Uncertainty Quantification and Management
University of Southern California
Problems
Recent innovations in science and technology have provided the impetus for a new paradigm in scientific discovery. Thus, while new sensing technologies allow us to probe nature with unprecedented accuracy, new computing resources allow us to account for great complexities in physical behavior. These newfound capabilities have heightened society's expectations from the scientific process, requiring it to provide foresight and thus mitigate risks associated with ever-increasing complexity. Of recent interest to us are risks associated with carbon sequestration, next generation (GEN IV) nuclear reactors, complex networks, and advanced materials. In these and other applications, a common challenge is to delineate the scope of predicted behaviors that can be certified given our current knowledge, while at the same time determining the worth of additional information, in the form of numerical resolution, experimental evidence, model complexity, or combinations thereof.
Approach
We adopt probability theory as logic for science, and rely on its mathematical structure to develop a methodology that permits the consistent description and characterization of discrepancies between predictions and observations. These discrepancies are associated with numerics, experiments, and models. In particular, we take advantage of the functional analytic structure that can be endowed on probabilistic objects, thus providing us with a geometric perspective, in a space whose so-called stochastic dimension reflects the complexity of the underlying phenomenon. We rely on the polynomial chaos decompositions to affect orthogonal projections and approximations in this space. Clearly, the curse of dimensionality is a ubiquitous challenge in our work, and we address it by relying on a mixture of model reduction approaches, ranging from informationtheoretic to multiscale and statistical mechanics methods.
Findings
By developing sampling distributions for the coefficients of the polynomial chaos expansions, construed as sample statistics, we tag some of the stochastic dimensions as reflecting epistemic uncertainty, and fold them into the probabilistic structure already in place. This has provided us with meaningful error bounds around the predicted probability of failure for various systems, which is of significance to policy and decision-making. In addition, we have been able to determine the cost of increasing the confidence in these predictions, providing owners and decision makers with a solid foundation for valuating performance-based designs.
Impact
Our research develops the necessary concept, methods and tools to transition from computational science to prediction science. Through suitable methods for uncertainty quantification and management, the promise of a computational laboratory providing an adequate surrogate to physical reality may finally be at hand. This will be a critical enabling technology that will greatly accelerate the transition from concept to market across many applications, while at the same time reducing lifecycle cost and facilitating the process of scientific discovery.
Core competencies
- Uncertainty propagation and management in computational science and engineering.
- Validation of predictive models.
- Risk analysis and management.
- Probabilistic models for complex materials and systems.
- Prognosis for multi scale and multiphysics behavior.
Current research team members
- Sonjoy Das (Postdoc)
- Maarten Arnst (Postdoc)
- Maud Comboul (Ph.D. Candidate)
- Arash Noshadravan (Ph.D. Candidate)
- Ramakrishna Tippireddy (Ph.D. Candidate)
- Hadi Meidani (Ph.D. Candidate)
- Daniel Lakeland (Ph.D. Candidate)
- Iman Yadegaran (Ph.D. Candidate)
Recent graduates
- Sonjoy Das (Ph.D. 2008), Postdoc at USC.
- Alireza Doostan (Ph.D. 2006), now Assistant Professor at UC Boulder.
- Debraj Ghosh (Ph.D. 2005), now Assistant Professor at the Indian Institute of Science.
- Zenon Medina-Cetina (Ph.D. 2005), now Assistant Professor at Texas A&M.
Current research collaborations
- PetaApps for Risk Assessment of Carbon Sequestration: Don Zhang (USC), Kevin Long (TexasTech), Mark Adams (Columbia).
- Uncertainty Modeling and Analysis in Complex Networks: Youssef Marzouk (MIT), Habib Najm (Sandia) and Omar Knio (Hopkins).
- Theory and Algorithms for Uncertainty in Multiphysics Multiscale Systems: Eric Phipps, Rodney Schmidt, John Red-Horse, and Roger Pawlowski (Sandia).
- Structural Health Monitoring for System Integrity: Aditi Chattopadhyay (ASU), Jim Spicer (Hopkins), Dan Inman (VT), Sami Masri (USC).
- Probabilistic Models for Manufacturing of Composite Materials : Christian Soize (Paris-Est).
- Anticipation in Population Dynamics: Yannis Kevrekidis (Princeton) and Paul Torrens (ASU).