Deep Learning Stiffness Matrix Generation for Cross-Domain FEM
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
The finite element method suffers from computational inefficiencies due to errors caused by assuming internal fields as interpolation functions that do not account for shape and physical property changes, leading to increased computation time, and trained deep learning networks are domain-specific, limiting their applicability when the analysis domain changes.
Innovation Solution
A deep learning system that generates a stiffness matrix by training a network with normalized finite elements, using a data generation unit to create training data, a strain computation unit to compute reference strain values, and a training control unit to minimize differences between computed and reference strain values, allowing the network to be applied to various domains.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the finite element method uses interpolation functions to assume internal fields, then the analysis can be performed, but computational efficiency is lowered due to errors from not reflecting shape and physical property changes
Solution Approach 1:
The patent replaces the traditional finite element method's mechanical interpolation function approach with a deep learning-based neural network system. The neural network directly approximates the relationship between geometric information and stiffness matrices without using conventional interpolation functions, thereby eliminating the computational inefficiencies and accuracy errors associated with shape function assumptions while maintaining high computational efficiency and accuracy.
Solution Approach 2:
The patent transforms the problem from using fixed interpolation functions to using learned parameters through neural network training. By training the neural network on normalized finite element data with various geometric configurations and physical properties, the system adapts its internal parameters to accurately represent different domains, achieving both high accuracy and computational efficiency without the limitations of conventional parameterization methods.
2Reliability
If a deep learning network is trained for a specific domain, then excellent numerical analysis performance is obtained, but the network cannot be used when the domain is changed
Solution Approach 1:
The patent creates a universal neural network model that can handle multiple different domains by training it on normalized finite element data representing various geometric configurations and physical properties. The network learns general patterns and relationships that are applicable across different domains, allowing it to be used for analysis in any domain without requiring domain-specific retraining, thus achieving both high performance and broad adaptability.
Solution Approach 2:
The patent employs parameter transformation through data normalization to enable the neural network to generalize across different domains. By normalizing the input data to a standard format and training the network on this normalized data, the model learns invariant features that allow it to adapt to different physical domains and geometric configurations without requiring retraining, achieving universal applicability while maintaining high numerical analysis performance.
Data Source
AI summary
The present disclosure includes a data generation unit to generate a normalized finite element as training data, a strain computation unit to compute reference strain values based on the generated training data, a deep learning network including a plurality of layers each having a preset weight and to generate a matching matrix, in which the reference strain values and displacements set for the training data match each other based on arbitrary attribute information and geometric information as position information related to variable points, and a training control unit to train the deep learning network based on a cost function by which differences between strain values computed according to the matching matrix and the reference strain values are equal to or smaller than a threshold value.