Related papers: Conservative data-driven finite element framework
This paper presents a practical case study of a data-driven magnetostatic finite element solver applied to a real-world three-dimensional problem. Instead of using a hard-coded phenomenological material model within the solver, the…
In the analysis of composite materials with heterogeneous microstructures, full resolution of the heterogeneities using classical numerical approaches can be computationally prohibitive. This paper presents a micromechanics-enhanced finite…
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…
A data driven finite element method (DDFEM) that accounts for more than two material state variables has been presented in this work. DDFEM framework is motivated from (1,2) and can account for multiple state variables, viz. stresses,…
Standard finite element discretizations of the Richards equation may violate the discrete minimum principle, producing unphysical negative saturations. While existing bound-preserving methods typically rely on computationally expensive…
Computational multiscale methods for analyzing and deriving constitutive responses have been used as a tool in engineering problems because of their ability to combine information at different length scales. However, their application in 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,…
We introduce the concept of data-driven finite element methods. These are finite-element discretizations of partial differential equations (PDEs) that resolve quantities of interest with striking accuracy, regardless of the underlying mesh…
We introduce a data-driven approach to the modelling and analysis of viscous fluid mechanics. Instead of including constitutive laws for the fluid's viscosity in the mathematical model, we suggest to directly use experimental data. Only a…
This paper presents a physics and data co-driven surrogate modeling method for efficient rare event simulation of civil and mechanical systems with high-dimensional input uncertainties. The method fuses interpretable low-fidelity physical…
Finite element methods provide accurate and efficient methods for the numerical solution of partial differential equations by means of restricting variational problems to finite-dimensional approximating spaces. However, they do not…
This paper presents a data-driven nonlinear safe control design approach for discrete-time systems under parametric uncertainties and additive disturbances. We first characterize a new control structure from which a data-based…
A conservative finite-volume framework, based on a collocated variable arrangement, for the simulation of flows at all speeds, applicable to incompressible, ideal-gas and real-gas fluids is proposed in conjunction with a fully-coupled…
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…
This paper presents a data-driven receding horizon control framework for discrete-time linear systems that guarantees robust performance in the presence of bounded disturbances. Unlike the majority of existing data-driven predictive control…
In this paper, we present a machine learning-based data generator framework tailored to aid researchers who utilize simulations to examine various physical systems or processes. High computational costs and the resulting limited data often…
Generative models such as denoising diffusion models are quickly advancing their ability to approximate highly complex data distributions. They are also increasingly leveraged in scientific machine learning, where samples from the implied…
Immersed finite element methods provide a convenient analysis framework for problems involving geometrically complex domains, such as those found in topology optimization and microstructures for engineered materials. However, their…
Computational modeling of a complex system is limited by the parts of the system with the least information. While detailed models and high-resolution data may be available for parts of a system, abstract relationships are often necessary…
We present a domain decomposition strategy for developing structure-preserving finite element discretizations from data when exact governing equations are unknown. On subdomains, trainable Whitney form elements are used to identify…