New Metaplectic Neural Networks Show Promise for Schrödinger Equation Approximation

Researchers have developed a new type of shallow neural network utilizing a dictionary based on metaplectic operators. This approach extends the concept of Barron spaces by incorporating a metaplectic transform, a symplectically motivated extension of the Fourier transform. The study establishes embeddings between these metaplectic Barron spaces and Sobolev spaces, demonstrating Monte Carlo approximation bounds for metaplectic Barron functions using dictionary atoms. A deep neural network architecture built with these dictionary atoms was tested and showed superior performance in approximating solutions to time-dependent Schrödinger equations compared to traditional physics-informed neural networks. AI

IMPACT Introduces a novel neural network architecture with potential for improved performance in solving complex differential equations.

RANK_REASON Academic paper detailing a new neural network architecture and its theoretical underpinnings. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv cs.LG →

• arXiv
• Barron spaces
• Fourier transform
• Metaplectic transformations and finite group actions on noncommutative tori
• Monte Carlo approximations of the Neumann problem
• neural metaplectic dictionary
• physics-informed neural networks
• Schrödinger equations with power potentials
• Sobolev spaces

• paper
• model release

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