discover dso: design, geometry and optimization · discover dso: design, geometry and optimization...

Discover DSO: Design, Geometry and Optimization

Fariba Fahroo and Jan Vandenbrande

1Distribution Statement “A” (Approved for Public Release, Distribution Unlimited)

Defense Sciences Office

How are we different from other funding agencies:

• Focused on fundamental limits, complexity and design• Ask questions to “open the door” to new possibilities• Not here to support existing communities• Create new communities or build bridges• Not interested in evolutionary approaches

Fundamental Example: REVEAL• What’s the maximal information we can extract from a photon?• Will it enable us to look around corners w/o mirrors?

Dr. Predrag Milojkovic


Goals and Agenda

Goals: • Current research portfolio • Where we are going• How to approach us

10:30 Fariba intro10:45 Jan intro11:00 Group questions11:10 Jan new research interests11:30 Fariba new research interests11:50 Questions/ closing


Interests: • Exploring the role of mathematics for analysis,

optimization, and control of high-dimensional complex systems in the age of big data and computing• Uncertainty Quantification for complex physical

systems (EQUiPS program)• Novel mathematical approaches for dynamic data sets

(MoDyL program)• Interplay of

• Geometry • Topology• Machine learning• Statistics• Dynamical systems

Fariba Fahroo


Brief Overview of My Programs

Uncertainty in the inputs, model, outputs: How to represent, quantify, manage Uncertainty

How to extract models from DYNAMIC data sets

How to do high-dimensional, data-driven, dynamic optimization

MoDyL

Lagrange

EQUiPS

Radically Transform Modeling and Design


• Parameter uncertainty and Model inadequacy

• Mostly Monte Carlo Methods (Slow, Expensive)

• No computationally effective and mathematically rigorous framework for design under uncertainty for large complex systems

Enabling Quantification of Uncertainty in Physical Systems (EQUiPS)

What is Uncertainty Quantification (UQ)?The mathematical framework that accounts for various sources of error and uncertainty that affect our simulation-based prediction of quantities of interest (QoI).

UQ certification criteria for prediction

• Scalable forward and inverse Uncertainty Quantification (UQ)

• Model inadequacy, Multi-fidelity• Risk-Averse stochastic design and

decision making under uncertainty

Challenges EQUiPS


EQUiPS

• New methods for forward and inverseUncertainty Quantification (UQ)

• A quantitative understanding ofuncertainties and inadequacies in themodels

• New paradigm for stochastic design anddecision making under uncertainty forcomplex systems

• Development of modeling and designalgorithms to consider high-dimensionalspaces of up to one million uncertainparameters

Advanced mathematics to model, quantify, and dynamically manage uncertainties from various sources (models, parameters) in complex DoD systems


Output: Range of Structural Response &

Reliability(Probabilistic)

EQUiPS’ Vision

Physics‐based Multi‐scale, Multi‐Discipline

Models

Applied Loads & Environments(Probabilistic)

Geometry & Material Data(Probabilistic)

InverseProblems

Input Parameters

Design UnderUncertainty

TA1: Scalable Methods

TA2: Model‐form

TA3: Design

EQUiPS brings together statistics and physical modelingEQUiPS brings UQ into complex physical applications


MoDyL: Models, Dynamics, and Learning

Persistent Diagrams identifies how microscopic

structures impact mesoscopic structures

State-vs-Time

State-vs-State

Newton

Poincare

Dynamics of Observables

Koopman

Joint visualization (c) of the topology of two functions shown in (a) and (b).

• Objective: Use geometry, topology, orspectral analysis to find and learn thekey dynamical features of highdimensional spatial-temporal data-sets

• Approach:• Model reduction capability• Uncovering new physics and physical

laws/mechanisms• Visualization/representation

How Do We Extract Models from Dynamic Data?For Dynamic, High‐Dimensional Datasets We Need to Go Beyond Statistical Machine Learning


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Questions?

?

Distribution Statement “A” (Approved for Public Release, Distribution Unlimited)


Jan Vandenbrande

Interests: How can we design and build things better and faster?

• How can we make the computer a true partner in design?

• How do we leverage precise control of material placement?

• How sloppy can we be?

• How do we leverage all available information?

• How could we generate novel designs?

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Jan’s active program portfolio: Design through manufacturing

TRADES MDP TFF

Generate Design

Analyze Physics

Optimize Materials

Prototype & Build

&

OM

Qualify & Certify

Shape & materials Acceleratematerial

development

Small affordablecomposites

Reduce testing


Open Manufacturing (OM)

Techniques and Tools for Rapid Qualification of Manufacturing and Materials

Quantify sources of uncertainty to reduce testing


Materials Development for Platforms (MDP)

Acceleration of new materials adoption into platforms by integrating material development with design intent

V‐T space

V‐M spaceT‐M space

Vehicle

Trajectory

Material


Tailorable Feedstock and Forming (TFF)

&

Affordable Aerospace Composites Produced at Automotive Efficiency

Short & thin composite fibers Flexible forming methodologies


Transformative Design (TRADES)

Computer as a partner to design shape and material distribution


Tie in with Fahroo’s portfolio

EQUIPSLAGRANGE (Future)

Uncertainty Quantification

Vandenbrande:

Geometric insights for optimization

Fahroo:

Massive Optimization Embrace uncertainty


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Questions?

?


Future program interests

“Go from disbelief to mere doubt”


Example of a radical departure in approach

How would you rethink design if you had unlimited compute power?

#include <omp.h>#define NUM_THREADS 1000 static long num_steps = 100000; double step;

void main () { int i; double x, pi, sum = 0.0;

step = 1.0/(double) num_steps; omp_set_num_threads(NUM_THREADS); #pragma omp parallel for private(x) reduction(+:sum)for (i=0;i< num_steps; i++){

x = (i+0.5)*step; sum = sum + 4.0/(1.0+x*x);

} pi = step * sum;

}Source: http://www.openmp.org/wp‐content/uploads/omp‐hands‐on‐SC08.pdf

static long num_steps = 100000; double step;

void main () { int i; double x, pi, sum = 0.0;

step = 1.0/(double) num_steps;

for (i=0;i< num_steps; i++){x = (i+0.5)*step; sum = sum + 4.0/(1.0+x*x);

} pi = step * sum;

}

Conventional approach


Dedicate one processor per node

A radically different approach

Source: Hod Lipson21


Jan’s future program interests…

Lessons Learned

New species?

Next Gen?

https://en.wikipedia.org/wiki/Lockheed_Martin_F‐35_Lightning_IIhttp://foxtrotalpha.jalopnik.com/the‐navys‐long‐overdue‐smart‐deadly‐patrol‐boat‐has‐a‐1631598708https://www.youtube.com/watch?v=6ejPC1zZjME

Virtual World Model?


How can you create a virtual world model?

Real World Object Virtual World Model

Design DataSimulations

SensorsFleet

Real World CharacterizationInteroperabilityResilient DesignHealth & ReadinessPerformance OptimizationEvent PredictionDamage MitigationReal Time AdaptationSpecies description

Examples:• Air & Space Vehicles• Marine• Ground• Infrastructure (Bridges)• ….• Soldier

Address core technical barriers to assemble and infer new facts from available data and models


How do you jump species to find radically new designs?

Carburetor(Holley 0‐82750 4150 Street HP 750 CFM Four Barrel Vacuum Secondary)

http://www.amazon.com/Holley‐0‐82750‐Street‐Secondary‐Carburetor/dp/B0006HK2GO

Fuel Injector(Bosch)

http://www.kfztech.de/kfztechnik/motor/diesel/duesen/duesen2.htm

?


How do you mutate species?

+ =?


Jan’s potential other future program interests…

https://en.wikipedia.org/wiki/Lockheed_Martin_F‐35_Lightning_IIhttp://foxtrotalpha.jalopnik.com/the‐navys‐long‐overdue‐smart‐deadly‐patrol‐boat‐has‐a‐1631598708https://www.youtube.com/watch?v=6ejPC1zZjME

Scale: 10‐5 <‐> 103 m Scale: 10‐8 <‐> 100 m

Source: http://www.livescience.com/52207‐faster‐3d‐computer‐chip.html

3D Electronic Devices• 3D Chips• Antenna arrays• Hi freq power amps

?


27

Questions?

?


Fariba’s future program interest


Lagrange: Optimization in the age of data and computation

Challenges with Optimization:• Modeling: Underlying objectives and constraints are discontinuous, non-differentiable, or

nonconvex• Computational Complexity: For many optimization problems we do not have efficient

algorithms (run time as a function of the input size)

GOAL: Discover and develop new mathematical approaches for solving high-dimensional dynamic data-driven optimization and decision making problems

What optimization is really about:• Assess the state of the system through modeling:

• Objective functions to describe how the system should behave• Constraints to determine the limitations of the system

• Discover the possible solution space and make decisions about the system


Lagrange program (Dynamic, Data-driven Optimization)

Minimize/maximize objective function, ( ) Subject to constraints: ( ) ≤ 0, ( ) = 0

Formal definition

In realistic situations:

May not know , , and/or – have to estimate as data/information becomes available

Key Insight:Geometric tools in analysis and estimation theory leading to scalable algorithms

We need to shift computational complexity to modeling complexity using geometry

ModelingData and Estimation Theory

Optimization

Geometry


• Geometric methodologies drive novel optimization:• Information Geometry• Morse theory• Lagrangian/Hamiltonian framework• Differential and algebraic geometry• Geometry of optimal mass transport (OMT)

• Lagrange BAA released: https://www.FBO.gov• Industry day (Webinar) June 19, 2017

What are the ways we can handle the challenges?

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Use ideas from Geometry, Dynamical System Theory, Algebra, Statistics, Information Theory

DataDistribution Manifold


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Questions?

?


It’s 2040, what do we need to do to…

Make a computer a symbiotic partner in design?

Find radically new design species?

Predict real world behavior of any design?

Explore the best of species, automatically?

Design at any scale (range) & complexity?


discover dso: design, geometry and optimization · discover dso: design, geometry and optimization...

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