Workshop III: Large-Scale Certified Numerical Methods in Quantum Mechanics


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Dates : 02 mai 2022 » 06 mai 2021

Lieu : Los Angeles, CA
États-Unis
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Organisateur : IPAM - Institute for Pure & Applied Mathematics, an NSF Math Institute at UCLA


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Simulating very large quantum systems require new numerical methods and algorithms. Such simulations indeed lead to solving linear and nonlinear systems of equations and eigenvalue problems, that are characterized by high dimensionality, large ranks (for tensor problems), and extreme scale. They must exploit massive parallelism in both space and time and rank-reduction methods, through deterministic or stochastic approaches, optimized data structures, and minimize communication. It is also key to have tools at hands to assess the quality of the simulation results. Error analysis is of major relevance in the simulation of quantum systems, but to date, it has received less attention than in other fields such as fluid or structure dynamics. The error between the exact and computed values of a given physical quantity of interest (QOI), e.g. the dissociation energy of a molecule, has several origins: a model error (resulting from the choice of a computationally tractable, but not extremely accurate, model, e.g. Kohn-Sham with B3LYP functional), a discretization error (resulting from the choice of a finite basis set), an algorithmic error (due to the choice of stopping criteria in Self-Consistent Field and other iterative algorithms), an implementation error (due to possible bugs or uncontrolled round-off errors), a computing error (due to random hardware failures). Quantifying these different sources of errors is key for two reasons. First, guaranteed estimates on these five components of the error would allow one to supplement the computed value of the QOI returned by the numerical simulation with guaranteed error bars (certification of the result). Second, this would allow one to choose the parameters of the simulation (approximate model, discretization parameters, algorithm and stopping criteria, data structures?) in an optimal way in order to minimize the computational effort required to reach the target accuracy (error balancing). Since molecular simulation consumes a massive amount of CPU time in scientific research centers worldwide, this would have a major impact on the use of scientific computing resources.


Workshop III: Large-Scale Certified Numerical Methods in Quantum Mechanics to be held in Los Angeles, CA, États-Unis between 02 mai 2022 and 06 mai 2021. It is organised by IPAM - Institute for Pure & Applied Mathematics, an NSF Math Institute at UCLA . It covers specific areas of Mathématiques et Statistiques such as 0. Visit the website of the conference for more detailed information or contact the organizer for specific questions.
Mathématiques et Statistiques; Physique; Sciences de l'ingénieur; Informatique;
Keywords: Analysis, Quantum Mechanics, Energy, Computing
Ajouter au calendrier 2022-05-02 2021-05-06 Europe/London Workshop III: Large-Scale Certified Numerical Methods in Quantum Mechanics https://www.sciencedz.net/fr/conference/78575-workshop-iii-large-scale-certified-numerical-methods-in-quantum-mechanics Los Angeles, CA - États-Unis IPAM - Institute for Pure & Applied Mathematics, an NSF Math Institute at UCLA

Los Angeles, États-Unis

Los Angeles, États-Unis

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Conférences et séminaires en États-Unis
Conférences et séminaires en États-Unis in 2022
Conférences et séminaires en Mathématiques et Statistiques
Conférences et séminaires en Mathématiques et Statistiques in 2022
Conférences et séminaires en Mathématiques et Statistiques in États-Unis
Conférences et séminaires en Mathématiques et Statistiques in États-Unis in 2022
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