Application of the Decision Based Uncertainty Propagation in CBRN incidents

1. Application of the Decision Based Uncertainty Propagation in CBRN incidents Gabriel Terejanu1, Peter Scott1, Puneet Singla2, Tarunraj Singh2 1Department of Computer Science & Engineering 2Department of Mechanical & Aerospace Engineering University at Buffalo Buffalo, New York 14260 April 24th, 2009

2. Chemical Blast !!! BOOM ! I hope the city will be safe!

3. Command and Control Center Tell me where the toxic cloud is heading… Yes Sir! I will compute the hazard maps for the next hours.

4. We have a plan ! Looks like the city is safe. No need to evacuate … Indeed.

5. After 3 hours … What have I done ?

6. What happened?

7. Conventional Methodology… NO evacuation action Decision Maker 0.5 0.2 0.3 Uncertainty Propagation (Approximations) params 0.4 0.5 0.1 10,000 residents

8. Uncertainty Propagation Linear Propagation 0.3 0.3 Initial guess pdf Linear Propagation 0.5 0.5 Linear Propagation 0.2 0.2 =

9. Better Uncertainty Propagation Forecast Weight Update Linear Propagation 0.3 0.5 Initial guess pdf Linear Propagation 0.5 0.2 Linear Propagation 0.3 0.2 ≠ Update I: Continuous-time dynamical systems Updates the weights by constraining the Gaussian sum approximation to satisfy the Fokker-Planck equation Update II: Discrete-time nonlinear systems Weights to minimize the integral square difference between the true forecast pdf, given by the Chapman-Kolmogorov equation, and its Gaussian sum approximation

10. But … … even by improving the propagation method, chances are that we will still get a poor approximation to the forecast probability distribution where it matters. Eq. in the tails of the distribution.

11. New Approach ! EVACUATE action Decision Maker 10,000 residents Interaction Level 0.5 0.2 0.2 0.1 Uncertainty Propagation (Approximations) params 0.4 0.5 0.1 0.0 10,000 residents

12. Progressive Selection of Gaussian Components Initial pdf

13. New Approach !

14. Conclusions Interaction Level between decision maker and the prediction module – incorporate contextual information held by the decision maker Progressive Selection of Gaussian Components to supplement the initial uncertainty with new Gaussian components that are sensitive to the loss function at the decision time. The cost of the overall improvement is an increase in the number of Gaussian components The new probability density function addresses the region of interest and provides a better approximation overall, if any probability density mass is moving naturally towards the region of interest. Significantly enhanced accuracy within the decision maker’s region of interest.

15. Thank you Prediction with a Purpose, not prediction for the sake of it.