uq
Differences
This shows you the differences between two versions of the page.
Both sides previous revisionPrevious revision | |||
uq [2018/12/03 11:08] – [Hessian Bracketing Algorithm] slongbottom | uq [2019/10/08 19:10] (current) – removed slongbottom | ||
---|---|---|---|
Line 1: | Line 1: | ||
- | ====== Uncertainty Quantification ====== | ||
- | |||
- | ---- | ||
- | |||
- | //potfit// uses the potential ensemble method ((Frederiksen, | ||
- | |||
- | To enable this feature, compile //potfit// with the '' | ||
- | |||
- | < | ||
- | |||
- | This generates an ensemble of potentials whose spread can be used to quantify the uncertainties in the fitted parameters. Taking an uncorrelated subsample of the MCMC output forms a potential ensemble representing the uncertainties in each parameter by the ensemble spread and covariance. Propagating the uncertainty represented by the ensemble members through molecular dynamics, the resultant uncertainties in quantities of interest can be obtained. For an example of this see ((Longbottom, | ||
- | |||
- | ===== The Ensemble Method ===== | ||
- | |||
- | An ensemble of potentials are generated by taking a series on Markov chain Monte Carlo steps starting from the best fit potential parameters. The step size in each parameter direction is scaled dependant on the curvature in each parameter. This is encoded using information about the eigenvalues of the hessian at the best fit potential minimum, for potential parameters $\Theta=\{\theta_1, | ||
- | |||
- | \begin{equation} | ||
- | \Delta\theta_{i}=\sum_{j=1}^{\rm N}\sqrt{\frac{\rm R}{{\rm{max}} (1, | ||
- | \end{equation} | ||
- | where $\lambda_j$ are the hessian eigenvalues, | ||
- | |||
- | The MCMC algorithm samples potentials from the distribution at a temperature, | ||
- | |||
- | ===== Hessian Bracketing Algorithm ===== | ||
- | |||
- | **Only use this if you know what you are doing! ** | ||
- | |||
- | If '' | ||
- | |||
- | If the landscape at this scale is not harmonic, the eigenvalues of the hessian will be negative. In this case a reduced sampling temperature may be required and the user should think about improving the reference data being fit to, as well as the suitability and possible limitations of the potential model being used. | ||
- | ===== Parameters ===== | ||
- | |||
- | |<100% 33% 33% 33%>| | ||
- | ^ parameter name | parameter type | default value | | ||
- | | short explanation. ||| | ||
- | |||
- | ==== Required parameters | ||
- | |||
- | |<100% 33% 33% 33%>| | ||
- | ^ **acc_rescaling*** | float | (none) | | ||
- | | R value to tune MCMC acceptance rate. ||| | ||
- | |||
- | |<100% 33% 33% 33%>| | ||
- | ^ **acc_moves*** | integer | (none) | | ||
- | | Number of accepted MCMC moves required. ||| | ||
- | |||
- | ==== Optional parameters | ||
- | |||
- | |<100% 33% 33% 33%>| | ||
- | ^ **ensemblefile** | string | '' | ||
- | | Potential ensemble output filename, '' | ||
- | |||
- | |<100% 33% 33% 33%>| | ||
- | ^ **uq_temp** | float | 1.0 | | ||
- | | Temperature scaling parameter $\alpha$. ||| | ||
- | |||
- | |<100% 33% 33% 33%>| | ||
- | ^ **use_svd** | boolean | 0 | | ||
- | | Use singular value decomposition to find Hessian eigenvalues (default is eigenvalue decomposition). ||| | ||
- | |||
- | |<100% 33% 33% 33%>| | ||
- | ^ **hess_pert** | float | 0.00001 | | ||
- | | Percentage parameter perturbation in Hessian finite difference calculation. (If '' | ||
- | |||
- | |<100% 33% 33% 33%>| | ||
- | ^ **eig_max** | float | 1.0 | | ||
- | | Alternative MCMC step perturbation maximum value in max('' | ||
- | |||
- | |<100% 33% 33% 33%>| | ||
- | ^ **write_ensemble** | integer | 0 | | ||
- | | Writes a potential file every '' | ||
- | |||