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--- uq [2018/11/27 16:30] – [Uncertainty Quantification] slongbottom
+++ uq [2019/10/08 19:10] (current) – removed slongbottom
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-====== Uncertainty Quantification ======
-----
-//potfit// uses the potential ensemble method ((Frederiksen, S. L., Jacobsen, K. W., Brown, K. S., and Sethna, J. P.: Bayesian ensemble approach to error estimation of interatomic potentials. //Phys. Rev. Lett.// **93** (16), 165501, 2004.)) to quantify the uncertainty in fitted potential parameters by generating an ensemble of candidate potentials of varying suitability sampled from around the best fit potential space.
-To enable this feature, compile //potfit// with the ''uq'' option, see [[:options:main|compiling]].
-<html><span style="color:red">This option is only available for analytic potentials.</span></html>
-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, S., Brommer, P.: Uncertainty Quantification for Classical Effective Potentials. //arxiv link// )).
-===== 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 $\Theta=\{\theta_1,..., \theta_N\}$.
-\begin{equation}
-\Delta\theta_{i}=\sum_{j=1}^{\rm N}\sqrt{\frac{\rm R}{{\rm{max}} (1,\lambda_{j})}}V_{ij}r_{j}
-\end{equation}
-where $\lambda_j$ are the hessian eigenvalues, $V_{ij}$ the eigenvector components and $r_j$ is Gaussian noise. The R value, ''acc_rescaling'', is a tunable parameter for the MCMC step acceptance rate.
-The MCMC algorithm samples potentials from the distribution at a temperature, $T_0$, set by the number of potential parameters and minimum cost value. In the majority of cases this temperature should be sufficient to generate a suitable ensemble. In the event that a reduced sampling temperature is required this can be scaled by a parameter $\alpha$ (''uq_temp''), such that $T=\alpha T_0$.
-===== 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 | ''startpot'' |
-| Potential ensemble output filename, ''ensemblefile.uq''. If this is not defined then ''output_prefix.uq'' is used. Should neither ''ensemblefile'' nor ''output_prefix'' be defined, the ''startpot'' filename is used, with a '.uq' extension. |||
-|<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 | (none) |
-| Percentage parameter perturbation in Hessian finite difference calculation. |||
-|<100% 33% 33% 33%>|
-^ **eig_max** | float | 1.0 |
-| Alternative MCMC step perturbation maximum value in max(''eig_max'', $\lambda_j$).|||