The ROMES method for statistical modeling of reduced-order-model error

This work presents a technique for statistically modeling errors introduced by reduced-order models. The method employs Gaussian-process regression to construct a mapping from a small number of computationally inexpensive `error indicators' to a distribution over the true error. The variance of this distribution can be interpreted as the (epistemic) uncertainty introduced by the reduced-order model. To model normed errors, the method employs existing rigorous error bounds and residual norms as indicators; numerical experiments show that the method leads to a near-optimal expected effectivity in contrast to typical error bounds. To model errors in general outputs, the method uses dual-weighted residuals---which are amenable to uncertainty control---as indicators. Experiments illustrate that correcting the reduced-order-model output with this surrogate can improve prediction accuracy by an order of magnitude; this contrasts with existing `multifidelity correction' approaches, which often fail for reduced-order models and suffer from the curse of dimensionality. The proposed error surrogates also lead to a notion of `probabilistic rigor', i.e., the surrogate bounds the error with specified probability

Reproducing kernel Hilbert spaces and variable metric algorithms in PDE constrained shape optimisation

In this paper we investigate and compare different gradient algorithms designed for the domain expression of the shape derivative. Our main focus is to examine the usefulness of kernel reproducing Hilbert spaces for PDE constrained shape optimisation problems. We show that radial kernels provide convenient formulas for the shape gradient that can be efficiently used in numerical simulations. The shape gradients associated with radial kernels depend on a so called smoothing parameter that allows a smoothness adjustment of the shape during the optimisation process. Besides, this smoothing parameter can be used to modify the movement of the shape. The theoretical findings are verified in a number of numerical experiments

The supremum of autoconvolutions, with applications to additive number theory

We adapt a number-theoretic technique of Yu to prove a purely analytic theorem: if f(x) is in L^1 and L^2, is nonnegative, and is supported on an interval of length I, then the supremum of the convolution f*f is at least 0.631 \| f \|_1^2 / I. This improves the previous bound of 0.591389 \| f \|_1^2 / I. Consequently, we improve the known bounds on several related number-theoretic problems. For a subset A of {1,2, ..., n}, let g be the maximum multiplicity of any element of the multiset {a+b: a,b in A}. Our main corollary is the inequality gn>0.631|A|^2, which holds uniformly for all g, n, and A.Comment: 17 pages. to appear in IJ

A reinterpretation of set differential equations as differential equations in a Banach space

Set differential equations are usually formulated in terms of the Hukuhara differential, which implies heavy restrictions for the nature of a solution. We propose to reformulate set differential equations as ordinary differential equations in a Banach space by identifying the convex and compact subsets of $\R^d$ with their support functions. Using this representation, we demonstrate how existence and uniqueness results can be applied to set differential equations. We provide a simple example, which can be treated in support function representation, but not in the Hukuhara setting

Comparison between different approaches for the evaluation of the hot spot structural stress in welded pressure vessel components

Fatigue cracks in welds often occur at the toe of a weld where stresses are difficult to calculate at the design stage. To circumvent this problem the ASME Boiler and PV code Section VIII Division 2 Part 5 [1] uses the structural stress normal to the expected crack to predict fatigue life using elastic analysis and as welded fatigue curves. The European Unfired Pressure Vessel Code [2] uses a similar approach. The structural stress excludes the notch stress at the weld toe itself. The predicted fatigue life has a strong dependency on the calculated value of structural stress. This emphasizes the importance of having a unique and robust way of extracting the structural stress from elastic finite element results. Different methods are available for the computation of the structural hotspotstress at welded joints. These are based on the extrapolation of surface stresses close to the weld toe, on the linearisation of stresses in the through-thickness direction or on the equilibrium of nodal forces. This paper takes a critical view on the various methods and investigates the effects of the mesh quality on the value of the structural stress. T-shaped welded plates under bending are considered as a means for illustration

SOME PERSPECTIVE ON THE US NATIONAL PORK PRODUCERS' COUNCIL'S CLAIMS ABOUT CANADIAN SWINE SUBSIDIES

Agricultural and Food Policy,

Financial intermediaries, markets and growth

We build a model in which financial intermediaries provide insurance to households against a liquidity shock. Households can also invest directly on a financial market if they pay a cost. In equilibrium, the ability of intermediaries to share risk is constrained by the market. This can be beneficial because intermediaries invest less in the productive technology when they provide more risk-sharing. Our model predicts that bank-oriented economies should grow slower than more market-oriented economies, which is consistent with some recent empirical evidence. We show that the mix of intermediaries and market that maximizes welfare under a given level of financial development depends on economic fundamentals. We also show the optimal mix of two structurally very similar economies can be very different. --Financial Intermediaries,Risk Sharing,Finance and Growth,Comparing Financial Systems