Dakota Reference Manual: mpp_search

| Dakota Reference Manual Version 6.15 Explore and Predict with Confidence

- Main Page
- Related Pages

All Pages
mpp_search

Specify which MPP search option to use

## Topics

This keyword is related to the topics:

- uncertainty_quantification
- reliability_methods

## Specification

Alias: none

Argument(s): none

Default: No MPP search (MV method)

Child Keywords:

| Required/Optional | Description of Group | Dakota Keyword | Dakota Keyword Description
--- | --- | --- | --- | ---
| Required (Choose One) | MPP Approximation (Group 1) | x_taylor_mean | Form Taylor series approximation in "x-space" at variable means
u_taylor_mean | Form Taylor series approximation in "u-space" at variable means
x_taylor_mpp | X-space Taylor series approximation with iterative updates
u_taylor_mpp | U-space Taylor series approximation with iterative updates
x_two_point | Predict MPP using Two-point Adaptive Nonlinear Approximation in "x-space"
u_two_point | Predict MPP using Two-point Adaptive Nonlinear Approximation in "u-space"
x_multi_point | MPP search for local reliability based on QMEA multi-point approximation in u-space
u_multi_point | MPP search for local reliability based on QMEA multi-point approximation in x-space
no_approx | Perform MPP search on original response functions (use no approximation)
| Optional (Choose One) | Optimization Solver (Group 2) | sqp | Uses a sequential quadratic programming method for underlying optimization
nip | Uses a nonlinear interior point method for underlying optimization
| Optional | integration | Integration approach

## Description

The `x_taylor_mean` MPP search option performs a single Taylor series approximation in the space of the original uncertain variables ("x-space") centered at the uncertain variable means, searches for the MPP for each response/probability level using this approximation, and performs a validation response evaluation at each predicted MPP. This option is commonly known as the Advanced Mean Value (AMV) method. The `u_taylor_mean` option is identical to the `x_taylor_mean` option, except that the approximation is performed in u-space. The `x_taylor_mpp` approach starts with an x-space Taylor series at the uncertain variable means, but iteratively updates the Taylor series approximation at each MPP prediction until the MPP converges. This option is commonly known as the AMV+ method. The `u_taylor_mpp` option is identical to the `x_taylor_mpp` option, except that all approximations are performed in u-space. The order of the Taylor-series approximation is determined by the corresponding `responses` specification and may be first or second-order. If second-order (methods named and in [20]), the series may employ analytic, finite difference, or quasi Hessians (BFGS or SR1). The `x_two_point` MPP search option uses an x-space Taylor series approximation at the uncertain variable means for the initial MPP prediction, then utilizes the Two-point Adaptive Nonlinear Approximation (TANA) outlined in[95] for all subsequent MPP predictions. The `u_two_point` approach is identical to `x_two_point`, but all the approximations are performed in u-space. The `x_taylor_mpp` and `u_taylor_mpp`, `x_two_point` and `u_two_point` approaches utilize the `max_iterations` and `convergence_tolerance` method independent controls to control the convergence of the MPP iterations (the maximum number of MPP iterations per level is limited by `max_iterations`, and the MPP iterations are considered converged when < `convergence_tolerance`). And, finally, the `no_approx` option performs the MPP search on the original response functions without the use of any approximations. The optimization algorithm used to perform these MPP searches can be selected to be either sequential quadratic programming (uses the `npsol_sqp` optimizer) or nonlinear interior point (uses the `optpp_q_newton` optimizer) algorithms using the `sqp` or `nip` keywords.

In addition to the MPP search specifications, one may select among different integration approaches for computing probabilities at the MPP by using the `integration` keyword followed by either `first_order` or `second_order`. Second-order integration employs the formulation of[50] (the approach of[11] and the correction of[51] are also implemented, but are not active). Combining the `no_approx` option of the MPP search with first- and second-order integrations results in the traditional first- and second-order reliability methods (FORM and SORM). These integration approximations may be subsequently refined using importance sampling. The `refinement` specification allows the seletion of basic importance sampling (`import`), adaptive importance sampling (`adapt_import`), or multimodal adaptive importance sampling (`mm_adapt_import`), along with the specification of number of samples (`samples`) and random seed (`seed`). Additional details on these methods are available in[22] and[20] and in the Uncertainty Quantification Capabilities chapter of the Users Manual [4].