, data requirements, and complexity of the resulting optimization problem using the 1-dimensional Burgers equation and the 2-dimensional Navier–Stokes equations as examples. Finally, an extension for online adaptivity is presented.
AU - Peitz, Sebastian
AU - Klus, Stefan
ID - 16289
SN - 0170-8643
T2 - Lecture Notes in Control and Information Sciences
TI - Feedback Control of Nonlinear PDEs Using Data-Efficient Reduced Order Models Based on the Koopman Operator
VL - 484
ER -
TY - JOUR
AU - Burkhardt, Lukas
AU - Vukadinovic, Yannik
AU - Nowakowski, Michał
AU - Kalinko, Aleksandr
AU - Rudolph, Julian
AU - Carlsson, Per-Anders
AU - Jacob, Christoph R.
AU - Bauer, Matthias
ID - 16311
JF - Inorganic Chemistry
SN - 0020-1669
TI - Electronic Structure of the Hieber Anion [Fe(CO)3(NO)]− Revisited by X-ray Emission and Absorption Spectroscopy
ER -
TY - GEN
AU - Droste, Jonas
ID - 16342
TI - Digital Nudging - Ein systematischer Literaturüberblick
ER -