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Karen Willcox

Professor, Department of Aeronautics & Astronautics
Co-Director, Center for Computational Engineering
Massachusetts Institute of Technology
77 Massachusetts Avenue
Cambridge, MA 02139

E-mail: kwillcox@mit.edu
Office: Rm 33-412a (map)
Phone: (617) 253-3503

Resume
     

Publications

Journal Publications

  1. Amaral, S., Allaire, D. and Willcox, K. A decomposition-based approach to uncertainty analysis of feed-forward multicomponent systems, International Journal for Numerical Methods in Engineering, to appear, 2014.
  2. Ng, L. and Willcox, K. Multifidelity Approaches for Optimization Under Uncertainty, International Journal for Numerical Methods in Engineering, published online 17 September, 2014, DOI: 10.1002/nme.4761. (An earlier version of this work appeared in AIAA Paper 2012-5602, September 2012.)
  3. Cui, T., Marzouk, Y. and Willcox, K. Data-driven model reduction for the Bayesian solution of inverse problems, International Journal for Numerical Methods in Engineering, published online 15 August, 2014, DOI: 10.1002/nme.4748.
  4. Allaire, D. and Willcox, K. Uncertainty assessment of complex models with application to aviation environmental policy-making, Transport Policy , Available online 20 March 2014, ISSN 0967-070X, http://dx.doi.org/10.1016/j.tranpol.2014.02.022.
  5. Allaire, D., Noel, G., Willcox, K. and Cointin, R. Uncertainty quantification of an aviation environmental toolsuite, Reliability Engineering & System Safety , Volume 126, June 2014, pp. 14-24. Available online 15 January 2014.
  6. Peherstorfer, B., Butnaru, D., Willcox, K. and Bungartz, H.-J., Localized discrete empirical interpolation method, SIAM J. Scientific Computing , Vol. 36, No. 1, pp. A168-A192, 2014.
  7. Allaire, D. and Willcox, K. A mathematical and computational framework for multifidelity design and analysis with computer models, International Journal on Uncertainty Quantification , Vol. 4, Issue 1, pp. 1-20, 2014.
  8. Burgiel, H., Lieberman, C., Miller, H. and Willcox, K. Interactive applets in calculus and engineering courses, chapter in Enhancing Mathematics Understanding through Visualization: The Role of Dynamical Software , S. Habre (Ed.), IGI Global, December 2013.
  9. Kaijima, S., Bouffanais, R., Willcox, K. and Naidu, S. Computational fluid dynamics for architectural design, in Computation Works: The Building of Algorithmic Thought, Architectural Design, X. De Kestelier, B. Peters (eds), March 2013.
  10. Lieberman, C. and Willcox, K. Goal-oriented inference: Approach, linear theory, and application to advection-diffusion , SIAM Review , Vol. 55, No. 3, pp. 493-519, 2013. (SIGEST award)
  11. Lieberman, C., Fidkowski, K, Willcox, K. and van Bloemen Waanders, B. Hessian-based model reduction: Large-scale inversion and prediction, International Journal of Numerical Methods in Fluids , Vol. 71, pp. 135-150, January 2013.
  12. Lieberman, C. and Willcox, K. Goal-oriented inference: Approach, linear theory, and application to advection-diffusion, SIAM Journal on Scientific Computing , Vol. 34, No.4, pp. 1880-1904, 2012.
  13. Allaire, D, He, Q., Deyst, J. and Willcox, K. An Information-theoretic Metric of System Complexity with Application to Engineering System Design, Journal of Mechanical Design , Vol. 134, Issue 10, October, 2012.
  14. Burgiel, H., Lieberman, C., Miller, H. and Willcox, K. Interactive applets in calculus and engineering courses, chapter to appear in Dynamical mathematical software and visualization in the learning of mathematics, S. Haber (Ed.), 2013.
  15. March, A. and Willcox, K. A Provably Convergent Multifidelity Optimization Algorithm not Requiring High-Fidelity Derivatives, AIAA Journal , Vol. 50, No. 5, pp. 1079-1089, 2012.
  16. March, A. and Willcox, K. Constrained multifidelity optimization using model calibration, Structural and Multidisciplinary Optimization , Vol. 46, pp. 93-109, 2012.
  17. March, A., Wang, Q. and Willcox, K. Gradient-based Multifidelity Optimization for Aircraft Design using Bayesian Model Calibration, The Aeronautical Journal , Vol. 115, No. 1174, December, 2011.
  18. Allaire, D. and Willcox, K. A Variance-Based Sensitivity Index Function for Factor Prioritization, Reliability Engineering and System Safety, Vol. 107, November 2012, pp. 107-114.
  19. Allaire, D. and Willcox, K. Distributional Sensitivity Analysis, Procedia -- Social and Behavioral Sciences , Vol. 2, Issue 6, pp. 7595-7596, 2010.
  20. Stirling, L., Willcox, K. and Newman, D., Development of a Computational Model for Astronaut Reorientation, Journal of Biomechanics , Vol. 43, Issue 12, pp. 2309-2314, August 2010.
  21. Lieberman, C., Willcox, K. and Ghattas, O., Parameter and State Model Reduction for Large-Scale Statistical Inverse Problems, SIAM Journal on Scientific Computing , Vol. 32, No.5, pp. 2523-2542, August 2010.
  22. Frangos, M., Marzouk, Y., Willcox, K. and van Bloemen Waanders, B., Surrogate and reduced-order modeling: a comparison of approaches for large-scale statistical inverse problems, to appear in Computational Methods for Large-Scale Inverse Problems and Quantification of Uncertainty , Biegler et al. (Eds.), Wiley, 2010.
  23. Allaire, D. and Willcox, K., Surrogate Modeling for Uncertainty Assessment with Application to Aviation Environmental System Models, AIAA Journal, Vol. 48, No. 8, August 2010.
  24. Galbally, D., Fidkowski, K., Willcox, K. and Ghattas, O., Nonlinear Model Reduction for Uncertainty Quantification in Large-Scale Inverse Problems, International Journal for Numerical Methods in Engineering, Volume 81, Issue 12, March 2010, pp. 1581-1608.
  25. Degroote, J., Vierendeels, J. and Willcox, K., Interpolation among reduced-order matrices to obtain parametrized models for design, optimization and probabilistic analysis, International Journal for Numerical Methods in Fluids, Vol. 63, No. 2, pp. 207-230, May 2010.
  26. Stirling, L., Ferguson, P., Willcox, K. and Newman, D., Kinetics and Kinematics for Translational Motions in Microgravity During Parabolic Flight. Journal of Aviation, Space, and Environmental Medicine, Vol. 80, No. 6, pp 522-531, June 2009.
  27. Stirling, L., Newman, D. and Willcox, K., Self-Rotations in Simulated Microgravity: Performance Effects of Strategy Training, Journal of Aviation, Space and Environmental Medicine, Vol. 80, No. 1, pp. 5-14, January 2009.
  28. Robinson, T., Willcox, K., Eldred, M., and Haimes, R. Multifidelity Optimization for Variable-Complexity Design, AIAA Journal, Vol. 46, No. 11, pp. 2814-2822, 2008.
  29. Bui-Thanh, T., Willcox, K., and Ghattas, O., Parametric Reduced-Order Models for Probabilistic Analysis of Unsteady Aerodynamic Applications, AIAA Journal, Vol. 46, No. 10, pp. 2520-2529, 2008.
  30. Bui-Thanh, T., Willcox, K., and Ghattas, O., Model Reduction for Large-Scale Systems with High-Dimensional Parametric Input Space, SIAM Journal on Scientific Computing, Vol. 30, No. 6, pp. 3270-3288, 2008.
  31. Hovland, S., Gravdahl, J., and Willcox, K., Explicit Model Predictive Control for Large-Scale Systems via Model Reduction, AIAA Journal for Guidance, Control, and Dynamics, Vol. 31, No. 4, July-August, 2008.
  32. Astrid, P., Weiland, S., Willcox, K., and Backx, T., Missing Point Estimation in Models Described by Proper Orthogonal Decomposition, IEEE Transactions on Automatic Control, Vol. 53, Issue 10, pp. 2237-2251, 2008. Also presented at 43rd IEEE Conference on Decision and Control, Paradise Island, Bahamas, December 2004.
  33. Bashir, O., Willcox, K., Ghattas, O., van Bloemen Waanders, B., and Hill, J., Hessian-Based Model Reduction for Large-Scale Systems with Initial Condition Inputs, International Journal for Numerical Methods in Engineering, Vol. 73, Issue 6, pp. 844-868, 2008.
  34. Gugercin, S. and Willcox, K., Krylov Projection Framework for Fourier Model Reduction, Automatica, Vol. 44, No. 1, pp. 209-215, 2008.
  35. Willcox, K. Model Reduction for Large-Scale Applications in Computational Fluid Dynamics, in Real-Time PDE-Constrained Optimization, Biegler, L., Ghattas, O., Heinkenschloss, M., Keyes, D., and van Bloemen Waanders, B. (Eds.), SIAM Book Series, pp. 217-233, 2007.
  36. Bui-Thanh, T., Willcox, K., Ghattas, O., and van Bloemen Waanders, B., Goal-Oriented, Model-Constrained Optimization for Reduction of Large-Scale Systems, Journal of Computational Physics, Vol. 224, No. 2, pp. 880-896, June 2007.
  37. My-Ha, D., Lim, K.M., Khoo, B.C. and Willcox, K., Real-Time Optimization Using Proper Orthogonal Decomposition: Free Surface Shape Prediction due to Underwater Bubble Dynamics, Computers and Fluids, Vol. 36, No. 3, March 2007, pp. 499-512.
  38. Peoples, R. and Willcox, K., Value-Based Multidisciplinary Optimization for Commercial Aircraft Design and Business Risk Assessment, Journal of Aircraft, Vol. 43, No. 4, July-August, 2006, pp. 913-921.
  39. Willcox, K., Unsteady Flow Sensing and Estimation via the Gappy Proper Orthogonal Decomposition, Computers & Fluids, Volume 35, Issue 2, February 2006, pp. 208-226.
  40. Willcox, K. and Lassaux, G., Model Reduction of an Actively Controlled Supersonic Diffuser, in Dimension Reduction of Large-Scale Systems, Springer Series on Lecture Notes in Computational Science and Engineering, Vol. 45, Benner, P. Mehrmann, V. and Sorensen, D. (Eds.), 2005, pp. 357-361.
  41. Willcox, K. and Megretski, A., Fourier Series for Accurate, Stable, Reduced-Order Models in Large-Scale Applications, SIAM Journal for Scientific Computing, Vol. 26, No. 3, 2005, pp. 944-962.
  42. Bui-Thanh, T., Damodaran, M. and Willcox, K., Aerodynamic Data Reconstruction and Inverse Design using Proper Orthogonal Decomposition, AIAA Journal, Vol. 42, No. 8, August 2004, pp. 1505-16.
  43. Markish, J. and Willcox, K., Value-Based Multidisciplinary Techniques for Commercial Aircraft System Design, AIAA Journal, Vol. 41, No. 10, October 2003, pp. 2004-12.
  44. Willcox, K. and Wakayama, S., Simultaneous Optimization of a Multiple-Aircraft Family, Journal of Aircraft, Vol. 40, No. 4, July 2003, pp. 616-622.
  45. Shapiro, B. and Willcox, K., Analyzing the Mistuning of Bladed Disks by Symmetry and Reduced-Order Aerodynamic Modeling. Journal of Power and Propulsion, Vol. 19, No. 2, March-April 2003, pp. 307-311.
  46. Willcox, K. and Peraire J., Balanced Model Reduction via the Proper Orthogonal Decomposition. AIAA Journal, Vol. 40, No. 11, November 2002, pp. 2323-30.
  47. Willcox, K., Peraire J. and White, J., An Arnoldi approach for generation of reduced-order models for turbomachinery. Computers and Fluids, Vol. 31, No. 3, pp. 369-89, March 2002.
  48. Willcox, K., Peraire J. and Paduano, J., Application of Model Order Reduction to Compressor Aeroelastic Models. Paper 2000-GT-0377, presented at the ASME International Gas Turbine and Aeroengine Technical Conference, May 2000, Munich, Germany. Journal of Engineering for Gas Turbines and Power, Vol. 124, No. 2, pp. 332-39, April 2002.
  49. Willcox, K. and Peraire J., Aeroelastic computations in the time domain using unstructured meshes, International Journal for Numerical Methods in Engineering, Vol. 40, No. 13, pp. 2413-31, July 1997.

Proceedings of Refereed Conferences (selected papers)

  1. Ng, L., Huynh, D.B.P. and Willcox, K. Multifidelity Uncertainty Propagation for Optimization Under Uncertainty, AIAA Paper 2012-5602, 14th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Indianapolis, IN, September 2012.
  2. Allaire, D. and Willcox, K., "A Bayesian-Based Approach to Multi-Fidelity Multidisciplinary Design Optimization," AIAA-2010-9183, presented at 13th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Fort Worth, TX, September 13-15, 2010.
  3. Buffoni, M. and Willcox, K., "Projection-Based Model Reduction for Reacting Flows," AIAA-2010-5008, presented at 40th Fluid Dynamics Conference and Exhibit, Chicago, IL, June 28-July 1, 2010
  4. Lehner, S., Lurati, L., Bower, G., Cramer, E., Crossley, W., Engelsen, F., Kroo, I., Smith, S., Willcox, K., "Advanced Multidisciplinary Optimization Techniques for Efficient Subsonic Aircraft Design ," AIAA-2010-1321, presented at 48th AIAA Aerospace Sciences Meeting, Orlando, FL, Jan. 4-7, 2010.
  5. Noel, G., Allaire, D., Jacobsen, S., Willcox, K., and Cointin, R., "Assessing the Uncertainty in FAA's Noise and Emissions Compliance Model," Inter-Noise Conference, Ottawa, Canada, August 23-26, 2009.
  6. Noel, G., Allaire, D., Jacobsen, S., Willcox, K., and Cointin, R., "Assessment of the Aviation Environmental Design Tool," Eighth USA/Europe Air Traffic Management Research and Development Seminar (ATM2009), Napa, CA, June 29 - July 2, 2009.
  7. March, A., Waitz, I., and Willcox, K. "A Methodology for Integrated Conceptual Design of Aircraft Configuration and Operation to Reduce Environmental Impact," AIAA-2009-7026, presented at 9th AIAA Aviation Technology, Integration, and Operations Conference, Hilton Head, SC, September 21-23, 2009.
  8. Lazzara, D., Haimes, R. and Willcox, K. "Multifidelity Geometry and Analysis in Aircraft Conceptual Design," AIAA-2009-3806, presented at 27th AIAA Applied Aerodynamics Conference, San Antonio, TX, June 22-25, 2009.
  9. Fidkowski, K., Engelsen, F., Willcox, K., and Kroo, I. "Stochastic Gust Analysis Techniques for Aircraft Conceptual Design," AIAA-2008-5848, presented at 12th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Victoria, British Columbia, September 10-12, 2008.
  10. Robinson, T., Ooi, B.H., Taff, B., Willcox, K. and Voldman, J., "Surrogate-Based Optimization of a Microfluidic Weir Structure for Single-Cell Manipulation," AIAA-2008-5889, presented at 12th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Victoria, British Columbia, September 10-12, 2008.
  11. Stirling, L., Arsie, A., Willcox, K., Frazzoli, E. and Newman, D., "Application of Quantized Control to Self-Rotation Maneuvers," 46th IEEE Conference on Decision and Control, New Orleans, LA, December 2007.
  12. Allaire, D., Waitz, I. And Willcox, K., "A Comparison of Two Methods for Predicting Emissions from Aircraft Gas Turbine Engine Combustors," ASME Paper GT2007-28346, presented at the ASME International Gas Turbine and Aeroengine Technical Conference, Montreal, Canada, June 2007.
  13. Allaire, D., Waitz, I. And Willcox, K., "A Comparison of Two Methods for Predicting Emissions from Aircraft Gas Turbine Engine Combustors," ASME Paper GT2007-28346, presented at the ASME International Gas Turbine and Aeroengine Technical Conference, Montreal, Canada, June 2007.
  14. Bashir, O., Ghattas, O., Hill, J., van Bloemen Waanders, B., and Willcox, K., "Hessian-Based Model Reduction for Large-Scale Data Assimilation Problems," Proceedings of International Conference on Computational Science, Beijing, China, Y. Shi et al. (Eds.): ICCS 2007, Part I, LNCS 4487, pp. 1010-1017, Springer-Verlag, May 2007.
  15. Stirling, L., Willcox, K. and Newman, D., "Development of Astronaut Orientation Strategies using Optimization Methodologies," Multibody Dynamics 2007, ECCOMAS Thematic Conference, Milan, Italy, June 2007.
  16. Bui-Thanh, T., Willcox, K., and Ghattas, O., "Model Reduction for Large-Scale Systems with High-Dimensional Parametric Input Space," AIAA Paper 2007-2049, presented at the 48th AIAA Structures, Structural Dynamics and Materials Conference, Waikiki, HI, April 2007.
  17. Jones, A., Willcox, K., and Hileman, J., "Distributed Multidisciplinary Optimization of Aircraft Design and Takeoff Operations for Low Noise," AIAA Paper 2007-1856, presented at the 2nd AIAA Multidisciplinary Design Optimization Specialist Conference, Waikiki, HI, April 2007.
  18. Hovland, S., Willcox, K., and Gravdahl, J., "MPC for large-scale systems via model reduction and multiparametric quadratic programming," 45th IEEE Conference on Decision and Control, San Diego, CA, December 2006.
  19. Robinson, T., Eldred, M., Willcox, K. and Haimes, R. "Strategies for Multi-fidelity Optimization with Variable Dimensional Hierarchical Models," AIAA paper 2006-1819, presented at the 1st Multidisciplinary Design Optimization Specialist Conference, Newport, RI, April 2006.
  20. Diedrich, A., Hileman, J., Tan, D., Willcox, K. and Spakovszky, Z. "Multidisciplinary Design and Optimization of the Silent Aircraft," AIAA paper 2006-1323, presented at the 44th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, January 2006.
  21. Willcox, K., Ghattas, O., van Bloemen Waanders, B., and Bader, B., "A Goal-Oriented Optimization Framework for Model Reduction of Large-scale Systems," 44th IEEE Conference on Decision and Control, Seville, Spain, December 2005.
  22. Bui-Thanh, T. and Willcox, K., "Model Reduction for Large-Scale CFD Applications Using the Balanced Proper Orthogonal Decomposition," AIAA Paper 2005-4617, presented at the 16th AIAA Computational Fluid Dynamics Conference, Toronto, Canada, June 2005.
  23. Astrid, P., Weiland, S. and Willcox, K., "On the acceleration of a POD-based model reduction technique," Proceedings of the 16th International Symposium on Mathematical Theory of Networks and Systems, Leuven, Belgium 5-9 July 2004.
  24. Willcox, K. and Bounova, G., "Mathematics in Engineering: Identifying, Enhancing and Linking the Implicit Mathematics Curriculum," presented at ASEE Annual Conference, Salt Lake City, UT, June 2004.
  25. Antoine, N., Kroo, I., Willcox, K. and Barter, G. "A Framework for Aircraft Conceptual Design and Environmental Performance Studies," AIAA Paper 2004-4314, presented at the 10th AIAA Multidisciplinary Analysis and Optimization Conference, Albany, NY, August 2004.
  26. Peoples, R. and Willcox, K., "A Value-Based MDO Approach to Assess Business Risk for Commercial Aircraft Design," AIAA Paper 2004-4438, presented at the 10th AIAA Multidisciplinary Analysis and Optimization Conference, Albany, NY, August 2004.
  27. Gratton, D. and Willcox, K., "Reduced-Order, Trajectory Piecewise-Linear Models for Nonlinear Computational Fluid Dynamics," in Proceedings of the 5th SMA Symposium, January 2004, also AIAA Paper 2004-2329, presented at 34th AIAA Fluid Dynamics conference, Portland, OR, June 2004.
  28. Peoples, R. and Willcox, K., "Value-Based Multidisciplinary Optimization for Commercial Aircraft Design," AIAA paper 2004-1542, presented at the 45th AIAA Structures, Structural Dynamics and Materials conference, Palm Springs, CA, April 2004.
  29. Willcox, K. and Megretski, A., "Model Reduction for Large-Scale Linear Applications", presented at the 13th IFAC Symposium on System Identification, Rotterdam, The Netherlands, August 2003.
  30. Bui-Thanh, T., Damodaran, M. and Willcox, K., "Applications of Proper Orthogonal Decomposition for Inviscid Transonic Aerodynamics", AIAA Paper 2003-4213, presented at 15th Computational Fluid Dynamics Conference, Orlando, FL, June 2003.
  31. Deremaux, Y. and Willcox, K., "Real-Time Visualization and Constraint Analysis in Multidisciplinary Design Optimization", AIAA Paper 2003-3876, presented at 15th Computational Fluid Dynamics Conference, Orlando, FL, June 2003.
  32. Lassaux, G. and Willcox, K., "Model reduction for active control design using multiple-point Arnoldi methods", AIAA Paper 2003-0616, presented at 41st Aerospace Sciences Meeting & Exhibit, Reno, NV, January 2003.
  33. Willcox, K., "Controllable and Observable Subspaces in Computational Fluid Dynamics", in Computational fluid dynamics, 2002 (Sydney), pp. 159-164, Springer, Berlin, 2003.
  34. Markish, J. and Willcox, K., "A Value-Based Approach for Commercial Aircraft Conceptual Design," in Proceedings of the ICAS2002 Congress, Toronto, Canada, September 2002.
  35. Willcox, K. and Peraire, J., "Application of Reduced-Order Aerodynamic Modeling to the Analysis of Structural Uncertainty in Bladed Disks". ASME Paper GT-30680, presented at the ASME International Gas Turbine and Aeroengine Technical Conference, Amsterdam, The Netherlands, June 2002.
  36. Willcox, K., Paduano, J., Peraire J. and Hall, K., "Low Order Aerodynamic Models for Aeroelastic Control of Turbomachines". AIAA paper 99-1467, presented at the 40th AIAA Structures, Structural Dynamics and Materials conference, April 1999, St Louis, MO.