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About this paper
Atiyo Ghosh, Antonio A. Gentile, Mario Dagrada, Chul Lee, Seong-Hyok Kim, Hyukgeun Cha, Yunjun Choi, Brad Kim and 2 more
Harmonic (Quantum) Neural Networks implement architectural inductive biases to represent harmonic functions, improving accuracy in solving partial differential equations like Laplace's equation. This approach, demonstrated in both classical and quantum settings, generally yields lower Root Mean Squared Error compared to Physics-Informed Neural Networks across various benchmarks.
Key insights
- Architectural inductive biases that directly embed physical laws can surpass soft-constrained methods like PINNs in accurately satisfying PDEs and achieving higher solution accuracy.
- Concepts from complex analysis (e.g., holomorphic functions) and exterior calculus (differential forms) offer powerful mathematical tools to design neural networks that are inherently harmonic by construction.
- The proposed harmonic inductive biases are broadly applicable across both classical and quantum neural network paradigms, providing a pathway for more robust and trainable quantum machine learning models for scientific computing.
Summary by alphaXiv.
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