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We present a general numerical approach to shape optimization with state constraints for 2-dimensional geometries, without relaxing the constraints. To do this we reformulate the problem on a fixed reference domain using a conformal…
This work explores an extension of machine learning-optimized piecewise polynomial approximation by incorporating energy optimization as an additional objective. Traditional closed-form solutions enable continuity and approximation targets…
Optimal experimental design (OED) aims to choose the observations in an experiment to be as informative as possible, according to certain statistical criteria. In the linear case (when the observations depend linearly on the unknown…
In this paper we propose a Bayesian method as a numerical way to correct and stabilise projection-based reduced order models (ROM) in computational fluid dynamics problems. The approach is of hybrid type, and consists of the classical…
Within the framework of complex system design, it is often necessary to solve mixed variable optimization problems, in which the objective and constraint functions can depend simultaneously on continuous and discrete variables.…
Automatic underwater vehicle hull Design optimization is a complex engineering process for generating a UUV hull with optimized properties on a given requirement. First, it involves the integration of involved computationally complex…
Designing robot morphologies and kinematics has traditionally relied on human intuition, with little systematic foundation. Motion-design co-optimization offers a promising path toward automation, but two major challenges remain: (i) the…
In this work, we investigate the use of data-driven equation discovery for dynamical systems to model and forecast continuous-time dynamics of unconstrained optimization problems. To avoid expensive evaluations of the objective function and…
In the construction of reduced-order models for dynamical systems, linear projection methods, such as proper orthogonal decompositions, are commonly employed. However, for many dynamical systems, the lower dimensional representation of the…
Sampling conditional distributions is a fundamental task for Bayesian inference and density estimation. Generative models, such as normalizing flows and generative adversarial networks, characterize conditional distributions by learning a…
We develop a method for optimization in shape spaces, i.e., sets of surfaces modulo re-parametrization. Unlike previously proposed gradient flows, we achieve superlinear convergence rates through a subtle approximation of the shape Hessian,…
In this work, we investigate a particular class of shape optimization problems under uncertainties on the input parameters. More precisely, we are interested in the minimization of the expectation of a quadratic objective in a situation…
We introduce Bayesian optimization, a technique developed for optimizing time-consuming engineering simulations and for fitting machine learning models on large datasets. Bayesian optimization guides the choice of experiments during…
We present an optimization-based motion planning algorithm to compute a smooth, collision-free trajectory for a manipulator used to transfer a liquid from a source to a target container. We take into account fluid dynamics constraints as…
In traditional topology optimization, the computing time required to iteratively update the material distribution within a design domain strongly depends on the complexity or size of the problem, limiting its application in real engineering…
In typical applications of Bayesian optimization, minimal assumptions are made about the objective function being optimized. This is true even when researchers have prior information about the shape of the function with respect to one or…
We develop data-driven methods for incorporating physical information for priors to learn parsimonious representations of nonlinear systems arising from parameterized PDEs and mechanics. Our approach is based on Variational Autoencoders…
Particle flow processing is widely employed across various industrial applications and technologies. Due to the complex interactions between particles and fluids, designing effective devices for particle flow processing is challenging. In…
In this paper, we apply the framework of optimal transport to the formulation of optimal design problems. By considering the Wasserstein space as a set of design variables, we associate each probability measure with a shape configuration of…
Established methods for unsupervised representation learning such as variational autoencoders produce none or poorly calibrated uncertainty estimates making it difficult to evaluate if learned representations are stable and reliable. In…