Harmonic (Quantum) Neural Networks

• URL: http://arxiv.org/abs/2212.07462v2
• Date: Sun, 13 Aug 2023 08:58:00 GMT
• Title: Harmonic (Quantum) Neural Networks
• Authors: Atiyo Ghosh, Antonio A. Gentile, Mario Dagrada, Chul Lee, Seong-Hyok Kim, Hyukgeun Cha, Yunjun Choi, Brad Kim, Jeong-Il Kye, Vincent E. Elfving
• Abstract summary: Harmonic functions are abundant in nature, appearing in limiting cases of Maxwell's, Navier-Stokes equations, the heat and the wave equation. Despite their ubiquity and relevance, there have been few attempts to incorporate inductive biases towards harmonic functions in machine learning contexts. We show effective means of representing harmonic functions in neural networks and extend such results to quantum neural networks.
• Score: 10.31053131199922
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Harmonic functions are abundant in nature, appearing in limiting cases of Maxwell's, Navier-Stokes equations, the heat and the wave equation. Consequently, there are many applications of harmonic functions from industrial process optimisation to robotic path planning and the calculation of first exit times of random walks. Despite their ubiquity and relevance, there have been few attempts to incorporate inductive biases towards harmonic functions in machine learning contexts. In this work, we demonstrate effective means of representing harmonic functions in neural networks and extend such results also to quantum neural networks to demonstrate the generality of our approach. We benchmark our approaches against (quantum) physics-informed neural networks, where we show favourable performance.

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