Related papers: A shape optimization algorithm for cellular compos…
Mesh optimization procedures are generally a combination of node smoothing and discrete operations which affect a small number of elements to improve the quality of the overall mesh. These procedures are useful as a post-processing step in…
Fluid-structure interactions are a widespread phenomenon in nature. Although their numerical modeling have come a long way, the application of numerical design tools to these multiphysics problems is still lagging behind. Gradient-based…
For minimizing a strongly convex objective function subject to linear inequality constraints, we consider a penalty approach that allows one to utilize stochastic methods for problems with a large number of constraints and/or objective…
Minimizing a convex function of a measure with a sparsity-inducing penalty is a typical problem arising, e.g., in sparse spikes deconvolution or two-layer neural networks training. We show that this problem can be solved by discretizing the…
A reinforcement learning approach to design optimised graded metamaterials for mechanical energy confinement and amplification is described. Through the proximal policy optimisation algorithm, the reinforcement agent is trained to optimally…
We study dendritic microstructure evolution using an adaptive grid, finite element method applied to a phase-field model. The computational complexity of our algorithm, per unit time, scales linearly with system size, rather than the…
The modeling of damage processes in materials constitutes an ill-posed mathematical problem which manifests in mesh-dependent finite element results. The loss of ellipticity of the discrete system of equations is counteracted by…
In this paper, we propose a shape optimization pipeline for propeller blades, applied to naval applications. The geometrical features of a blade are exploited to parametrize it, allowing to obtain deformed blades by perturbating their…
In this work, we propose a disentangled latent optimization-based method for parameterizing grouped deforming 3D objects into shape and deformation factors in an unsupervised manner. Our approach involves the joint optimization of a…
An algorithm is devised for solving minimization problems with equality constraints. The algorithm uses first-order derivatives of both the objective function and the constraints. The step is computed as a sum between a steepest-descent…
Example-based mesh deformation methods are powerful tools for realistic shape editing. However, existing techniques typically combine all the example deformation modes, which can lead to overfitting, i.e. using a overly complicated model to…
Structured convex optimization on weighted graphs finds numerous applications in machine learning and computer vision. In this work, we propose a novel adaptive preconditioning strategy for proximal algorithms on this problem class. Our…
We introduce the isogeometric shape optimisation of thin shell structures using subdivision surfaces. Both triangular Loop and quadrilateral Catmull-Clark subdivision schemes are considered for geometry modelling and finite element…
In this paper we present a shape optimization scheme which utilizes the alternating direction method of multipliers (ADMM) to approximate a direction of steepest descent in $W^{1,\infty}$. The followed strategy is a combination of the…
This contribution presents a hierarchical multigrid approach for the solution of large-scale finite cell problems on both uniform grids and multi-level hp-discretizations. The proposed scheme leverages the hierarchical nature of the basis…
Multilevel optimization has gained renewed interest in machine learning due to its promise in applications such as hyperparameter tuning and continual learning. However, existing methods struggle with the inherent difficulty of efficiently…
We present a novel optimization-based decoding algorithm for LDPC codes that is suitable for hardware architectures specialized to feed-forward neural networks. The algorithm is based on the projected gradient descent algorithm with a…
The Projected Gradient Descent (PGD) algorithm is a widely used and efficient first-order method for solving constrained optimization problems due to its simplicity and scalability in large design spaces. Building on recent advancements in…
Meshless methods are commonly used to determine numerical solutions to partial differential equations (PDEs) for problems involving free surfaces and/or complex geometries, approximating spatial derivatives at collocation points via local…
Recent numerical experiments have demonstrated that the choice of optimization geometry used during training can impact generalization performance when learning expressive nonlinear model classes such as deep neural networks. These…