Related papers: Data-Driven Solvers for Strongly Nonlinear Materia…

In this paper, we present a data-driven controller design method for continuous-time nonlinear systems, using no model knowledge but only measured data affected by noise. While most existing approaches focus on systems with polynomial…

The increasing decentralization of power systems driven by a large number of renewable energy sources poses challenges in power flow optimization. Partially unknown power line properties can render model-based approaches unsuitable. With…

Neuromorphic computing approaches become increasingly important as we address future needs for efficiently processing massive amounts of data. The unique attributes of quantum materials can help address these needs by enabling new…

In the paper, we present an integrated data-driven modeling framework based on process modeling, material homogenization, mechanistic machine learning, and concurrent multiscale simulation. We are interested in the injection-molded short…

Direct numerical simulation of hierarchical materials via homogenization-based concurrent multiscale models poses critical challenges for 3D large scale engineering applications, as the computation of highly nonlinear and path-dependent…

This paper presents an integrated model-free data-driven approach to solid mechanics, allowing to perform numerical simulations on structures on the basis of measures of displacement fields on representative samples, without postulating a…

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…

Multiple time scale stochastic dynamical systems are ubiquitous in science and engineering, and the reduction of such systems and their models to only their slow components is often essential for scientific computation and further analysis.…

In this paper we develop magnetic induction conforming multiscale formulations for magnetoquasistatic problems involving periodic materials. The formulations are derived using the periodic homogenization theory and applied within a…

We introduce the concept of decision-focused surrogate modeling for solving computationally challenging nonlinear optimization problems in real-time settings. The proposed data-driven framework seeks to learn a simpler, e.g. convex,…

Finite elasticity problems commonly include material and geometric nonlinearities and are solved using various numerical methods. However, for highly nonlinear problems, achieving convergence is relatively difficult and requires small load…

Real-time simulation of elastic structures is essential in many applications, from computer-guided surgical interventions to interactive design in mechanical engineering. The Finite Element Method is often used as the numerical method of…

In this work, we bridge standard adaptive mesh refinement and coarsening on scalable octree background meshes and robust unfitted finite element formulations for the automatic and efficient solution of large-scale nonlinear solid mechanics…

Understanding how complex systems respond to perturbations, such as whether they will remain stable or what their most sensitive patterns are, is a fundamental challenge across science and engineering. Traditional stability and receptivity…

The design of data-driven formulations for machine learning and decision-making with good out-of-sample performance is a key challenge. The observation that good in-sample performance does not guarantee good out-of-sample performance is…

We consider goal-oriented adaptive space-time finite-element discretizations of the parabolic heat equation on completely unstructured simplicial space-time meshes. In some applications, we are interested in an accurate computation of some…

We develop a data-driven framework for learning and correcting non-autonomous vehicle dynamics. Physics-based vehicle models are often simplified for tractability and therefore exhibit inherent model-form uncertainty, motivating the need…

A new fully discrete linearized $H^1$-conforming Lagrange finite element method is proposed for solving the two-dimensional magneto-hydrodynamics equations based on a magnetic potential formulation. The proposed method yields numerical…

Solving different types of optimization models (including parameters fitting) for support vector machines on large-scale training data is often an expensive computational task. This paper proposes a multilevel algorithmic framework that…

This work proposes a data-driven regulator design that drives the output of a nonlinear system asymptotically to a time-varying reference and rejects time-varying disturbances. The key idea is to design a data-driven feedback controller…