Mixed Precision in Uncertainty Quantification Methods
| Název práce v češtině: | Mixed Precision in Uncertainty Quantification Methods |
|---|---|
| Název v anglickém jazyce: | Mixed Precision in Uncertainty Quantification Methods |
| Klíčová slova: | Uncertainty quantification|Multilevel|Monte Carlo|Mixed precision|Iterative refinement |
| Klíčová slova anglicky: | Uncertainty quantification|Multilevel|Monte Carlo|Mixed precision|Iterative refinement |
| Akademický rok vypsání: | 2021/2022 |
| Typ práce: | diplomová práce |
| Jazyk práce: | angličtina |
| Ústav: | Katedra numerické matematiky (32-KNM) |
| Vedoucí / školitel: | doc. Erin Claire Carson, Ph.D. |
| Řešitel: | skrytý - zadáno a potvrzeno stud. odd. |
| Datum přihlášení: | 01.02.2022 |
| Datum zadání: | 01.02.2022 |
| Datum potvrzení stud. oddělením: | 14.02.2022 |
| Datum a čas obhajoby: | 09.06.2023 09:00 |
| Datum odevzdání elektronické podoby: | 01.05.2023 |
| Datum odevzdání tištěné podoby: | 09.05.2023 |
| Datum proběhlé obhajoby: | 09.06.2023 |
| Oponenti: | doc. RNDr. Iveta Hnětynková, Ph.D. |
| Konzultanti: | Robert Scheichl |
| Zásady pro vypracování |
| This works involves studying the opportunities for the use of mixed precision within uncertainty quantification methods. After developing a background on mixed precision computation and methods in uncertainty quantification, a model problem (ODE or PDE) will be chosen for study. Numerical experiments will be performed, varying the precision used in different parts of the code to determine how this affects the output. The potential for theoretical explanation and/or generalization to other methods will be explored. |
| Seznam odborné literatury |
| Abdelfattah, A., Anzt, H., Boman, E. G., Carson, E., Cojean, T., Dongarra, J., et al. (2021). A survey of numerical linear algebra methods utilizing mixed-precision arithmetic. The International Journal of High Performance Computing Applications, 35(4), 344-369.
Higham, N. J. (2002). Accuracy and stability of numerical algorithms. Society for industrial and applied mathematics. Dodwell, T. J., Ketelsen, C., Scheichl, R., & Teckentrup, A. L. (2019). Multilevel markov chain monte carlo. Siam Review, 61(3), 509-545. Sullivan, T. J. (2015). Introduction to uncertainty quantification (Vol. 63). Springer. Ghanem, R., Higdon, D., & Owhadi, H. (Eds.). (2017). Handbook of uncertainty quantification (Vol. 6). New York: Springer. |
| Předběžná náplň práce |
| Mathematical models for real-world problems often have parameters that are impossible to fully or accurately determine. In order to access the reliability of model output, it is necessary to quantify the uncertainty in model outputs due to uncertainty in model inputs. This can be achieved through stochastic modeling involving sampling from a posterior distribution. As sampling from the posterior distribution is often intractable, one method is to use a Markov chain Monte Carlo (MCMC) approach. For large-scale applications, however, the high number of samples and accuracy requirements result in the MCMC approach being computationally expensive. A recent development is the idea of multilevel MCMC (MLMCMC), which uses samples at difference resolution levels to reduce the computational cost.
A natural idea is to determine whether we can use low precision in select parts of this computation (i.e., the samples on coarse grid resolutions) to further reduce the computational cost without affecting the output. This could be especially beneficial from a performance standpoint for scenarios where coarse sampling is still the dominant computational cost. |
| Předběžná náplň práce v anglickém jazyce |
| Mathematical models for real-world problems often have parameters that are impossible to fully or accurately determine. In order to access the reliability of model output, it is necessary to quantify the uncertainty in model outputs due to uncertainty in model inputs. This can be achieved through stochastic modeling involving sampling from a posterior distribution. As sampling from the posterior distribution is often intractable, one method is to use a Markov chain Monte Carlo (MCMC) approach. For large-scale applications, however, the high number of samples and accuracy requirements result in the MCMC approach being computationally expensive. A recent development is the idea of multilevel MCMC (MLMCMC), which uses samples at difference resolution levels to reduce the computational cost.
A natural idea is to determine whether we can use low precision in select parts of this computation (i.e., the samples on coarse grid resolutions) to further reduce the computational cost without affecting the output. This could be especially beneficial from a performance standpoint for scenarios where coarse sampling is still the dominant computational cost. |