Quantitative Sobolev Approximation Bounds for Neural Operators with Empirical Validation on Burgers’ Equation
Published in Machine Learning: Science and Technology (In Submission), 2025
This research derives quantitative approximation bounds for neural operators in Sobolev norms and provides empirical validation using Fourier Neural Operators on Burgers’ Equation. The work establishes theoretical foundations for understanding the approximation capabilities of neural operators in solving partial differential equations.
Recommended citation: Nicole Hao. (2025). "Quantitative Sobolev Approximation Bounds for Neural Operators with Empirical Validation on Burgers Equation." In submission to Mach. Learn.: Sci. DOI: 10.13140/RG.2.2.32739.62248
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