Multi-fidelity Data Aggregation Using Convolutional Neural Networks
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Solution Overview
Problem
Current multi-fidelity data aggregation methods face limitations in handling high-dimensional problems, discontinuous functions, and efficiently utilizing all available low-fidelity data, particularly in engineering and scientific applications where high-fidelity and low-fidelity models differ in accuracy and computational cost.
Innovation Solution
The Multi-fidelity Data Aggregation using Convolutional Neural Networks (MDA-CNN) framework treats multi-fidelity data as image data, employing a deep neural network with a local receptive field and convolutional section to capture relationships between high-fidelity and low-fidelity data, allowing for scalable handling of multiple fidelities and flexible nonlinear mappings without assuming specific relationships between data sources.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If Gaussian process methods are used for multi-fidelity modeling, then surrogate modeling capability is provided, but difficulties arise in optimization, approximation of discontinuous functions, and handling high-dimensional problems
Solution Approach 1:
The patent replaces traditional Gaussian process mechanical/mathematical framework with a deep neural network framework. The CNN architecture with local receptive fields substitutes the GP optimization and approximation mechanisms, enabling handling of discontinuous functions and high-dimensional problems while maintaining surrogate modeling capability through learned representations rather than probabilistic inference
Solution Approach 2:
The patent segments the multi-fidelity data processing into distinct convolutional layers, each handling specific fidelity levels. The local receptive field approach divides the input space into localized regions that can be independently processed and then aggregated, enabling efficient handling of high-dimensional data by breaking it into manageable segments
2Productivity
If traditional multi-fidelity methods are used, then some data aggregation is achieved, but not all available low-fidelity data are efficiently utilized
Solution Approach 1:
The patent creates a universal CNN framework that can process any combination of fidelity levels. The architecture is designed to accept multiple input channels representing different fidelity data sources, and the local receptive fields are configured to aggregate information from all available low-fidelity data points, ensuring no data is left unused while maintaining the ability to handle varying data configurations
Solution Approach 2:
The patent transforms the multi-fidelity data aggregation problem into a spatial dimension problem by treating fidelity levels as spatial channels. The local receptive fields operate in this extended dimension space, allowing simultaneous utilization of all low-fidelity data points across multiple dimensions (spatial locations × fidelity levels) rather than processing them sequentially or selecting subsets
3Measurement precision
If high-fidelity models are used, then high accuracy is achieved, but computational cost increases
Solution Approach 1:
The patent merges low-fidelity and high-fidelity data into a unified training framework. The CNN model is trained simultaneously on both fidelity levels with the high-fidelity data serving as ground truth for the local regions where it is available. This merging allows the model to learn accurate mappings in high-fidelity regions while generalizing from low-fidelity data in other regions, achieving high accuracy without requiring high-fidelity computations everywhere
Solution Approach 2:
The patent applies local quality by using local receptive fields that adaptively focus computational resources on regions where high-fidelity data is available. The model learns different mapping relationships in different local regions: in high-fidelity regions, it learns precise mappings from the accurate data, while in low-fidelity regions, it learns approximate mappings that can be refined. This localized approach achieves overall high accuracy while minimizing computational cost by applying high-fidelity processing only where necessary
Data Source
AI summary
A machine-learning framework for multi-fidelity modeling provides three components: multi-fidelity data compiling, multi-fidelity perceptive field and convolution, and deep neural network for mapping. This framework captures and utilizes implicit relationships between any high-fidelity datum and all available low-fidelity data using a defined local perceptive field and convolution. First, the framework treats multi-fidelity data as image data and processes them using a CNN, which is very scalable to high dimensional data with more than two fidelities. Second, the flexibility of nonlinear mapping facilitates the multi-fidelity aggregation and does not need to assume specific relationships among multiple fidelities. Third, the framework does not assume that multi-fidelity data are at the same order or from the same physical mechanisms (e.g., assumptions are needed for some error estimation-based multi-fidelity model).