An energy-based a posteriori error bound is proposed for the physics-informed neural network solutions of elasticity problems. An admissible displacement-stress solution pair is obtained from a mixed form of physics-informed neural networks, and the proposed error bound is formulated as the constitutive relation error defined by the solution pair. Such an error estimator provides an upper bound of

Somaliasvenskar som flyttar till Storbritannien upplever inte bara att det är lättare att få jobb utan mycket lättare att starta eget, skriver bland andra ­ekonomihistorikern Benny Carlson.

I Kanada, USA och Storbritannien står etniska organisationer för centrala delar av integrationsarbetet - men i Sverige är det myndig­heter som ska integrera, skriver Benny Carlson.

Despite tremendous progress seen in the computational fluid dynamics community for the past few decades, numerical tools are still too slow for the simulation of practical flow problems, consuming thousands or even millions of computational core-hours. To enable feasible multi-disciplinary analysis and design, the numerical techniques need to be accelerated by orders of magnitude. Reduced-order mo

A data-driven reduced basis (RB) method for parametrized time-dependent problems is proposed. This method requires the offline preparation of a database comprising the time history of the full-order solutions at parameter locations. Based on the full-order data, a reduced basis is constructed by the proper orthogonal decomposition (POD), and the maps between the time/parameter values and the proje

Purpose - For eigenvalue problems containing uncertain inputs characterized by fuzzy basic parameters, first-order perturbation methods have been developed to extract eigen solutions, but either the result accuracy or the computational efficiency of these methods is less satisfactory. The purpose of this paper is to present an efficient method for estimation of fuzzy eigenvalues with high accuracy

We propose a non-intrusive reduced basis (RB) method for parametrized nonlinear partial differential equations (PDEs) that leverages models of different accuracy. From a collection of low-fidelity (LF) snapshots, parameter locations are extracted for the evaluations of high-fidelity (HF) snapshots to recover a reduced basis. Multi-fidelity Gaussian process regression (GPR) is employed to approxima

BACKGROUND: Our aim was to examine the prevalence and characteristics of difficult-to-treat HIV in the current Swedish HIV cohort and to compare treatment outcomes between people with difficult and non-difficult-to-treat HIV.METHODS: In this cross-sectional analysis of the Swedish HIV cohort, we identified all people with HIV currently in active care in 2023 from the national register InfCareHIV.

When evaluating quantities of interest that depend on the solutions to differential equations, we inevitably face the trade-off between accuracy and efficiency. Especially for parametrized, time-dependent problems in engineering computations, it is often the case that acceptable computational budgets limit the availability of high-fidelity, accurate simulation data. Multi-fidelity surrogate modeli

Highly accurate numerical or physical experiments are often very time-consuming or expensive to obtain. When time or budget restrictions prohibit the generation of additional data, the amount of available samples may be too limited to provide satisfactory model results. Multi-fidelity methods deal with such problems by incorporating information from other sources, which are ideally well-correlated

This work proposes a Bayesian inference method for the reduced-order modeling of time-dependent systems. Informed by the structure of the governing equations, the task of learning a reduced-order model from data is posed as a Bayesian inverse problem with Gaussian prior and likelihood. The resulting posterior distribution characterizes the operators defining the reduced-order model, hence the pred

A non-intrusive reduced basis (RB) method is proposed for parametrized nonlinear structural analysis undergoing large deformations and with elasto-plastic constitutive relations. In this method, a reduced basis is constructed from a set of full-order snapshots by the proper orthogonal decomposition (POD), and the Gaussian process regression (GPR) is used to approximate the projection coefficients.

In solid mechanics, linear structures often exhibit (local) nonlinear behavior when close to failure. For instance, the elastic deformation of a structure becomes plastic after being deformed beyond recovery. To properly assess such problems in a real-life application, we need fast and multi-query evaluations of coupled linear and nonlinear structural systems, whose approximations are not straight

In this paper, goal-oriented error estimation for Timoshenko beams on Pasternak foundation, which involves double shear effect, is performed. The constitutive relation error (CRE) estimation is used in finite element analysis (FEA) to acquire strict bounds on quantities of interest. Due to the coupling of the displacement field and the internal force field in the equilibrium equations of the beam,

Purpose - The purpose of this paper is to acquire strict upper and lower bounds on quantities of slender beams on Winkler foundation in finite element analysis. Design/methodology/approach - It leans on the dual analysis wherein the constitutive relation error (CRE) is used to perform goal-oriented error estimation. Due to the coupling of the displacement field and the stress field in the equilibr

On the basis of the dual variational formulation of a class of elliptic variational inequalities, a constitutive relation error is defined for the variational inequalities as an a posteriori error estimator, which is shown to guarantee strict upper bounds of the global energy-norm errors of kinematically admissible solutions. A numerical example is presented to validate the strictly bounding prope

A method is proposed for the solution of boundary-value problems of linear and non-linear 2mth-order Fredholm integro-differential equations. A set of algebraic equations are obtained after introduction of Gauss–Lobatto quadrature and the generalized differential quadrature analog into the weak form description of a Fredholm integro-differential equation. Numerical examples are presented to demons

A procedure to identify the imperfection in thin plates is proposed in this paper. The modified potential energy principle, which serves as the theoretical basis of the identification procedure, is improved to allow for the experimental measurements in static tests. Several typical examples are studied to illustrate the effectiveness of the procedure.

In this paper, a goal-oriented error estimation technique for static response sensitivity analysis is proposed based on the constitutive relation error (CRE) estimation for finite element analysis (FEA). Strict upper and lower bounds of various quantities of interest (QoI) that are associated with the response sensitivity derivative fields are acquired. Numerical results are presented to assess th

For model verification which is mainly focused on the control of discretization errors of numerical results, a posteriori error estimation plays an important role in various numerical tools such as the finite element method. The outputs of interest are usually converted into integral functionals over the problem domain for a posteriori error analysis. Among the available techniques for goal-orient