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Handling and Quantifying Uncertainty in Dynamical Systems

The ability to conduct fast and reliable simulations of dynamical systems is of special interest to Army operations. Because such simulations can be very complex and involve millions of variables, it can be prohibitive in CPU time to run repeatedly on many different configurations. Reduced-Order Modeling (ROM) provides a concrete way to handle such complex simulations using a realistic amount of resources. However, uncertainty is hardly taken into account. Changes in the definition of a model for instance could have dramatic effects on the outcome of simulations. Therefore, reduced models as well as general decisions based on simulations should be informed and not assume that models are 100% correct. The AHPCRC team at UTEP worked on developing techniques to be able to handle and quantify uncertainty, with the goal that all results should be guaranteed. In particular, major accomplishments include:

The ability to conduct Model-Order Reduction in the presence of uncertainty in the model

In the development of smart sensors, the idea is to exploit observed data (with uncertainty, since measurements are never 100% accurate) to identify features of a given dynamical phenomenon (e.g., values of the input parameters, initial conditions) so as to be able to propagate this new knowledge forward and predict future behavior. This is very important in Army applications as a reliable understanding of a developing situation can allow taking preventive or palliative action before a situation worsens. We were able to do this by coupling interval computations with interval constraint solving techniques.

Figure 1:  On the right-hand side, we show how we are able to reconstruct the behavior of a known phenomenon, in this case, FitzHugh-Nagumo solely based on one observed data of variable v:v40 at time 4.  Using this one measurement, we are able to identify the initial conditions of the observed phenomenon (on v and w) and predict its future behavior through v100 and w100

The ability to (re)compute values of parameters of on-going dynamical phenomena that specifically allow enforcing given behavior (and, similarly, avoiding given behaviors). This can be performed “on the fly”, for instance in the middle of a mission affected by an unexpected event threatening personnel or material, to re-compute parameters to ensure the safety of the mission.

Professor Ceberio has developed a computational framework for quantifying uncertainty that is flexible and scalable during her participation in the AHPCRC program.  The framework combines techniques from model order reduction and interval computing and will be further developed in collaboration with ARL teams.  It will be applied to applilcations such as sampling distributations and machine learning algorithms.  – Dr. Radkrishnan Balu, ARL