# Presentation: 301554

## LTE Review (September 2005 – January 2006)

January 17, 2006

Daniel M. Dunlavy
John von Neumann Fellow
Optimization and Uncertainty Estimation (1411)
(8962 intern in 2001)

SAND2006-0759P

**January 17, 2006**
**Daniel M. Dunlavy**
***John von Neumann Fellow***
*Optimization and Uncertainty Estimation (1411)*
*(8962 intern in 2001)*
***SAND2006-0759P***

- Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company,for the United States Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.

**Optimization, Linear Algebra,****and a Little Bit of HOPE**

## Outline

**Biography**
**DAKOTA (Optimization)**
- Research and Product Impact
- Collaborators: Mike Eldred, Bill Hart
**Space-Time Preconditioners (Linear Algebra)**
- Research
- Collaborator: Andy Salinger
**HOPE**
- Future Impact
**Other Contributions**

## Biography

**Ph.D., University of Maryland, August 2005**
*Advisor:* Dianne O’Leary
- Homotopy Optimization Methods and Protein Structure Prediction
**M.S., University of Maryland, December 2003**
*Advisor:* Dianne O’Leary
- QCS: An Information Retrieval System for Improving Efficiency in Scientific Literature Searches
**M.S., Western Michigan University, April 2001**
*Advisor:* Niloufer Mackey
- Structure Preserving Algorithms for Perplectic Eigenproblems

## DAKOTA

**Research Contributions**
-  Constraint relaxation for surrogate-based optimization (SBO) [M. Eldred]
** ****Goal: **Balance feasibility and optimality satisfaction  	within infeasible regions
** ****Contributions:**
- Prototyped algorithm → production code
- Identification of algorithmic enhancements
** ****Target:** Simulation-based optimization
** ****Impact:**  *External customers*, design optimization, MEMS
**Product Contributions**
-  Testing, documentation, COLINY [B. Hart]

## DAKOTA – Constraint Relaxation

**	****Original****	****Surrogate****	****Relaxed**

## DAKOTA – Constraint Relaxation

## Space-Time Preconditioners

**Space-Time Preconditioners**

**Research Contributions**
-  Preconditioners for space-time formulations of transient problems [A. Salinger]
** ****Goal: **Efficiently solve (large) space-time problems
** ****Benefits:**
- Achieve parallelism in time (and space)
- Find initial values for particular solutions
- More computation for parameter continuation
**Contributions:**
- Implementation of preconditioner framework
- Development of 4 preconditioners
- Tutorial example
** ****Target:** Reacting fluid flows
-  **Impact: **MPSalsa, QASPR (Charon), Aria

## Space-Time Preconditioners

- Transient Simulation of:

- First solve:

- Then solve:

- Then solve:

**Instead, solve for all solutions ****at once:**

**where**

**... ****and with Newton solve:**

## Space-Time Preconditioners

**Space-Time Preconditioners**

**Global**
**Sequential**
**Parallel **(procs ≥ # time domains)
**Parareal (Multilevel)**

- = Solve

- = Mult, Add

## HOPE for Global Optimization

**Original****	****Homotopy Optmization**
-                is a continuous deformation of           into
- Leverage known information about            (e.g., global minimizer)
** ****Applications**
- Successfully finds minimizers of several protein energy models
- Standard global optimization test problems
** ****Future Directions**
- Constrained problems (function homotopy + constraint relaxation)
- Homotopies on models
- Sandia applications (param. estimation, multiscale, multiphysics)

## Other Contributions

**Funding**
- 1)	Co-PI (T. Kolda, B. Hart), “Derivative-Free Methods for Local and Global Optimization,” *3-year MICS Proposal*, Dec. 2005.
- 2)	Co-PI (T. Bauer), “Extending Retrieval and Analysis Capabilities in STANLEY using Multilinear Algebra Tools,” *in preparation.*
**Publications**
- 1)	HOPE: A Homotopy Optimization Method for Protein Structure Prediction (D. O'Leary, D. Klimov, D. Thirumalai), *J. Comput. Biol.*, 12(10):1275-1288. Dec. 2005.
- 2)	Homotopy Optimization Methods for Global Optimization (D. O'Leary), SAND2005-7495. Dec. 2005.
- 3)	Formulations for Surrogate-Based Optimization with Data Fit, Multifidelity, and Reduced-Order Models (M. Eldred) , *in preparation*.
- 4)	QCS:  A Tool for Querying, Clustering and Summarizing Documents (D. O’Leary, J. Conroy), *in preparation*.
- 5)	Global Optimization of a Simplified Protein Energy Model, *in preparation*.
**Presentations**
- 1)	Homotopy Optimization Methods, *Copper Mountain Conference on Iterative Methods*, Apr. 2006.
- 2)	Preconditioners for Space-Time Systems, *SIAM Conference on Parallel Processing*, Feb. 2006.
**Service**
- Grader,  *Go Figure!* [C. Phillips]
- Journal Referee,  *SIAM Review (1)*

## 

Thank You

Questions?

**Thank You**
**Questions?**

## Space-Time Preconditioners

**Space-Time Preconditioners**

**Global**
**Sequential**
**Parallel **(procs ≥ # time domains)
**Parareal (Multilevel)**

- = Solve

- = Mult, Add

## HOPE for Global Optimization

**Original****	****Homotopy Optmization**
- 		Steps to solution:
- 		1. Start at       s.t.
- 		2. Increase      , solve                        w.r.t.
- 		3. Repeat until
** ****Applications**
- Successfully finds minimizers of several protein energy models
- Standard global optimization test problems
** ****Future Directions**
- Constrained problems (function homotopy + constraint relaxation)
- Homotopies on models
- Sandia applications (param. estimation, multiscale, multiphysics)