Directed Exploration of Complex Systems

1
Directed Exploration of Complex Systems

• AISR PI Meeting
• 2008/05/06

Michael C. Burl, Brian Enke, William J.
Merline
Jet Propulsion Laboratory
Southwest Research Institute
2
Motivation

• Numerical simulations widely used within NASA and
  other agencies to investigate complex phenomena
  that could not be studied otherwise.
• Long run times limit amount of knowledge that can
  be extracted.
• Some parallels with autonomous exploration agent
  that is able to perform experiments in the
  world.
• Serendipitous discovery of Ida-Dactyl pair by
  Galileo Spacecraft.

3
Simulations to Study Formation
4
Courtesy D. Durda, SwRI
5
Dynamical Systems Viewpoint
M. C. Burl V-0615-b

• Simulator as discrete-time dynamical system

• Restrict attention to non-chaotic simulations
  with known initial state x0, no control input (uk
  0) and no process or measurement noise (wk 0,
  vk 0).
• State at time T is completely determined by q
  q, x0

INPUT SPACE Q set of possible parameter vectors
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Landscape Characterization
M. C. Burl V-0616
Simulator xT, zT
1
q
q(q)
-1
Grading Script
Which input values q result in q(q) 1?
q1
Inverse Mapping
q2
Solution Region
1
q3
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Example Grading Scripts

• Do satellites exist in bound orbits about the
  Largest Remnant (LR) at T4 days (SMATs)?
• Did the collision produce any EEBs?
• Was the collision catastrophic? (threshold on
  mass of LR)
• Is the shape of the LR elongated?
• Does the resulting size-frequency distribution
  match that of a particular (observed) asteroid
  family with sufficient fidelity?
• Does the collision produce a binary pair that is
  likely to be observable (e.g., to a ground
  telescope)?

Within the scope of one simulator, we can address
many different science questions by swapping in
different grading scripts.
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Modification of Concept Learning
M. C. Burl V-0617

• Q is typically continuous-valued

• cannot just enumerate all points in solution
  region

• Really want a function

-1, 1
q Q
such that q agrees with q over most of domain

• Like concept learning, but some key differences

CL
Simulators

• Fixed set of training
• examples drawn iid

• Simulator serves as an oracle

• Choice of examples conditional
• on previous choices

• Very expensive to get labels

• Potential for introspection

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Represent q with SVM
M. C. Burl V-0618

• q(q) S bi K(q, si)

i
i-th support vector
scalar weight
kernel function

• Learned SVM depends on hyperparameters (l)

Kernel type, kernel-specific variables, C
(n)
ql (q) SVM learned after n-th iteration
using hyperparameters l.
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Active Learning
M. C. Burl V-0619

• Determine which new point(s) in input space, if
  labeled, would be most informative for refining
  the boundaries of the solution region
• Imagine discretized input space
• L(n) set of labeled instances at end of trial
  n (red or green)
• U(n) set of unlabeled instances at end of
  trial n (black)
• Choose q(n1) from U(n) such that the SVM learned
  from
• L(n1) L(n) q(n1)
• will bring q closer to q.

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Active Learning (cont)
M. C. Burl V-0620

• Simple TongKoller, 01 choose unlabeled point
  closest to current SVM decision boundary
• q(n1) arg min ql(n) (q)
• q in U(n)
• Other methods (MaxMin Margin, Diverse) have not
  worked particularly well.
• Probabilistic Simple choose higher-ranked
  queries with higher probability (dont always
  pick best)
• Trade-off between exploration and exploitation.
• Information-theoretic selection (recent)

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Exploration vs Exploitation
M. C. Burl V-0626
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Simulator Details
M. C. Burl V-0630

• Asteroid Collisions
• SPH and N-body code
• q(q) formation of gravitationally bound system
• Q impact velocity, angle, mass ratio
• 5 X 5 X 6 grid (150pts)
• 25 positives on grid
• 10 days on 1GHz CPU!

• Magnetosphere
• 10-parameter Roelof Model to determine plasma
  distribution and predict ENA image
• q(q) smoothness and match to spacecraft-observed
  ENA image.
• Q 3 key Roelof params
• 9 X 9 X 9 grid (729pts)
• 4 hours on 1GHz CPU

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Evaluation Methodology
M. C. Burl V-0621

• Underlying q() function is not known
• Evaluate q() on as fine a grid as practical
• Consider problem solved if q_hat() and q() agree
  on sufficient fraction of grid points
• Look at learning curves (agreement vs n)
• Subgrid accuracy?

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Decision Surface
M. C. Burl V-0627
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Magnetospheric Inversion
M. C. Burl V-0623
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Reduction in Simulation Trials (catastrophic
collision subproblem)
Percentages of total number of grid runs required
to achieve a desired level of agreement between
the grid and active learning. Low percentages
are good (for example, 20 a 5x speed-up by
using active learning).
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Leveraging the Time-Savings

• Same final result can be obtained with fewer
  simulation trials.
• More simulation trials can be conducted in a
  given amount of time.
• Higher-fidelity (e.g., finer spatio-temporal
  resolution) simulation trials can be used.
• More trials can be concentrated at the region
  between interesting and non-interesting regions.

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Hyperparameters Accuracy
M. C. Burl V-0629

• Choose l l0 upfront
• Consider finite pool L
• Try to get accuracy estimate
• Use best or combine wishes of multiple SVMs
• Instantaneous x-val
• Bayesian approach
• Maintain posterior distribution on accuracy
• Choose next point based on weighted utility
• Provides smoothing of accuracy estimates

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Hyperparameter Experiments
L. Scharenbroich, D. Mazzoni
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Battleship Game
M. C. Burl V-0631

• Spatial coherence/correlation
• Can the simulator be compressed?
• Kolmogorov complexity
• Can an SVM efficiently represent q(q)?

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Upcoming Work

• Maturing
• Software and deployment issues
• Optimization of resources
• Explicit balancing of exploration vs exploitation
• Completion
• Broadening
• New simulations
• High-dimensional input spaces
• Information-theoretic active learning
• Gaussian Processes to describe spatial
  correlation
• Markov Chain Monte Carlo Sampling
• Continuous-valued landscapes

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Acknowledgments

• Dennis DeCoste, Dominic Mazzoni, Lucas
  Scharenbroich, Kiri Wagstaff, Alex Holub, Pietro
  Perona
• Dan Durda, Bill Bottke, Jorg Micha-Jahn
• Erik Asphaug, Derek Richardson, Zoe Leinhardt
• NASA Intelligent Systems Program (early
  prototype)
• NASA Applied Information Systems Program

Publications

• SIAM Data Mining
• Icarus
• European Conf. on Machine Learning (ECML)
• CVPR Workshop on Online Learning
• NASA Tech Briefs
• JPL New Technology Report