Related papers: Conservative data-driven finite element framework
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…
We introduce a novel hybrid methodology combining classical finite element methods (FEM) with neural networks to create a well-performing and generalizable surrogate model for forward and inverse problems. The residual from finite element…
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…
We study mixed finite element methods for the rotating shallow water equations with linearized momentum terms but nonlinear drag. By means of an equivalent second-order formulation, we prove long-time stability of the system without energy…
We present a novel computational paradigm for process design in manufacturing processes that incorporates simulation responses to optimize manufacturing process parameters in high-dimensional temporal and spatial design spaces. We developed…
Numerical simulations of brittle fracture using phase-field approaches often employ a discrete approximation framework that applies the same order of interpolation for the displacement and phase-field variables. Most common is to use linear…
This work is devoted to the development of an efficient and robust technique for accurate capturing of the electric field in multi-material problems. The formulation is based on the finite element method enriched by the introduction of…
Dynamical systems with high intrinsic dimensionality are often characterized by extreme events having the form of rare transitions several standard deviations away from the mean. For such systems, order-reduction methods through projection…
Accurate models are essential for design, performance prediction, control, and diagnostics in complex engineering systems. Physics-based models excel during the design phase but often become outdated during system deployment due to changing…
We present an approach for synthesising observational data with elastodynamic finite element models by extending the statistical finite element method (statFEM) framework. The proposed formulation adopts a Bayesian filtering approach to…
This work presents a general finite element formulation based on a six--field variational principle that incorporates the consistent couple stress theory. A simple, efficient and local iteration free solving procedure that covers both…
We consider a stabilized nonconforming finite element method for data assimilation in incompressible flow subject to the Stokes' equations. The method uses a primal dual structure that allows for the inclusion of nonstandard data. Error…
We present and analyze a linearized finite element method (FEM) for the dynamical incompressible magnetohydrodynamics (MHD) equations. The finite element approximation is based on mixed conforming elements, where Taylor--Hood type elements…
In this paper, we introduce a data-driven modeling approach for dynamics problems with latent variables. The state-space of the proposed model includes artificial latent variables, in addition to observed variables that can be fitted to a…
Thanks to modern manufacturing technologies, heterogeneous materials with complex inner structures (e.g., foams) can be easily produced. However, their utilization is not straightforward, as the classical constitutive laws are not…
In recent years, computational power and data availability breakthroughs have revolutionized our ability to analyze complex physical systems through the inverse problem approach. Data-driven techniques like system identification and machine…
We extend to finite elasticity the Data-Driven formulation of geometrically linear elasticity presented in Conti, M\"uller, Ortiz, Arch.\ Ration.\ Mech.\ Anal.\ 229, 79-123, 2018. The main focus of this paper concerns the formulation of a…
A novel data-driven constitutive modeling approach is proposed, which combines the physics-informed nature of modeling based on continuum thermodynamics with the benefits of machine learning. This approach is demonstrated on…
We propose a novel finite element-based physics-informed operator learning framework that allows for predicting spatiotemporal dynamics governed by partial differential equations (PDEs). The proposed framework employs a loss function…
We propose a novel finite element method scheme for singularly perturbed advection-diffusion-reaction problems, which combines certain quantum-assisted stabilization scheme with a classical h-adaptive approach to provide automatic error…