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

This paper proposes a novel approach to addressing the output synchronization problem in unknown heterogeneous multi-agent systems (MASs) using noisy data. Unlike existing studies that focus on noiseless data, we introduce a distributed…

In this contribution, we present a new Materials Knowledge System framework for microstructure-sensitive predictions of effective stress--strain responses in composite materials. The model is developed for composites with a wide range of…

We propose, analyze, and test new robust iterative solvers for systems of linear algebraic equations arising from the space-time finite element discretization of reduced optimality systems defining the approximate solution of hyperbolic…

We develop a fully data-driven model of anisotropic finite viscoelasticity using neural ordinary differential equations as building blocks. We replace the Helmholtz free energy function and the dissipation potential with data-driven…

This paper presents a robust data-driven controller design based on the noisy input-output data without assumptions on the statistical properties of the noises. We start with the direct data-representation of system models that take…

We present a novel data-driven model predictive control (MPC) approach to control unknown nonlinear systems using only measured input-output data with closed-loop stability guarantees. Our scheme relies on the data-driven system…

Conservation laws are an inherent feature in many systems modeling real world phenomena, in particular, those modeling biological and chemical systems. If the form of the underlying dynamical system is known, linear algebra and algebraic…

In a variational denoising model, weight in the data fidelity term plays the role of enhancing the noise-removal capability. It is profoundly correlated with noise information, while also balancing the data fidelity and regularization…

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.…

This work addresses inverse linear optimization where the goal is to infer the unknown cost vector of a linear program. Specifically, we consider the data-driven setting in which the available data are noisy observations of optimal…

We present a novel data-driven distributionally robust Model Predictive Control formulation for unknown discrete-time linear time-invariant systems affected by unknown and possibly unbounded additive uncertainties. We use off-line collected…

We show that machine learning can improve the accuracy of simulations of stress waves in one-dimensional composite materials. We propose a data-driven technique to learn nonlocal constitutive laws for stress wave propagation models. The…

We consider goal-oriented adaptive space-time finite-element discretizations of the regularized parabolic p-Laplace problem on completely unstructured simplicial space-time meshes. The adaptivity is driven by the dual-weighted residual…

In order to generate initial data for nonlinear relativistic simulations, one needs to solve the Einstein constraints, which can be cast into a coupled set of nonlinear elliptic equations. Here we present an approach for solving these…

We propose a robust data-driven output feedback control algorithm that explicitly incorporates inherent finite-sample model estimate uncertainties into the control design. The algorithm has three components: (1) a subspace identification…

Obtaining predictive low-order models is a central challenge in fluid dynamics. Data-driven frameworks have been widely used to obtain low-order models of aerodynamic systems; yet, resulting models tend to yield predictions that grow…

A three-dimensional multi-scale computational homogenisation framework is developed for the prediction of nonlinear micro/meso-mechanical response of the fibre-reinforced polymer (FRP) composites. Two dominant damage mechanisms, i.e. matrix…

Data-driven methods are becoming an essential part of computational mechanics due to their unique advantages over traditional material modeling. Deep neural networks are able to learn complex material response without the constraints of…

In solid mechanics, Data-driven approaches are widely considered as the new paradigm that can overcome the classic problems of constitutive models such as limiting hypothesis, complexity, and high dependence on training data. However,…

For more than two centuries, solutions of differential equations have been obtained either analytically or numerically based on typically well-behaved forcing and boundary conditions for well-posed problems. We are changing this paradigm in…