Matches in SemOpenAlex for { <https://semopenalex.org/work/W4308462146> ?p ?o ?g. }
Showing items 1 to 88 of
88
with 100 items per page.
- W4308462146 abstract "Abstract Non-periodic solutions are an essential property of chaotic dynamical systems. Simulations with deterministic finite-precision numbers, however, always yield orbits that are eventually periodic. With double-precision 64-bit floating-point numbers such periodic orbits are typically negligible due to very long periods. The emerging trend to accelerate simulations with low-precision numbers, such as 16-bit half-precision floats, raises questions on the fidelity of such simulations of chaotic systems. Here, we revisit the 1-variable chaotic generalised Bernoulli map with various number formats and precisions: floats, posits and logarithmic fixed-point. Simulations are improved with higher precision but stochastic rounding prevents periodic orbits even at low precision. For larger systems the performance gain from low-precision simulations is often reinvested in higher resolution or complexity, increasing the number of variables. In the Lorenz 1996 system, the period lengths of orbits increase exponentially with the number of variables. Moreover, invariant measures are better approximated with an increased number of variables than with increased precision. Extrapolating to large simulations of natural systems, such as million-variable climate models, periodic orbit lengths are far beyond reach of present-day computers. Such orbits are therefore not expected to be problematic compared to high-precision simulations but the deviation of both from the continuum solution remains unclear." @default.
- W4308462146 created "2022-11-12" @default.
- W4308462146 creator A5013131077 @default.
- W4308462146 creator A5021423474 @default.
- W4308462146 creator A5066453821 @default.
- W4308462146 creator A5074719970 @default.
- W4308462146 date "2022-11-08" @default.
- W4308462146 modified "2023-10-14" @default.
- W4308462146 title "Periodic orbits in chaotic systems simulated at low precision" @default.
- W4308462146 cites W2204310803 @default.
- W4308462146 cites W2207050309 @default.
- W4308462146 cites W2763018387 @default.
- W4308462146 cites W2944526643 @default.
- W4308462146 cites W3014370804 @default.
- W4308462146 cites W3047358464 @default.
- W4308462146 cites W3097283637 @default.
- W4308462146 cites W3101543398 @default.
- W4308462146 cites W3132840842 @default.
- W4308462146 doi "https://doi.org/10.21203/rs.3.rs-2223046/v1" @default.
- W4308462146 hasPublicationYear "2022" @default.
- W4308462146 type Work @default.
- W4308462146 citedByCount "0" @default.
- W4308462146 crossrefType "posted-content" @default.
- W4308462146 hasAuthorship W4308462146A5013131077 @default.
- W4308462146 hasAuthorship W4308462146A5021423474 @default.
- W4308462146 hasAuthorship W4308462146A5066453821 @default.
- W4308462146 hasAuthorship W4308462146A5074719970 @default.
- W4308462146 hasBestOaLocation W43084621461 @default.
- W4308462146 hasConcept C111919701 @default.
- W4308462146 hasConcept C11413529 @default.
- W4308462146 hasConcept C121332964 @default.
- W4308462146 hasConcept C121864883 @default.
- W4308462146 hasConcept C127413603 @default.
- W4308462146 hasConcept C134306372 @default.
- W4308462146 hasConcept C136625980 @default.
- W4308462146 hasConcept C146978453 @default.
- W4308462146 hasConcept C151510863 @default.
- W4308462146 hasConcept C152361515 @default.
- W4308462146 hasConcept C154945302 @default.
- W4308462146 hasConcept C182365436 @default.
- W4308462146 hasConcept C196644772 @default.
- W4308462146 hasConcept C2777052490 @default.
- W4308462146 hasConcept C33923547 @default.
- W4308462146 hasConcept C35912277 @default.
- W4308462146 hasConcept C39927690 @default.
- W4308462146 hasConcept C41008148 @default.
- W4308462146 hasConcept C62520636 @default.
- W4308462146 hasConcept C79379906 @default.
- W4308462146 hasConcept C84211073 @default.
- W4308462146 hasConcept C97355855 @default.
- W4308462146 hasConceptScore W4308462146C111919701 @default.
- W4308462146 hasConceptScore W4308462146C11413529 @default.
- W4308462146 hasConceptScore W4308462146C121332964 @default.
- W4308462146 hasConceptScore W4308462146C121864883 @default.
- W4308462146 hasConceptScore W4308462146C127413603 @default.
- W4308462146 hasConceptScore W4308462146C134306372 @default.
- W4308462146 hasConceptScore W4308462146C136625980 @default.
- W4308462146 hasConceptScore W4308462146C146978453 @default.
- W4308462146 hasConceptScore W4308462146C151510863 @default.
- W4308462146 hasConceptScore W4308462146C152361515 @default.
- W4308462146 hasConceptScore W4308462146C154945302 @default.
- W4308462146 hasConceptScore W4308462146C182365436 @default.
- W4308462146 hasConceptScore W4308462146C196644772 @default.
- W4308462146 hasConceptScore W4308462146C2777052490 @default.
- W4308462146 hasConceptScore W4308462146C33923547 @default.
- W4308462146 hasConceptScore W4308462146C35912277 @default.
- W4308462146 hasConceptScore W4308462146C39927690 @default.
- W4308462146 hasConceptScore W4308462146C41008148 @default.
- W4308462146 hasConceptScore W4308462146C62520636 @default.
- W4308462146 hasConceptScore W4308462146C79379906 @default.
- W4308462146 hasConceptScore W4308462146C84211073 @default.
- W4308462146 hasConceptScore W4308462146C97355855 @default.
- W4308462146 hasLocation W43084621461 @default.
- W4308462146 hasOpenAccess W4308462146 @default.
- W4308462146 hasPrimaryLocation W43084621461 @default.
- W4308462146 hasRelatedWork W2021921500 @default.
- W4308462146 hasRelatedWork W2034761477 @default.
- W4308462146 hasRelatedWork W2118569990 @default.
- W4308462146 hasRelatedWork W2134876043 @default.
- W4308462146 hasRelatedWork W2535419677 @default.
- W4308462146 hasRelatedWork W2544512391 @default.
- W4308462146 hasRelatedWork W2624158749 @default.
- W4308462146 hasRelatedWork W2950918715 @default.
- W4308462146 hasRelatedWork W4232872402 @default.
- W4308462146 hasRelatedWork W4234915478 @default.
- W4308462146 isParatext "false" @default.
- W4308462146 isRetracted "false" @default.
- W4308462146 workType "article" @default.