Authors: Daniel Zhengyu Huang, Nicholas H. Nelsen, Margaret Trautner

Published on: February 08, 2024

Impact Score: 8.22

Arxiv code: Arxiv:2402.06031

Summary

• What is new: Introduces Fourier Neural Mappings (FNMs) for handling finite-dimensional parametrized physical models, with a focus on efficiency and effectiveness in data use.
• Why this is important: Existing surrogates struggle with finite-dimensional data for inputs and outputs of physical models.
• What the research proposes: Fourier Neural Mappings framework that accommodates finite-dimensional data and analyzes the efficiency of learning parametrized physical models directly versus an indirect approach.
• Results: Numerical experiments show FNMs offer significant improvements in approximating non-linear parametrized models, demonstrating the advantage of the proposed method.

Technical Details

Technological frameworks used: Fourier Neural Operators extended into Fourier Neural Mappings

Models used: Bayesian nonparametric regression of linear functionals for theoretical analysis

Data used: Finite-dimensional parametrizations of model inputs and outputs

Potential Impact

Sectors relying on computational modeling and simulation, like aerospace, automotive, climate science, and engineering software providers.

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