A computer-implemented method for predicting a cardiovascular behavior of a newborn to birth from his/her fetus physiological parameters. The method comprises obtaining physiological parameters of the fetus, obtaining a non-calibrated surrogate cardiovascular model modeling a cardiovascular system of the fetus and modelling at least one physiological change triggered by the birth, calibrating the non-calibrated surrogate cardiovascular model with a data assimilation algorithm using the obtained physiological parameters of the fetus, thereby obtaining a calibrated surrogate cardiovascular model of the fetus, and predicting the cardiovascular behavior of the newborn by triggering the at least one physiological change of the calibrated surrogate cardiovascular model of the fetus, thereby obtaining a calibrated surrogate cardiovascular model of the newborn.
Published in Mathematical Models & Methods in Applied Sciences (M3AS), 2026
Defeaturing, the process of simplifying computational geometries, is a critical step in industrial simulation pipelines for reducing computational cost. Rigorous a posteriori estimators exist for the global energy-norm error introduced by geometry simplifications. However, practitioners are usually more concerned with the accuracy of specific quantities of interest (QoIs) in the solution. This paper bridges that gap by developing mathematically certified, goal-oriented a posteriori defeaturing error estimators for Poisson’s equation, linear elasticity, and Stokes flow. First, we derive new reliable energy-norm estimators for features subject to Dirichlet boundary conditions in linear elasticity and Stokes flow, based on existing results for Poisson’s equation. Second, we formulate general energy-norm estimators for multiple negative features, subject to either Dirichlet or Neumann boundary conditions for the first time. Finally, we combine these estimators with the dual-weighted residual (DWR) method to obtain reliable estimates for linear QoIs and demonstrate their effectiveness across a range of numerical experiments.
Talk on analysis-aware defeaturing of Dirichlet features in Poisson problems, including goal-oriented estimates. The abstract of the talk can be found here.
Geometry simplification, also known as defeaturing, is crucial for industrial simulations. It not only simplifies the meshing process but also reduces the computational costs of subsequent simulations by decreasing the number of degrees of freedom. Traditional defeaturing methods often rely on geometric criteria alone, overlooking the underlying physics of the problem. In contrast, analysis-aware defeaturing employs a posteriori error estimation, combining the defeatured simulation outputs with the exact geometry information to better inform the defeaturing process.
Simplifying complex computational geometries, also called defeaturing, is essential in industrial simulation pipelines. Defeaturing simplifies the meshing process and reduces the computational complexity of the simulation. Standard defeaturing methods typically rely on geometric criteria and ignore the underlying physics. In contrast, analysis-aware defeaturing offers a posteriori error estimates for geometry simplifications. It does so by combining the defeatured simulation output with the exact geometry information to guide the process. Introduced by Buffa, Chanon, and Vázquez for a single geometrical feature subject to Neumann boundary conditions in Poisson problems, the analysis-aware defeaturing framework has since been extended to various settings: multiple Neumann features in linear elasticity and Stokes flow problems, features subject to Dirichlet conditions, goal-oriented estimates, and adaptivity in combination with a posteriori estimates for the numerical error. However, the latter works only deal with geometrical features located on the boundary of the domain. In this work, we consider geometry simplifications of complex material interfaces within a computational domain. Even when interfaces are handled using immersed methods, accurately resolving complex features still requires expensive quadrature rules. Consequently, defeaturing remains an effective means of reducing the overall computational cost. In this context, we derive a reliable a posteriori estimator for the combined defeaturing and numerical error for a Poisson model problem with discontinuous diffusion coefficients. To capture the numerical component of the error, we employ a standard equilibrated flux reconstruction. To address the defeaturing error, we develop a reliable indicator by adapting the arguments from the boundary feature case to the interface case. In particular, we prove that the indicator’s effectivity index is independent of the feature’s size. This robustness is crucial for comparing features of different scales. Finally, we validate our approach through extensive numerical experiments.
