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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.09412 |
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| _version_ | 1866912733109157888 |
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| author | Lionello, Chiara Becchi, Matteo Martino, Simone Pavan, Giovanni M. |
| author_facet | Lionello, Chiara Becchi, Matteo Martino, Simone Pavan, Giovanni M. |
| contents | Extracting from trajectory data meaningful information to understand complex molecular systems might be non-trivial. High-dimensional analyses are typically assumed to be desirable, if not required, to prevent losing important information. But to what extent such high-dimensionality is really needed/beneficial often remains unclear. Here we challenge such a fundamental general problem. As a representative case of a system with internal dynamical complexity, we study atomistic molecular dynamics trajectories of liquid water and ice coexisting in dynamical equilibrium at the solid/liquid transition temperature. To attain an intrinsically high-dimensional analysis, we use as an example the Smooth Overlap of Atomic Positions (SOAP) descriptor, obtaining a large dataset containing 2.56e6 576-dimensional SOAP vectors that we analyze in various ways. Our results demonstrate how the time-series data contained in one single SOAP dimension accounting only <0.001% of the total dataset's variance (neglected and discarded in typical variance-based dimensionality-reduction approaches) allows resolving a remarkable amount of information, classifying/discriminating the bulk of water and ice phases, as well as two solid-interface and liquid-interface layers as four statistically distinct dynamical molecular environments. Adding more dimensions to this one is found not only ineffective but even detrimental to the analysis due to recurrent negligible-information/non-negligible-noise additions and "frustrated information" phenomena leading to information loss. Such effects are proven general and are observed also in completely different systems and descriptors' combinations. This shows how high-dimensional analyses are not necessarily better than low-dimensional ones to elucidate the internal complexity of physical/chemical systems, especially when these are characterized by non-negligible internal noise. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_09412 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Relevant, hidden, and frustrated information in high-dimensional analyses of complex dynamical systems with internal noise Lionello, Chiara Becchi, Matteo Martino, Simone Pavan, Giovanni M. Chemical Physics Extracting from trajectory data meaningful information to understand complex molecular systems might be non-trivial. High-dimensional analyses are typically assumed to be desirable, if not required, to prevent losing important information. But to what extent such high-dimensionality is really needed/beneficial often remains unclear. Here we challenge such a fundamental general problem. As a representative case of a system with internal dynamical complexity, we study atomistic molecular dynamics trajectories of liquid water and ice coexisting in dynamical equilibrium at the solid/liquid transition temperature. To attain an intrinsically high-dimensional analysis, we use as an example the Smooth Overlap of Atomic Positions (SOAP) descriptor, obtaining a large dataset containing 2.56e6 576-dimensional SOAP vectors that we analyze in various ways. Our results demonstrate how the time-series data contained in one single SOAP dimension accounting only <0.001% of the total dataset's variance (neglected and discarded in typical variance-based dimensionality-reduction approaches) allows resolving a remarkable amount of information, classifying/discriminating the bulk of water and ice phases, as well as two solid-interface and liquid-interface layers as four statistically distinct dynamical molecular environments. Adding more dimensions to this one is found not only ineffective but even detrimental to the analysis due to recurrent negligible-information/non-negligible-noise additions and "frustrated information" phenomena leading to information loss. Such effects are proven general and are observed also in completely different systems and descriptors' combinations. This shows how high-dimensional analyses are not necessarily better than low-dimensional ones to elucidate the internal complexity of physical/chemical systems, especially when these are characterized by non-negligible internal noise. |
| title | Relevant, hidden, and frustrated information in high-dimensional analyses of complex dynamical systems with internal noise |
| topic | Chemical Physics |
| url | https://arxiv.org/abs/2412.09412 |