核心概念
Efficiently generate tailored quadrature rules for computational models using tensor structures.
要約
The article introduces a novel framework for generating partially tensor-structured quadrature rules to enhance the efficiency of the graph-accelerated non-intrusive polynomial chaos method. It addresses uncertainty quantification problems in multidisciplinary systems by optimizing computational model evaluations. The content is structured as follows:
- Introduction to Uncertainty Quantification (UQ) and Polynomial Chaos Expansion (PCE)
- Background on NIPC Method and Numerical Quadrature Rules
- Computational Graph Transformations for Efficient Model Evaluations on Tensor Grids
- Methodology for Generating Tensor-Structured Quadrature Rules with AMTC Integration
The article discusses the challenges of scaling full-grid integration-based NIPC methods to higher dimensions due to the exponential increase in quadrature points. It proposes a new approach of generating tailored, partially tensor-structured quadrature rules that outperform traditional methods in terms of computational costs.
Key Highlights:
- Introduction to UQ and PCE methods for uncertainty quantification.
- Comparison of integration-based and regression-based NIPC methods.
- Explanation of numerical quadrature rules like Gauss quadrature and designed quadrature methods.
- Introduction of AMTC method for efficient model evaluations on tensor grids.
- Proposal of a novel framework for generating tailored, partially tensor-structured quadrature rules.
統計
Recently, the graph-accelerated non-intrusive polynomial chaos (NIPC) method has been proposed for solving uncertainty quantification (UQ) problems.
Numerical results show that the proposed approach generates a partially tensor-structured quadrature rule that outperforms existing methods by more than 40% in computational costs.