Harmonic Neural Networks

Atiyo Ghosh, Antonio Andrea Gentile, Mario Dagrada, Chul Lee, Seong-Hyok Sean Kim, Hyukgeun Cha, Yunjun Choi, Dongho Kim, Jeong-Il Kye, Vincent Emanuel Elfving
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:11340-11359, 2023.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-ghosh23b, title = {Harmonic Neural Networks}, author = {Ghosh, Atiyo and Gentile, Antonio Andrea and Dagrada, Mario and Lee, Chul and Kim, Seong-Hyok Sean and Cha, Hyukgeun and Choi, Yunjun and Kim, Dongho and Kye, Jeong-Il and Elfving, Vincent Emanuel}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {11340--11359}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/ghosh23b/ghosh23b.pdf}, url = {https://proceedings.mlr.press/v202/ghosh23b.html}, 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.} }
Endnote
%0 Conference Paper %T Harmonic Neural Networks %A Atiyo Ghosh %A Antonio Andrea Gentile %A Mario Dagrada %A Chul Lee %A Seong-Hyok Sean Kim %A Hyukgeun Cha %A Yunjun Choi %A Dongho Kim %A Jeong-Il Kye %A Vincent Emanuel Elfving %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-ghosh23b %I PMLR %P 11340--11359 %U https://proceedings.mlr.press/v202/ghosh23b.html %V 202 %X 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.
APA
Ghosh, A., Gentile, A.A., Dagrada, M., Lee, C., Kim, S.S., Cha, H., Choi, Y., Kim, D., Kye, J. & Elfving, V.E.. (2023). Harmonic Neural Networks. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:11340-11359 Available from https://proceedings.mlr.press/v202/ghosh23b.html.

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