Frequency Domain Neural Networks for Sharp Edge Simulation
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Conventional Fourier Neural Operator (FNO) networks face performance issues in applications with sharp edges or discontinuities due to reduced dimensionality in the frequency domain, leading to inaccurate numerical simulations.
Innovation Solution
The method involves decomposing input data into low-pass and high-pass filtered components, transforming only the low-pass filtered data into the frequency domain, applying weights, and then transforming it back to the original domain, allowing for reduced computational power usage and maintaining higher frequency components relevant to sharp edges.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Power
If data is down-sampled in the frequency domain to reduce computational resources, then computational cost is reduced, but simulation accuracy deteriorates particularly for data with sharp edges
Solution Approach 1:
The patent segments the frequency spectrum into multiple bands (low-pass and high-pass components) and processes them separately. The low-pass components are transformed to the frequency domain for neural network processing, while high-pass components are handled through wavelet transforms, allowing selective processing that preserves accuracy for sharp edges while reducing overall computational load.
Solution Approach 2:
The patent applies different processing quality to different frequency components based on their characteristics. High-frequency components (sharp edges) are processed with higher fidelity through wavelet transforms, while low-frequency components are processed through standard Fourier neural operators, optimizing the balance between computational resources and accuracy for different data features.
2Productivity
If conventional FNO networks are used with reduced dimensionality in frequency domain, then processing speed is improved, but accuracy for applications with sharp edges deteriorates
Solution Approach 1:
The patent segments frequency processing into multiple pathways: a Fourier neural operator pathway for low-pass components and a wavelet transform pathway for high-pass components. This segmentation allows the system to maintain processing speed through efficient Fourier operations while preserving sharp edge accuracy through wavelet-based high-frequency handling.
Solution Approach 2:
The patent creates a hybrid neural operator that combines Fourier neural operator techniques with wavelet transform methods. This composite approach integrates the computational efficiency of Fourier-based methods with the sharp-edge preservation capabilities of wavelet transforms, achieving both speed and accuracy simultaneously.
Data Source
AI summary
In a numerical simulation, input data expressed in at least a first domain is received. The input data is decomposed into at least i) low-pass filtered data that captures a low-pass filtered version of the input data in the at least the first domain and ii) high-pass filtered data that captures a high-pass filtered version of the input data in the at least the first domain. The low-pass filtered data is transformed to frequency domain, and weights are applied to the low-pass filtered data in the frequency domain to generate weighted low-pass filtered data in the frequency domain. The weighted low-pass filtered data is transformed from the frequency domain to the at least the first domain, and output data for the numerical simulation is composed based on at least the weighted low-pass filtered data in the at least the first domain.