MapNet Model-Order Reduction for Topology Optimization
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Solution Overview
Problem
Existing methods for topology optimization in large-scale designs face high computational costs due to the need for extensive numerical evaluations and poor transferability of machine learning models across different design settings, particularly in large-scale structural designs.
Innovation Solution
An ANN-based model-order-reduction technique using MapNet, which discretizes structures into fine-scale and coarse-scale meshes, applies FEM to coarse-scale structures, and uses convolutional layers to map coarse-scale mechanical fields to fine-scale fields, reducing computational costs and improving transferability by fragmenting the domain into smaller subdomains.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional FEM-based numerical simulations are used for topology optimization in large-scale designs, then accurate mechanical field computation is achieved, but computational cost becomes prohibitively large
Solution Approach 1:
The patent divides the large-scale design domain into multiple coarse subdomains, trains separate neural network models for each subdomain, and combines their predictions. This segmentation allows the system to achieve fine-scale computational accuracy through coordinated coarse-scale models, dramatically reducing overall computational time while maintaining precision.
Solution Approach 2:
The patent introduces neural network models as intermediary components that map coarse-scale finite element results to fine-scale mechanical fields. These neural networks act as mediators between coarse computational models and fine-scale accuracy requirements, enabling fast predictions without direct fine-scale FEM computations.
2Measurement precision
If machine learning models are trained on entire design domains to improve prediction accuracy, then transferability across different design settings deteriorates
Solution Approach 1:
The patent segments the design domain into multiple coarse subdomains, each with its own trained neural network model. This segmentation enables each model to learn local patterns specific to its subdomain while maintaining the ability to generalize to similar subdomains in different design settings, thereby improving both accuracy and transferability.
Solution Approach 2:
The patent implements local quality by training neural network models specifically for each coarse subdomain rather than using a single global model. Each local model adapts to the specific characteristics of its subdomain while maintaining consistent architecture and training procedures, enabling accurate local predictions that can be combined for global results across varying design settings.
3Measurement precision
If extensive training data is collected to improve model accuracy, then computational cost and data generation time increase
Solution Approach 1:
The patent generates training data by segmenting the design domain into coarse subdomains and computing mechanical fields only at these coarse levels. This segmentation dramatically reduces the computational effort required for training data generation while providing sufficient information for the neural networks to learn accurate mappings to fine-scale fields.
Solution Approach 2:
The patent performs preliminary coarse-scale FEM computations to generate training data before training the neural networks. By pre-computing coarse-scale mechanical fields that serve as training inputs, the system avoids the need for extensive fine-scale FEM computations during the training phase, significantly reducing data generation time.
Data Source
AI summary
In topology optimization (TO) of a structure, a mechanical field of the structure is required to evaluate the objective function and/or constraints. In a model-order-reduction method for efficiently computing the mechanical field, a fine-scale structure modelling the structure is first coarsened to give a coarse-scale structure. A finite element method (FEM) is applied to the coarse-scale structure to obtain a coarse-scale mechanical field. A fine-scale mechanical field is computed from the coarse-scale one instead of using the FEM to directly compute the fine-scale mechanical field from the fine-scale structure, allowing the fine-scale mechanical field with a higher accuracy than the coarse-scale one to be used as the mechanical field while achieving computation cost saving. In generating the fine-scale mechanical field, an artificial neural network, entitled as MapNet, is used to map the coarse-scale mechanical field to the fine-scale one. The MapNet is realizable with convolutional layers and deconvolutional layers.