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Adaptive gradient methods, such as AdaGrad, are among the most successful optimization algorithms for neural network training. While these methods are known to achieve better dimensional dependence than stochastic gradient descent (SGD) for…
As more and more multiphysics effects are entering the field of CFD simulations, this raises the question how they can be accurately captured in gradient computations for shape optimization. The latter has been successfully enriched over…
In this paper we show a simplified optimisation approach for free boundary problems in arbitrary space dimensions. This approach is mainly based on an extended operator splitting which allows a decoupling of the domain deformation and…
Many control applications can be formulated as optimization constrained by conservation laws. Such optimization can be efficiently solved by gradient-based methods, where the gradient is obtained through the adjoint method. Traditionally,…
We develop and analyze a set of new sequential simulation-optimization algorithms for large-scale multi-dimensional discrete optimization via simulation problems with a convexity structure. The "large-scale" notion refers to that the…
This paper presents an adaptive discretization strategy for level set topology optimization of structures based on hierarchical B-splines. This work focuses on the influence of the discretization approach and the adaptation strategy on the…
Optimization over the Stiefel manifold is a fundamental computational problem in many scientific and engineering applications. Despite considerable research effort, high-dimensional optimization problems over the Stiefel manifold remain…
Decentralized optimization is a promising parallel computation paradigm for large-scale data analytics and machine learning problems defined over a network of nodes. This paper is concerned with decentralized non-convex composite problems…
This paper considers a class of convex constrained nonsmooth convex stochastic composite optimization problems whose objective function is given by the summation of a differentiable convex component, together with a general nonsmooth but…
We consider minimizing a function consisting of a quadratic term and a proximable term which is possibly nonconvex and nonsmooth. This problem is also known as scaled proximal operator. Despite its simple form, existing methods suffer from…
This article deals with the problem of finding the best topology, pipe diameter choices, and operation parameters for realistic district heating networks. Present design tools that employ non-linear flow and heat transport models for…
We propose a new numerical scheme for approximating level-sets of Lipschitz multivariate functions which is robust to stochastic noise. The algorithm's main feature is an adaptive grid-based stochastic approximation strategy which…
Aerodynamic design optimization is an important problem in aircraft design that depends on the interplay between a numerical optimizer and a high-fidelity flow physics solver. Derivative-based, first and (quasi) second order, optimization…
We present two stochastic descent algorithms that apply to unconstrained optimization and are particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained…
Multidisciplinary engineering system design typically employs a sequential process, progressing from system dynamics to design variables and control. However, this process is inefficient and may lead to a suboptimal design. We propose…
An adjoint based technique is applied to a shallow water model in order to estimate the influence of the model's parameters on the solution. Among parameters the bottom topography, initial conditions, boundary conditions on rigid…
Many physical questions in fluid dynamics can be recast in terms of norm constrained optimisation problems; which in-turn, can be further recast as unconstrained problems on spherical manifolds. Due to the nonlinearities of the governing…
In this paper we present a topology optimization technique applicable to a broad range of flow design problems. We propose also a discrete adjoint formulation effective for a wide class of Lattice Boltzmann Methods (LBM). This adjoint…
In this paper we develop automatic shape differentiation techniques for unfitted discretisations and link these to recent advances in shape calculus for unfitted methods. We extend existing analytic shape calculus results to the case where…
Shallow free surface flows are often characterized by both subdomains that require high modeling complexity and subdomains that can be sufficiently accurately modeled with low modeling complexity. Moreover, these subdomains may change in…