Reduced order models based on pod method for schrödinger equations

POD-Enhanced Deep Learning-Based Reduced Order Models for the Real-Time Simulation of Cardiac Electrophysiology in the Left Atrium
by: Stefania Fresca, et al.
Published: (2021-09-01)

Integrating Proper Orthogonal Decomposition with the Crank–Nicolson Finite Element Method for Efficient Solutions of the Schrödinger Equation
by: Xiaohui Chang, et al.
Published: (2025-09-01)

A reduced-order extrapolating collocation spectral method based on POD for the 2D Sobolev equations
by: Shiju Jin, et al.
Published: (2019-03-01)

IGBT Temperature Field Monitoring Based on Reduced-order Model
by: Ziyu Zhou, et al.
Published: (2023-06-01)

POD-based reduced-order modeling study for thermal analysis of gas-cooled microreactor core
by: Erhui Chen, et al.
Published: (2023-04-01)

Reduced-order modeling using the frequency-domain method for parabolic partial differential equations
by: Jeong-Kweon Seo, et al.
Published: (2023-04-01)

Tandem Cascade Flow Prediction by POD-RBFN Reduced Order Model
by: SHANG Xun, et al.
Published: (2022-10-01)

A Galerkin/POD Reduced-Order Model from Eigenfunctions of Non-Converged Time Evolution Solutions in a Convection Problem
by: Jesús Cortés, et al.
Published: (2022-03-01)

Study on Burnup Calculation Method Based on Proper Orthogonal Decomposition Reduced-order
by: ZHANG Binhang1;BI Yanzhao1;GONG Hanyuan1;ZHANG Yonghong1,*;YUAN Xianbao2
Published: (2023-10-01)

Uncertainty Analysis of Neutron Diffusion Eigenvalue Problem Based on Reduced-order Model
by: In order to improve the efficiency of core physical uncertainty analysis based on sampling statistics, the proper orthogonal decomposition (POD) and Galerkin projection method were combined to study the application feasibility of reduced-order model based on POD-Galerkin method in core physical uncertainty analysis. The two-dimensional two group TWIGL benchmark question was taken as the research object, the key variation characteristics of the core flux distribution were extracted under the finite perturbation of the group constants of each material region, and the full-order neutron diffusion problem was projected on the variation characteristics to establish a reduced-order neutron diffusion model. The reduced-order model was used to replace the full-order model to carry out the uncertainty analysis of the group constants of the material region. The results show that the bias of the mathematical expectation of keff calculated by reduced-order and full-order models is close to 1 pcm. In addition, compared with the calculation time required for uncertainty analysis of full-order model, the analysis time of reduced-order model (including the calculation time of the full-order model required for the construction of reduced-order model) is only 11.48%, which greatly improves the efficiency of uncertainty analysis. The biases of mathematical expectation of keff calculated by reduced-order and full-order models based on Latin hypercube sampling and simple random sampling are less than 8 pcm, and under the same sample size, the bias from the Latin hypercube sampling result is smaller. From the TWIGL benchmark test results, under the same sample size, Latin hypercube sampling method is more recommended for POD-Galerkin reduced-order model.
Published: (2023-08-01)

Stability of the higher-order splitting methods for the nonlinear Schrödinger equation with an arbitrary dispersion operator
by: Shalva Amiranashvili, et al.
Published: (2024-06-01)

Computational Modeling of Gurney Flaps and Microtabs by POD Method
by: Unai Fernandez-Gamiz, et al.
Published: (2018-08-01)

POD-Based Model-Order Reduction for Discontinuous Parameters
by: Niklas Karcher
Published: (2022-07-01)

Variational Reduced-Order Modeling of Thermomechanical Shape Memory Alloy Based Cooperative Bistable Microactuators
by: Muhammad Babar Shamim, et al.
Published: (2023-01-01)

A data-driven reduced-order modeling approach for parameterized time-domain Maxwell's equations
by: Mengjun Yu, et al.
Published: (2024-11-01)

Stability of the Additive Splitting Methods for the Generalized Nonlinear Schrödinger Equation
by: Shalva Amiranashvili, et al.
Published: (2025-04-01)

An Application of a Modified Gappy Proper Orthogonal Decomposition on Complexity Reduction of Allen-Cahn Equation
by: Chutipong Dechanubeksa, et al.
Published: (2020-06-01)

Implementation of Reduced-Order Model to Design of Electric Powertrain Rubber Mount
by: Danko Ján, et al.
Published: (2024-05-01)

POD-Galerkin reduced order models and physics-informed neural networks for solving inverse problems for the Navier–Stokes equations
by: Saddam Hijazi, et al.
Published: (2023-03-01)

Projection-based reduced order modeling of an iterative scheme for linear thermo-poroelasticity
by: Francesco Ballarin, et al.
Published: (2024-02-01)

Order reduction of matrix exponentials by proper orthogonal decomposition
by: Mohammad Dehghan Nayyeri, et al.
Published: (2023-11-01)

POD-Galerkin FSI Analysis for Flapping Motion
by: Shigeki Kaneko, et al.
Published: (2023-11-01)

A Reduced-Order Extrapolation (ROE) Method for Solution Coefficient Vectors in the Mixed Finite Element (MFE) Method for the Two-Dimensional (2D) Fourth-Order Hyperbolic Equation
by: Changbiao Yu, et al.
Published: (2022-01-01)

Applying Proper Orthogonal Decomposition to Parabolic Equations: A Reduced Order Numerical Approach
by: Mircea MORARU
Published: (2024-03-01)

Estimating flow fields with reduced order models
by: Kamil David Sommer, et al.
Published: (2023-11-01)

Proper orthogonal decomposition method of constructing a reduced-order model for solving partial differential equations with parametrized initial values
by: Yuto Nakamura, et al.
Published: (2024-03-01)

Reduced-Order Modelling Applied to the Multigroup Neutron Diffusion Equation Using a Nonlinear Interpolation Method for Control-Rod Movement
by: Claire E. Heaney, et al.
Published: (2021-03-01)

Solution of the Schrödinger equation using quadratic B-Spline collocation on non-uniform grids
by: R.A. Adetona, et al.
Published: (2024-03-01)

Data-driven non-intrusive reduced order modelling of selective laser melting additive manufacturing process using proper orthogonal decomposition and convolutional autoencoder
by: Shubham Chaudhry, et al.
Published: (2025-08-01)

Study of Reduced Order Model for Parameterized Flow and Heat Transfer Problems
by: YANG Di1, DUAN Chengjie2, DING Peng2, SONG Juqing3, SONG Zifan2, ZHANG Chunyu1,
Published: (2024-07-01)

Reduced Numerical Approximation of Reduced Fluid-Structure Interaction Problems With Applications in Hemodynamics
by: Claudia M. Colciago, et al.
Published: (2018-06-01)

A POD-Based Reduced-Dimension Method for Solution Coefficient Vectors in the Crank–Nicolson Mixed Finite Element Method for the Fourth-Order Parabolic Equation
by: Xiaohui Chang, et al.
Published: (2025-02-01)

A Comparative Study on the Efficiencies of Aerodynamic Reduced Order Models of Rigid and Aeroelastic Sweptback Wings
by: Özge Özkaya Yılmaz, et al.
Published: (2024-07-01)

Flow Field Prediction of Gas-Solid Fluidized Bed Based on POD and Surrogate Model
by: Jialei FENG, et al.
Published: (2025-01-01)

Real-Time Simulation of Parameter-Dependent Fluid Flows through Deep Learning-Based Reduced Order Models
by: Stefania Fresca, et al.
Published: (2021-07-01)

Parameterized Reduced-Order Models for Probabilistic Analysis of Thermal Protection System Based on Proper Orthogonal Decomposition
by: Kun Zhang, et al.
Published: (2024-03-01)