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Fredrik Larsson

Publications and source records attributed to Fredrik Larsson.

5 recordsLinked to original sources
arXiv2026

Online Learning of Correspondences between Images

We propose a novel method for iterative learning of point correspondences between image sequences. Points moving on surfaces in 3D space are projected into two images. Given a point in either view, the considered problem is to determine the corresponding location in the other view. The geometry and distortions of the projections are unknown as is the shape of the surface. Given several pairs of point-sets but no access to the 3D scene, correspondence mappings can be found by excessive global optimization or by the fundamental matrix if a perspective projective model is assumed. However, an iterative solution on sequences of point-set pairs with general imaging geometry is preferable. We derive such a method that optimizes the mapping based on Neyman's chi-square divergence between the densities representing the uncertainties of the estimated and the actual locations. The densities are represented as channel vectors computed with a basis function approach. The mapping between these vectors is updated with each new pair of images such that fast convergence and high accuracy are achieved. The resulting algorithm runs in real-time and is superior to state-of-the-art methods in terms of convergence and accuracy in a number of experiments.

cs.CV↗
arXiv2022

A micromorphic phase-field model for brittle and quasi-brittle fracture

The phase-field model for fracture, despite its popularity and ease of implementation comes with its set of computational challenges. They are the non-convex energy functional, variational inequality due to fracture irreversibility, the need for extremely fine meshes to resolve the fracture. In this manuscript, the focus is on the numerical treatment of variational inequality. In this context, the popular history-variable approach suffers from variationally inconsistency and non-quantifiable nature of the error introduced. A better alternative, the penalisation approach, has the potential to render the stiffness matrix ill-conditioned. In order to circumvent both aforementioned issues, a micromorphic approach towards phase-field fracture modelling is proposed in this manuscript. Within this approach, a micromorphic extension of the energy functional is carried out. This transforms the phase-field into a local variable, while introducing a micromorphic variable that regularises the fracture problem. This reduction the regularity requirements for the phase-field enables an easier implementation of the fracture irreversibility constraint through simple 'max' operation, with system level precision. Numerical experiments carried out on benchmark brittle and quasi-brittle problems demonstrate the applicability and efficacy of the proposed model for a wide range of fracture problems.

math.NA↗
arXiv2022

Phase-field fracture irreversibility using the slack variable approach

In this manuscript, the phase-field fracture irreversibility constraint is transformed into an equality-based constraint using the slack variable approach. The equality-based fracture irreversibility constraint is then introduced in the phase-field fracture energy functional using the Lagrange Multiplier Method and the Penalty method. Both methods are variationally consistent with the conventional variational inequality phase-field fracture problem, unlike the history-variable approach. Thereafter, numerical experiments are carried out on benchmark problems in brittle and quasi-brittle fracture to demonstrate the efficacy of the proposed method.

math.NA↗
arXiv2019

On-the-fly adaptivity for nonlinear twoscale simulations using artificial neural networks and reduced order modeling

A multi-fidelity surrogate model for highly nonlinear multiscale problems is proposed. It is based on the introduction of two different surrogate models and an adaptive on-the-fly switching. The two concurrent surrogates are built incrementally starting from a moderate set of evaluations of the full order model. Therefore, a reduced order model (ROM) is generated. Using a hybrid ROM-preconditioned FE solver, additional effective stress-strain data is simulated while the number of samples is kept to a moderate level by using a dedicated and physics-guided sampling technique. Machine learning (ML) is subsequently used to build the second surrogate by means of artificial neural networks (ANN). Different ANN architectures are explored and the features used as inputs of the ANN are fine tuned in order to improve the overall quality of the ML model. Additional ANN surrogates for the stress errors are generated. Therefore, conservative design guidelines for error surrogates are presented by adapting the loss functions of the ANN training in pure regression or pure classification settings. The error surrogates can be used as quality indicators in order to adaptively select the appropriate -- i.e. efficient yet accurate -- surrogate. Two strategies for the on-the-fly switching are investigated and a practicable and robust algorithm is proposed that eliminates relevant technical difficulties attributed to model switching. The provided algorithms and ANN design guidelines can easily be adopted for different problem settings and, thereby, they enable generalization of the used machine learning techniques for a wide range of applications. The resulting hybrid surrogate is employed in challenging multilevel FE simulations for a three-phase composite with pseudo-plastic micro-constituents. Numerical examples highlight the performance of the proposed approach.

physics.comp-ph↗