Abstract The integration of machine learning (Keplerian paradigm) and more general artificial intelligence technologies with physical modeling based on first principles (Newtonian will impact scientific computing in engineering fundamental ways. Such hybrid models combine principle-based data-based into a joint architecture. This paper give some background, explain trends showcase recent achievements from an applied mathematics industrial perspective. Examples include characterization...

Abstract This work presents a data‐driven magnetostatic finite‐element solver that is specifically well suited to cope with strongly nonlinear material responses. The computing framework essentially multiobjective optimization procedure matching the operation points as closely possible given data while obeying Maxwell's equations. Here, extended heterogeneous (local) weighting factors—one per finite element—equilibrating goal function locally according behavior. modification allows...

This paper developes a data-driven magnetostatic finite-element (FE) solver which directly exploits measured material data instead of curve constructed from it. The distances between the field solution and measurement points are minimized while enforcing Maxwell's equations. minimization problem is solved by employing Lagrange multiplier approach. procedure wraps FE method within an outer iteration. capable considering anisotropic materials adapted to deal with models featuring combination...

We present an algorithm for computing sparse, least squares-based polynomial chaos expansions, incorporating both adaptive bases and sequential experimental designs. The is employed to approximate stochastic high-frequency electromagnetic models in a black-box way, particular, given only dataset of random parameter realizations the corresponding observations regarding quantity interest, typically scattering parameter. construction basis based on greedy, adaptive, sensitivity-related method....

This paper introduces an $hp$-adaptive multi-element stochastic collocation method, which additionally allows to re-use existing model evaluations during either $h$- or $p$-refinement. The method is based on weighted Leja nodes. After $h$-refinement, local interpolations are stabilized by adding and sorting nodes each newly created sub-element in a hierarchical manner. For $p$-refinement, the polynomial approximations total-degree dimension-adaptive bases. applied context of forward inverse...

Abstract This work introduces a novel data‐driven model‐free modified nodal analysis (MNA) circuit solver. The solver is capable of handling problems featuring elements for which solely measurement data are available. Rather than utilizing hard‐coded phenomenological model representations, the MNA reformulates problem such that solution found by minimizing distance between states fulfill Kirchhoff's laws, and belonging to data. In this way, formerly inevitable demand representations...

Accurate and efficient thermal simulations of induction machines are indispensable for detecting hot spots hence avoiding potential material failure in an early design stage. A goal is the better utilization with reduced safety margins due to a knowledge critical conditions. In this work, parameters two-dimensional machine model calibrated according evidence from measurements, by solving inverse field problem. The set comprise as well that three-dimensional effects. This allows consideration...

This work addresses uncertainty quantification of electromagnetic devices determined by the eddy current problem. The multilevel Monte Carlo (MLMC) method is used for treatment uncertain parameters while are discretized in space finite element method. Both methods yield numerical approximations such that total errors split into stochastic and spatial contributions. We propose a particular implementation where error controlled based on Richardson-extrapolation-based indicator. turn...

This paper presents a practical case study of data-driven magnetostatic finite element solver applied to real-world three-dimensional problem. Instead using hard-coded phenomenological material model within the solver, computing approach reformulates boundary value problem such that field solution is directly computed on measurement data. The formulation results in minimization with Lagrange multiplier, where sought must conform Maxwell's equations while at same time being closest available...

This work introduces a novel data-driven modified nodal analysis (MNA) circuit solver. The solver is capable of handling problems featuring elements for which solely measurement data are available. Rather than utilizing hard-coded phenomenological model representations, the MNA reformulates problem such that solution found by minimizing distance between states fulfill Kirchhoff's laws, to belonging data. In this way, previously inevitable demand representations abolished, thus avoiding...

The multilevel Monte Carlo method is applied to an academic example in the field of electromagnetism. exhibits a reduced variance by assigning samples multiple models with varying spatial resolution. For given it found that main costs are spent on coarsest level.

This paper introduces an $hp$-adaptive multi-element stochastic collocation method, which additionally allows to re-use existing model evaluations during either $h$- or $p$-refinement. The method is based on weighted Leja nodes. After $h$-refinement, local interpolations are stabilized by adding and sorting nodes each newly created sub-element in a hierarchical manner. For $p$-refinement, the polynomial approximations total-degree dimension-adaptive bases. applied context of forward inverse...

A standard circuit solver is based on modified nodal analysis (MNA), resolving Kirchhoffs voltage law explicitly by defining potentials and enforcing current as a differential algebraic system of equations [1] (Fig. 1a). Thereby, the lumped elements are represented models, from which chord or conductances, capacitances inductances derived entered in system. Many are, however, only known through set measurement data. The selection an appropriate model determination parameters thereof may be...

This work presents a data-driven finite element magnetic field solver which bypasses material law modelling by directly incorporating measurements into the solver. The seeks for solution that conforms to Maxwell's equations while at same time being closest given measurement data. formulation is described two-step minimization based on Lagrange multipliers. resulting applied two-dimensional quadrupole magnet model. Numerical results data sets of increasing cardinality verify datadriven...