Related papers: Data-driven finite element method with RVE generat…
A Finite Element procedure based on a full implicit backward Euler predictor/corrector scheme for the Cosserat continuum is here presented. Since this is based on invariants of the stress and couple stress tensors and on the spectral…
The dual aims of accuracy and computational efficiency in computational plasma physics lend themselves well to the use of fluid models. The first of these goals, however, is only satisfied for such models insofar as the utilized closure can…
In this article, we analyze a two-level finite element method for the equations of motion arising in the flow of 2D Oldroyd model with non-smooth initial data. It involves solving the non-linear problem on a coarse grid of mesh-size $H$ and…
Modeling complex dynamical systems under varying conditions is computationally intensive, often rendering high-fidelity simulations intractable. Although reduced-order models (ROMs) offer a promising solution, current methods often struggle…
We develop a methodology to construct low-dimensional predictive models from data sets representing essentially nonlinear (or non-linearizable) dynamical systems with a hyperbolic linear part that are subject to external forcing with…
The synthesis of robust invariant sets for nonlinear systems has traditionally been hindered by the inherent non convexity and a strict reliance on exact analytical models. This paper presents a purely data-driven framework to compute…
This survey presents recent research on determining control-theoretic properties and designing controllers with rigorous guarantees using semidefinite programming and for nonlinear systems for which no mathematical models but measured…
We present an approach for the data-driven modeling of nonlinear viscoelastic materials at small strains which is based on physics-augmented neural networks (NNs) and requires only stress and strain paths for training. The model is built on…
Driven by the need to accelerate numerical simulations, the use of machine learning techniques is rapidly growing in the field of computational solid mechanics. Their application is especially advantageous in concurrent multiscale finite…
We introduce a method that combines neural operators, physics-informed machine learning, and standard numerical methods for solving PDEs. The proposed approach extends each of the aforementioned methods and unifies them within a single…
Important classes of active matter systems can be modeled using kinetic theories. However, kinetic theories can be high dimensional and challenging to simulate. Reduced-order representations based on tracking only low-order moments of the…
We present a physics-informed neural network framework for predicting the mechanical performance of elastomers exposed to concurrent thermal and gamma-radiation exposure, such as elastomers in nuclear cables or space electronics. Our…
A consistent stress-driven nonlocal integral model for nonisothermal structural analysis of elastic nano- and microbeams is proposed. Most nonlocal models of literature are strain-driven and it was shown that such approaches can lead toward…
This paper presents a computational model, based on the Finite Element Method (FEM), that simulates the thermal response of laser-irradiated tissue. This model addresses a gap in the current ecosystem of surgical robot simulators, which…
The increased availability of observation data from engineering systems in operation poses the question of how to incorporate this data into finite element models. To this end, we propose a novel statistical construction of the finite…
The finite element method (FEM) is a well-established numerical method for solving partial differential equations (PDEs). However, its mesh-based nature gives rise to substantial computational costs, especially for complex multiscale…
Correctly capturing intraoperative brain shift in image-guided neurosurgical procedures is a critical task for aligning preoperative data with intraoperative geometry for ensuring accurate surgical navigation. While the finite element…
We propose a Pretrained Finite Element Method (PFEM),a physics driven framework that bridges the efficiency of neural operator learning with the accuracy and robustness of classical finite element methods (FEM). PFEM consists of a physics…
The investigation of fluid-solid systems is very important in a lot of industrial processes. From a computational point of view, the simulation of such systems is very expensive, especially when a huge number of parametric configurations…
In this paper we study the problem of computing minimum-energy controls for linear systems from experimental data. The design of open-loop minimum-energy control inputs to steer a linear system between two different states in finite time is…