Mixed Precision in Uncertainty Quantification Methods
| Thesis title in Czech: | Mixed Precision in Uncertainty Quantification Methods |
|---|---|
| Thesis title in English: | Mixed Precision in Uncertainty Quantification Methods |
| Key words: | Uncertainty quantification|Multilevel|Monte Carlo|Mixed precision|Iterative refinement |
| English key words: | Uncertainty quantification|Multilevel|Monte Carlo|Mixed precision|Iterative refinement |
| Academic year of topic announcement: | 2021/2022 |
| Thesis type: | diploma thesis |
| Thesis language: | angličtina |
| Department: | Department of Numerical Mathematics (32-KNM) |
| Supervisor: | Erin Claire Carson, Ph.D. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 01.02.2022 |
| Date of assignment: | 01.02.2022 |
| Confirmed by Study dept. on: | 14.02.2022 |
| Date and time of defence: | 09.06.2023 09:00 |
| Date of electronic submission: | 01.05.2023 |
| Date of submission of printed version: | 09.05.2023 |
| Date of proceeded defence: | 09.06.2023 |
| Opponents: | doc. RNDr. Iveta Hnětynková, Ph.D. |
| Advisors: | Robert Scheichl |
| Guidelines |
| 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. |
| References |
| 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. |
| Preliminary scope of work |
| 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. |
| Preliminary scope of work in English |
| 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. |