Related papers: Machine Learning and Finite Element Method for Phy…
The development of accurate constitutive models for materials that undergo path-dependent processes continues to be a complex challenge in computational solid mechanics. Challenges arise both in considering the appropriate model assumptions…
Data-driven modeling and machine learning are widely used to model the behavior of dynamic systems. One application is the residual evaluation of technical systems where model predictions are compared with measurement data to create…
Machine learning is finding increasingly broad application in the physical sciences. This most often involves building a model relationship between a dependent, measurable output and an associated set of controllable, but complicated,…
Modeling biological processes is a highly demanding task because not all processes are fully understood. Mathematical models allow us to test hypotheses about possible mechanisms of biological processes. The mathematical mechanisms…
Over the past decade inter-atomic potentials based on machine-learning (ML) techniques have become an indispensable tool in the atomic-scale modeling of materials. Trained on energies and forces obtained from electronic-structure…
The simulation of large nonlinear dynamical systems, including systems generated by discretization of hyperbolic partial differential equations, can be computationally demanding. Such systems are important in both fluid and kinetic…
Machine learning has emerged as a significant approach to efficiently tackle electronic structure problems. Despite its potential, there is less guarantee for the model to generalize to unseen data that hinders its application in real-world…
The integration of machine learning (ML) with traditional physics-based models is reshaping the landscape of weather and climate prediction. On their own, ML-based and physics-based approaches each have significant benefits - but also…
Machine learning has been increasingly applied in climate modeling on system emulation acceleration, data-driven parameter inference, forecasting, and knowledge discovery, addressing challenges such as physical consistency, multi-scale…
Modeling an unknown dynamical system is crucial in order to predict the future behavior of the system. A standard approach is training recurrent models on measurement data. While these models typically provide exact short-term predictions,…
Molecular dynamics simulations are an important tool for describing the evolution of a chemical system with time. However, these simulations are inherently held back either by the prohibitive cost of accurate electronic structure theory…
We develop an interpolation-based modeling framework for parameter-dependent partial differential equations arising in control, inverse problems, and uncertainty quantification. The solution is discretized in the physical domain using…
Finite mixture models have been a very important tool for exploring complex data structures in many scientific areas, for example, economics, epidemiology, finance. In the past decade, semiparametric techniques have been popularly…
High-throughput data generation methods and machine learning (ML) algorithms have given rise to a new era of computational materials science by learning relationships among composition, structure, and properties and by exploiting such…
We formulate a cut finite element method for linear elasticity based on higher order elements on a fixed background mesh. Key to the method is a stabilization term which provides control of the jumps in the derivatives of the finite element…
Computer simulation models are widely used to study complex physical systems. A related fundamental topic is the inverse problem, also called calibration, which aims at learning about the values of parameters in the model based on…
The ability to construct, use, and revise models is a crucial experimental physics skill. Many existing frameworks describe modeling in science education at introductory levels. However, most have limited applicability to the context of…
With the evolution of numerical methods, we are now aiming at not only qualitative understanding but also quantitative prediction and design of quantum many-body phenomena. As a novel numerical approach, machine learning techniques have…
This article takes the form of a tutorial on the use of a particular class of mixed finite element methods, which can be thought of as the finite element extension of the C-grid staggered finite difference method. The class is often…
The Finite Element Method (FEM) is a powerful computational tool for solving partial differential equations (PDEs). Although commercial and open-source FEM software packages are widely available, an independent implementation of FEM…