Learning the intrinsic dynamics of spatio-temporal processes through Latent Dynamics Networks
Abstract Predicting the evolution of systems with spatio-temporal dynamics in response to external stimuli is essential for scientific progress. Traditional equations-based approaches leverage first principles through the numerical approximation of differential equations, thus demanding extensive co...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2024-02-01
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| Series: | Nature Communications |
| Online Access: | https://doi.org/10.1038/s41467-024-45323-x |
| _version_ | 1797273973196587008 |
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| author | Francesco Regazzoni Stefano Pagani Matteo Salvador Luca Dede’ Alfio Quarteroni |
| author_facet | Francesco Regazzoni Stefano Pagani Matteo Salvador Luca Dede’ Alfio Quarteroni |
| author_sort | Francesco Regazzoni |
| collection | DOAJ |
| description | Abstract Predicting the evolution of systems with spatio-temporal dynamics in response to external stimuli is essential for scientific progress. Traditional equations-based approaches leverage first principles through the numerical approximation of differential equations, thus demanding extensive computational resources. In contrast, data-driven approaches leverage deep learning algorithms to describe system evolution in low-dimensional spaces. We introduce an architecture, termed Latent Dynamics Network, capable of uncovering low-dimensional intrinsic dynamics in potentially non-Markovian systems. Latent Dynamics Networks automatically discover a low-dimensional manifold while learning the system dynamics, eliminating the need for training an auto-encoder and avoiding operations in the high-dimensional space. They predict the evolution, even in time-extrapolation scenarios, of space-dependent fields without relying on predetermined grids, thus enabling weight-sharing across query-points. Lightweight and easy-to-train, Latent Dynamics Networks demonstrate superior accuracy (normalized error 5 times smaller) in highly-nonlinear problems with significantly fewer trainable parameters (more than 10 times fewer) compared to state-of-the-art methods. |
| first_indexed | 2024-03-07T14:51:50Z |
| format | Article |
| id | doaj.art-aa3772de0c44430999b6e551a1853e49 |
| institution | Directory Open Access Journal |
| issn | 2041-1723 |
| language | English |
| last_indexed | 2024-03-07T14:51:50Z |
| publishDate | 2024-02-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Nature Communications |
| spelling | doaj.art-aa3772de0c44430999b6e551a1853e492024-03-05T19:40:12ZengNature PortfolioNature Communications2041-17232024-02-0115111610.1038/s41467-024-45323-xLearning the intrinsic dynamics of spatio-temporal processes through Latent Dynamics NetworksFrancesco Regazzoni0Stefano Pagani1Matteo Salvador2Luca Dede’3Alfio Quarteroni4MOX, Department of Mathematics, Politecnico di MilanoMOX, Department of Mathematics, Politecnico di MilanoMOX, Department of Mathematics, Politecnico di MilanoMOX, Department of Mathematics, Politecnico di MilanoMOX, Department of Mathematics, Politecnico di MilanoAbstract Predicting the evolution of systems with spatio-temporal dynamics in response to external stimuli is essential for scientific progress. Traditional equations-based approaches leverage first principles through the numerical approximation of differential equations, thus demanding extensive computational resources. In contrast, data-driven approaches leverage deep learning algorithms to describe system evolution in low-dimensional spaces. We introduce an architecture, termed Latent Dynamics Network, capable of uncovering low-dimensional intrinsic dynamics in potentially non-Markovian systems. Latent Dynamics Networks automatically discover a low-dimensional manifold while learning the system dynamics, eliminating the need for training an auto-encoder and avoiding operations in the high-dimensional space. They predict the evolution, even in time-extrapolation scenarios, of space-dependent fields without relying on predetermined grids, thus enabling weight-sharing across query-points. Lightweight and easy-to-train, Latent Dynamics Networks demonstrate superior accuracy (normalized error 5 times smaller) in highly-nonlinear problems with significantly fewer trainable parameters (more than 10 times fewer) compared to state-of-the-art methods.https://doi.org/10.1038/s41467-024-45323-x |
| spellingShingle | Francesco Regazzoni Stefano Pagani Matteo Salvador Luca Dede’ Alfio Quarteroni Learning the intrinsic dynamics of spatio-temporal processes through Latent Dynamics Networks Nature Communications |
| title | Learning the intrinsic dynamics of spatio-temporal processes through Latent Dynamics Networks |
| title_full | Learning the intrinsic dynamics of spatio-temporal processes through Latent Dynamics Networks |
| title_fullStr | Learning the intrinsic dynamics of spatio-temporal processes through Latent Dynamics Networks |
| title_full_unstemmed | Learning the intrinsic dynamics of spatio-temporal processes through Latent Dynamics Networks |
| title_short | Learning the intrinsic dynamics of spatio-temporal processes through Latent Dynamics Networks |
| title_sort | learning the intrinsic dynamics of spatio temporal processes through latent dynamics networks |
| url | https://doi.org/10.1038/s41467-024-45323-x |
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