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Boundary Element Methods for the Laplace Hypersingular Integral Equation on Multiscreens: A Two-Level Substructuring Preconditioner
(2023)SAM Research ReportWe present a preconditioning method for the linear systems arising from the boundary element discretization of the Laplace hypersingular equation on a \(2\)-dimensional triangulated surface \(\Gamma\) in \(\mathbb{R}^3\). We allow \(\Gamma\) to belong to a large class of geometries that we call polygonal multiscreens, which can be non-manifold. After introducing a new, simple conforming Galerkin discretization, we analyze a substructuring ...Report -
DACH Operation Center 2021-2022 Report
(2023)International VLBI Service for Geodesy and Astrometry 2021+2022 Biennial ReportReport -
ETHZ Analysis Center Report
(2023)International VLBI Service for Geodesy and Astrometry 2021+2022 Biennial ReportReport -
Deep ReLU networks and high-order finite element methods II: Chebyshev emulation
(2023)SAM Research ReportExpression rates and stability in Sobolev norms of deep ReLU neural networks (NNs) in terms of the number of parameters defining the NN for continuous, piecewise polynomial functions, on arbitrary, finite partitions \(\mathcal{T}\) of a bounded interval \((a,b)\) are addressed. Novel constructions of ReLU NN surrogates encoding the approximated functions in terms of Chebyshev polynomial expansion coefficients are developed. Chebyshev ...Report -
An operator preconditioning perspective on training in physics-informed machine learning
(2023)SAM Research ReportIn this paper, we investigate the behavior of gradient descent algorithms in physics-informed machine learning methods like PINNs, which minimize resid uals connected to partial differential equations (PDEs). Our key result is that the difficulty in training these models is closely related to the conditioning of a specific differential operator. This operator, in turn, is associated to the Hermi tian square of the differential operator ...Report -
The Gevrey class implicit mapping theorem with application to UQ of semilinear elliptic PDEs
(2023)SAM Research ReportThis article is concerned with a regularity analysis of parametric operator equations with a perspective on uncertainty quantification. We study the regularity of mappings between Banach spaces near branches of isolated solutions that are implicitly defined by a residual equation. Under \(s\)-Gevrey assumptions on on the residual equation, we establish \(s\)-Gevrey bounds on the Fréchet derivatives of the local data-to-solution mapping. ...Report -
Seven routes to experimentation in policymaking: A guide to applied behavioural science methods
(2023)OECD Working Papers on Public GovernanceBehavioural science methods are increasingly used to design and evaluate public policies that better reflect human behaviour and decision making. However, there is a lack of standardization in selecting and labelling these methods, making it difficult for policymakers to choose the appropriate one for a specific policy context. To address this, this working paper proposes guidelines and a visual roadmap, including five key questions to ...Report -
Using algorithms to provide bridge managers with consistent and complete early estimates of possible future maintenance interventions
(2023)It is advantageous in the development of train schedules to know far in advance when interventions are required on bridges, as well as the types of intervention and the extent of track possession required. So that SBB bridge managers can provide this information, it would be advantageous for them to obtain a consistent and complete overview of the required interventions and associated track possessions for all their bridges up to 25 years ...Report -
Coupled Surface and Volume Integral Equations for Electromagnetism
(2023)SAM Research ReportWe study frequency domain electromagnetic scattering at a bounded, penetrable, and inhomogeneous obstacle. By defining constant reference coefficients, a new representation formula for interior and exterior vector fields is proposed, based on the general form of the Stratton-Chu integral representation. The final integral equation system consists of surface integral operators arising from a Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) ...Report -
Fit through Flexibility?
(2023)Reports / Swedish Institute for European Plicy Studies ~ Fit for 35? Reforming the Politics and Institutions of the EU for an Enlarged UnionReport