Related papers: Towards a machine learning pipeline in reduced ord…

Topology Optimization (TO) provides a systematic approach for obtaining structure design with optimum performance of interest. However, the process requires numerical evaluation of objective function and constraints at each iteration, which…

Machine Learning (ML) methods and tools have gained great success in many data, signal, image and video processing tasks, such as classification, clustering, object detection, semantic segmentation, language processing, Human-Machine…

This paper provides a novel framework for solving multiobjective discrete optimization problems with an arbitrary number of objectives. Our framework formulates these problems as network models, in that enumerating the Pareto frontier…

Recently deep neural networks have been widely and successfully applied in computer vision tasks and attracted growing interests in medical imaging. One barrier for the application of deep neural networks to medical imaging is the need of…

We introduce a manifold-based framework for addressing optimization problems with equality and inequality constraints found in robotics. Our approach transforms the original problem into an unconstrained optimization problem directly on the…

In this work, we describe a new approach that uses deep neural networks (DNN) to obtain regularization parameters for solving inverse problems. We consider a supervised learning approach, where a network is trained to approximate the…

In many areas of engineering, nonlinear numerical analysis is playing an increasingly important role in supporting the design and monitoring of structures. Whilst increasing computer resources have made such formerly prohibitive analyses…

Reduced order models are computationally inexpensive approximations that capture the important dynamical characteristics of large, high-fidelity computer models of physical systems. This paper applies machine learning techniques to improve…

This paper discusses an outer-approximation guided optimization method for constrained neural network inverse problems with rectified linear units. The constrained neural network inverse problems refer to an optimization problem to find the…

Recently developed reduced-order modeling techniques aim to approximate nonlinear dynamical systems on low-dimensional manifolds learned from data. This is an effective approach for modeling dynamics in a post-transient regime where the…

Deep learning-based methods have revolutionized the field of imaging inverse problems, yielding state-of-the-art performance across various imaging domains. The best performing networks incorporate the imaging operator within the network…

In this document, a neural network is employed in order to estimate the solution of the initial value problem in the context of non linear trajectories. Such trajectories can be subject to gravity, thrust, drag, centrifugal force,…

Parametric model order reduction using reduced basis methods can be an effective tool for obtaining quickly solvable reduced order models of parametrized partial differential equation problems. With speedups that can reach several orders of…

This paper proposes a supervised machine learning framework for the non-intrusive model order reduction of unsteady fluid flows to provide accurate predictions of non-stationary state variables when the control parameter values vary. Our…

We consider the problem of learning optimal solutions of a partially known linear optimization problem and recovering its underlying cost function where a set of past decisions and the feasible set are known. We develop a new framework,…

In a wide range of applications it is desirable to optimally control a dynamical system with respect to concurrent, potentially competing goals. This gives rise to a multiobjective optimal control problem where, instead of computing a…

We develop an interpolation-based modeling framework for parameter-dependent partial differential equations arising in control, inverse problems, and uncertainty quantification. The solution is discretized in the physical domain using…

Solving inverse problems, such as parameter estimation and optimal control, is a vital part of science. Many experiments repeatedly collect data and rely on machine learning algorithms to quickly infer solutions to the associated inverse…

We develop a general framework for data-driven approximation of input-output maps between infinite-dimensional spaces. The proposed approach is motivated by the recent successes of neural networks and deep learning, in combination with…

Inverse Problems in medical imaging and computer vision are traditionally solved using purely model-based methods. Among those variational regularization models are one of the most popular approaches. We propose a new framework for applying…