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Computational design optimization in fluid dynamics usually requires to solve non-linear partial differential equations numerically. In this work, we explore a Bayesian optimization approach to minimize an object's drag coefficient in…
High fidelity simulations, e.g., large eddy simulation are often needed for accurately predicting pressure losses due to wake mixing in turbomachinery applications. An unsteady adjoint of such high fidelity simulations is useful for design…
We study a method based on Balancing Domain Decomposition by Constraints (BDDC) for a numerical solution of a single-phase flow in heterogenous porous media. The method solves for both flux and pressure variables. The fluxes are resolved in…
We present a distributed conjugate gradient method for distributed optimization problems, where each agent computes an optimal solution of the problem locally without any central computation or coordination, while communicating with its…
We propose new sequential simulation-optimization algorithms for general convex optimization via simulation problems with high-dimensional discrete decision space. The performance of each choice of discrete decision variables is evaluated…
Mathematical models that couple partial differential equations (PDEs) and spatially distributed ordinary differential equations (ODEs) arise in biology, medicine, chemistry and many other fields. In this paper we discuss an extension to the…
This paper considers the optimal control problem for realizing logical gates in a closed quantum system. The quantum state is governed by Schrodinger's equation, which we formulate as a time-dependent Hamiltonian system in terms of the real…
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 automotive engineering, designing for optimal vehicle dynamics is challenging due to the complexities involved in analysing the behaviour of a multibody system. Typically, a simplified set of dynamics equations for only the key bodies of…
We address the problem of solving convex optimization problems with many convex constraints in a distributed setting. Our approach is based on an extension of the alternating direction method of multipliers (ADMM) that recently gained a lot…
Accurate and efficient prediction of multi-scale flows remains a formidable challenge. Constructing theoretical models and numerical methods often involves the design and optimization of parameters. While gradient descent methods have been…
Distributed machine learning has recently become a critical paradigm for training large models on vast datasets. We examine the stochastic optimization problem for deep learning within synchronous parallel computing environments under…
Differentiable simulation enables gradients to be back-propagated through physics simulations. In this way, one can learn the dynamics and properties of a physics system by gradient-based optimization or embed the whole differentiable…
Many engineering problems involve learning hidden dynamics from indirect observations, where the physical processes are described by systems of partial differential equations (PDE). Gradient-based optimization methods are considered…
With the maturation of differentiable physics, its role in various downstream applications: such as model predictive control, robotic design optimization, and neural PDE solvers, has become increasingly important. However, the derivative…
We consider a scalar function depending on a numerical solution of an initial value problem, and its second-derivative (Hessian) matrix for the initial value. The need to extract the information of the Hessian or to solve a linear system…
Matched layers are commonly used in numerical simulations of wave propagation to model (semi-)infinite domains. Attenuation functions describe the damping in layers, and provide a matching of the wave impedance at the interface between the…
Free-form shape optimization techniques are investigated to improve the separation efficiency of structured packings in laboratory-scale distillation columns. A simplified simulation model based on computational fluid dynamics (CFD) for the…
The paper is concerned with an adjoint complement to the Volume-of-Fluid (VoF) method for immiscible two-phase flows, e.g. air and water, which is widely used in marine engineering due to its computational efficiency. The particular…
We derive a formula for the adjoint $\overline{A}$ of a square-matrix operation of the form $C=f(A)$, where $f$ is holomorphic in the neighborhood of each eigenvalue. We then apply the formula to derive closed-form expressions in particular…