Related papers: Data-driven computational mechanics
Data-driven control offers a powerful alternative to traditional model-based methods, particularly when accurate system models are unavailable or prohibitively complex. While existing data-driven control methods primarily aim to construct…
This paper is concerned with the finite element discretization of the data driven approach according to arXiv:1510.04232 for the solution of PDEs with a material law arising from measurement data. To simplify the setting, we focus on a…
We study the problem of designing optimal learning and decision-making formulations when only historical data is available. Prior work typically commits to a particular class of data-driven formulation and subsequently tries to establish…
In this article, we present an extension of the formulation recently developed by the authors (A Framework for Data-Driven Computational Mechanics Based on Nonlinear Optimization, arXiv:1910.12736 [math.NA]) to the structural dynamics…
Many stochastic optimization problems include chance constraints that enforce constraint satisfaction with a specific probability; however, solving an optimization problem with chance constraints assumes that the solver has access to the…
Inverse problems are concerned with the reconstruction of unknown physical quantities using indirect measurements and are fundamental across diverse fields such as medical imaging, remote sensing, and material sciences. These problems serve…
Resolvent analysis identifies the most responsive forcings and most receptive states of a dynamical system, in an input--output sense, based on its governing equations. Interest in the method has continued to grow during the past decade due…
Finding extended hydrodynamics equations valid from the dense gas region to the rarefied gas region remains a great challenge. The key to success is to obtain accurate constitutive relations for stress and heat flux. Data-driven models…
This paper presents a model-free data-driven strategy for linear and non-linear finite element computations of open-cell foam. Employing sets of material data, the data-driven problem is formulated as the minimization of a distance function…
At the core of some of the most important problems in plasma physics -- from controlled nuclear fusion to the acceleration of cosmic rays -- is the challenge to describe nonlinear, multi-scale plasma dynamics. The development of reduced…
With the recent wave of digitalization, specifically in the context of safety-critical applications, there has been a growing need for computationally efficient, accurate, generalizable, and trustworthy models. Physics-based models have…
This paper presents a data-driven finite volume method for solving 1D and 2D hyperbolic partial differential equations. This work builds upon the prior research incorporating a data-driven finite-difference approximation of smooth solutions…
We present a data-driven approach to efficiently approximate nonlinear transient dynamics in solid-state systems. Our proposed machine-learning model combines a dimensionality reduction stage with a nonlinear vector autoregression scheme.…
Many real-world scientific processes are governed by complex nonlinear dynamic systems that can be represented by differential equations. Recently, there has been increased interest in learning, or discovering, the forms of the equations…
Data-driven algorithm design is a paradigm that uses statistical and machine learning techniques to select from a class of algorithms for a computational problem an algorithm that has the best expected performance with respect to some…
Data-driven control is a powerful tool that enables the design and implementation of control strategies directly from data without explicitly identifying the underlying system dynamics. While various data-driven control techniques, such as…
The optimization of composition and processing to obtain materials that exhibit desirable characteristics has historically relied on a combination of scientist intuition, trial and error, and luck. We propose a methodology that can…
Attention to data-driven optimization approaches, including the well-known stochastic gradient descent method, has grown significantly over recent decades, but data-driven constraints have rarely been studied, because of the computational…
The distance-minimizing data-driven computational mechanics has great potential in engineering applications by eliminating material modeling error and uncertainty. In this computational framework, the solution-seeking procedure relies on…
This paper proposes a data-driven framework to solve time-varying optimization problems associated with unknown linear dynamical systems. Making online control decisions to regulate a dynamical system to the solution of an optimization…