Black Swans, Dragon Kings and the Science of Rare Events: Problems for the Exascale Era and Beyond

The purpose of the project is to develop the computational frameworks for exploring the tails of distributions, which lead to rare but consequential (and often catastrophic) outcomes. Two such rare events are “Black Swans” (occurring from pre-existing but unencountered events) and “Dragon Kings (occurring due to an external shock to the system). The methods developed are expected to have application in aerospace sciences, power generation and utilization, chemical processing, weather prediction, computational chemistry, and other fields.

The prediction of risk is emerging as a research focus in a broad set of fields, ranging from economics and evolutionary biology to propulsion. The risk in these systems arises from the possibility of anomalous or rare events given a macroscopic initial state. Such events are often associated with severe human or financial costs, requiring mitigation or robust prediction methods. Consider the following examples:
Certification of aircraft engines require demonstration of so-called high altitude relight, where the engine is shut off at a prescribed altitude, and restarted. Due to the highly turbulent flow inside the engine, ignition is an unpredictable and stochastic event. However, failure to ignite within a prescribed time-frame can lead to the loss of the aircraft.
The response to the Great Recession has been the development of stress tests for financial institutions. However, these tests only evaluate present conditions at a single institution without any prognostic capabilities. An emerging approach is to model the interconnections between banks and other financial institutions as a global network and understand the role of emergent behavior – a homogenization of practices and movement of capital that marks a threshold towards an anomalous event.

Research: We have established a theoretical framework for studying rare events in nonlinear dynamical systems. The goal here is to develop a generalized exascale workflow that allows applications to be invoked as modules in the rare event search algorithm. For this, we will leverage existing uncertainty quantification apparatus for simultaneous execution of multiple realizations of a solver, as well as optimization strategies for reducing energy required for high performance computing (HPC). This suite of tools will allow risk prediction to be implemented across scientific disciplines by switching to domain-specific application solvers. We will demonstrate this using model problems involving a) flame stabilization relevant to aircraft engines, and b) protein folding relevant to evolutionary biology.

Advocacy & Planning: One of the primary goals of this work will be to advocate risk prediction as a class of problems for designing, developing and testing future high-performance computing systems. In particular, this class of problems introduces a set of questions that cannot be answered using experimental sciences or conventional large scale computing. The co-PIs at the national labs will help implement these tools in a generalized framework so that other groups will be able to readily adopt these concepts. Further, we will actively engage the U-M community in both adopting these tools as well as contributing to the different scientific aspects.

In evolutionary biology, recent research2 suggests some protein functions are developed based on so- called “permissive” mutations, which involve accumulation of non-deterministic events during the process of evolution. In fact, the chance of such events is small enough (< 0.03%) that if biological evolution is replayed, it is almost guaranteed that the organisms of today will not exist in their present form. In many of these fields, statistical tools that rely on past data form the main predictive framework. Such tools are necessarily empirical, need extensive data on prior risk events, and require risk events to be in- duced by similar causes as that in pre-existing data/information. Here, we seek a radically different approach. The objective of this work is to establish a fundamental science based approach to risk prediction. Here, we will use pre-existing models derived using physical principles, or from data-driven techniques, to construct the set of outcomes feasible given operating, boundary and initial conditions. Since the approach is theory-based, the underlying cause for anomalous events can be directly obtained, which can then be subject to validation using experiments or existing data. However, these methods will require leadership computing resources even for otherwise computationally “simple” problems. We believe that this approach will form the basis for reducing or

U-M Researchers

Venkat Raman

Other Researchers

Jacqueline Chen (Sandia National Laboratory)

Ramanan Sankaran (Oak Ridge National Laboratory)