- This essential course taught by experts from the AIAA Multidisciplinary Design Optimization (MDO) Technical Committee introduces optimization, particularly for engineering applications.
- All students will receive an AIAA Certificate of Completion at the end of the course
OVERVIEW
This course introduces theory and practical usage of modern
optimization methods. The foundation of this course is optimization problem
formulation and core algorithms for both gradient-based and gradient-free
optimization. Users will work on several
hands-on engineering optimization problems focusing on formulation, setup,
convergence, interpretation and practical tips. Building on this foundation we
will discuss and practice a variety of more specialized topics. These topics
include convex optimization, surrogate-based optimization, Bayesian
optimization, neural nets, and topology optimization. All topics will include a
mix of theory, examples, and hands-on exercises.
Students will need to have access to and existing familiarity with Python. We will use freely available software within the Python ecosystem.
By the end of the course participants should be able to
- Formulate an engineering design problem as a formal optimization problem with an objective, design variables, and constraints.
- Implement and solve optimization problems in software.
- Use gradient-based methods in software and understand the basics of how they work and how to use them effectively.
- Understand different approaches to derivative computation and be able to use these methods in software.
- Use gradient-free methods in software and understand the basics of how they work and how to use them effectively.
- Identify use cases of convex optimization and setup and solve these problems.
- Understand surrogate-based optimization and be able to use various approaches with engineering models including Bayesian methods and neural nets in a deep learning framework.
- Formulate and solve topology optimization problems.
AUDIENCE
This course is intended for aerospace professionals, graduate
students, or any other person who would like to be able to use optimization
methods for engineering work, and/or would like to deepen their understand of
how to select and use optimization algorithms effectively.
COURSE FEES (Sign-In
To Register)
- AIAA
Member Price: $995 USD
-
AIAA Student Member Price: $495 USD
- Non-Member Price: $1195 USD
MODULE OUTLINE:
Each module is a two-hour session that includes exercises
and Q&A with the instructor.
- Design variables, objective(s), constraints
- Classifying an optimization problem
- Using an optimizer to solve problems
Unconstrained Gradient-Based Optimization (Andrew Ning, Professor, Brigham Young University)
- Gradients, directional derivatives, Hessians
- Line Searches
- Search directions (steepest descent, conjugate gradient, Newton, Quasi-Newton, stochastic gradient descent, Adam)
- Solving unconstrained problems, understanding convergence
Constrained Gradient-Based Optimization (Andrew Ning, Professor, Brigham Young University)
- KKT conditions for equality and inequality constraints
- Penalty methods, sequential quadratic programming, interior point methods
- Solving constrained problems, understanding solver options
- Fundamentals of basic neural nets
- Setting up, training, and testing neural nets
- Optimization algorithms and overview of engineering architectures in deep learning
- Convexity
- LPs and QPs
- Geometric programming
- Setting up and solving convex optimization problems
Derivative-Free Optimization (Ashwin Renganathan, Assistant Professor, Penn State University)
- Model-based methods (trust-region)
- Pattern and coordinate search methods
- Nelder-Mead
- Evolutionary algorithms: genetic algorithm and particle swarm
- Setting up and solving gradient-free methods
Surrogate-Based Optimization (Nathalie Bartoli, Senior Researcher, ONERA)
- Sampling
- Surrogate construction
- Infill
Gaussian Process and Bayesian Optimization (Nathalie Bartoli, Senior Researcher, ONERA)
- Gaussian Process or Kriging
- Acquisition function (Expected Improvement criterion, etc…) for Bayesian optimization with constraints
- Extension to multi-objective Bayesian optimization
- Finite differencing and complex step
- Algorithmic differentiation
- Implicit differentiation (direct and adjoint methods)
- Sparse Jacobians
- Computing total derivatives for engineering problems
Topology Optimization (H Alicia Kim, Professor, University of California San Diego)
- Density-based and boundary-based methods.
- Setting numerical parameters and their effects on design solutions.
- Application to structural and multiphysics design problems.
INSTRUCTORS
Dr. Andrew Ning is a professor in mechanical engineering at Brigham Young University with
a joint appointment at the National Renewable Energy Laboratory. His research lab specializes in
multidisciplinary optimization, deep learning, and aerodynamics as applied to
wind energy and aircraft systems. He
received a PhD in Aeronautics & Astronautics from Stanford University in
2011. He is co-author of the textbook
Engineering Design Optimization and regularly teaches semester-length-graduate
courses on optimization, deep learning, aerodynamics, and undergraduate courses
on aircraft design and numerical methods.
Dr. Christopher Lupp
is a Research Aerospace Engineer at the Air Force Research Laboratory (AFRL) in
Dayton, Ohio. At AFRL Dr. Lupp leads several digital engineering and
multi-disciplinary analysis and design optimization (MDO/MDAO/MADO) projects.
His research interests include gradient-based and computationally distributed
MDO, MDO including mission utility analyses, and geometrically nonlinear
aeroelasticity. He received his Ph.D. from the Department of Aerospace
Engineering at the University of Michigan, investigating the integration of
nonlinear aeroelasticity into gradient-based MDO.
Dr. Ashwin Renganathan is an assistant professor in the department of
aerospace engineering and the Institute of Computational and Data Sciences
(ICDS) at Penn State. He directs the Computational complex engineered Systems
Design Lab (CSDL) at Penn State, where his research focuses on developing
scalable and theoretically sound mathematical and computational methods toward
the design of complex engineered systems. He has designed and regularly teaches
a graduate-level numerical optimization course every year at Penn State. He
previously earned his Ph.D. in aerospace engineering at Georgia Tech and
completed and postdoctoral appointment in applied mathematics from the Argonne
National Laboratory.
Dr. Dan Berkenstock
is a Science Fellow at The Hoover Institution and also a lecturer in the
Department of Aeronautics and Astronautics at Stanford University. Dan's
research focuses on the application of convex, quasiconvex, & polynomial
optimization methods to the design of aerodynamic shapes. His research is
primarily driven by an interest in extending the breadth of known problems that
can be shown to conform to these techniques. Dan received his PhD from Stanford
University in 2024, working in the Aerospace Design Laboratory with Juan
Alonso. He previously received an M.S. in Aeronautics and Astronautics at
Stanford University and a B.S.E in Aerospace Engineering at the University of
Michigan, Ann Arbor.
Nathalie Bartoli is a
research director at ONERA (French Aerospace Lab in Toulouse, France) in a team
dedicated to multidisciplinary optimization and conceptual aircraft design She
worked on optimization algorithms within the framework of national projects or
Europeans with a joint supervision of several PhDs on these subjects. She is in
charge of some courses at ISAE-SUPAERO in the field of optimization and machine
learning techniques.
H Alicia Kim is
a professor in the Department of Structural Engineering and the Materials
Science and Engineering Program at UC San Diego. Her primary research area has been in
topology optimization and computational mechanics since the 90s and has published
over 250 publications. Her current research focuses on coupled multiscale and
multiphysics topology optimization. She has been teaching structural and
topology optimization for over 15 years, to undergraduate students at the
University of Bath (UK) then to graduate students at UC San Diego (USA), as
well as short courses to industry.
Cancellation Policy: On-demand course purchases are non-refundable.
Contact: Please contact Lisa Le or Customer Service if you have questions about the course or group discounts (for 5+ participants).
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