Wednesday 8:30 AM

March 1, 2017

Room: 10

Location: San Diego Convention Ctr

We present mathematical tools for deriving optimal, computable bounds on local and global sensitivity indices of observables for complex stochastic models arising in biology, reaction kinetics and materials science. The presented technique allows for deriving bounds also for path-dependent functionals and risk sensitive functionals. We discuss problems and solutions to sensitivity estimation in stochastic systems with multiple disparate time scales. The use of variational representation of relative entropy also allows for error estimation, and uncertainty quantification in coarse-grained models.

In this paper, a mathematical model coupling electromagnetic field, flow field and temperature field using the finite element analysis software ANSYS was developed to understand the solidification at the secondary cooling zone of round billet under the application of pulse magneto-oscillation (PMO). The distribution of electromagnetic field, flow field and temperature field in the round billet was systematically studied under different electromagnetic parameters. The results showed that the intensity of magnetic field and electromagnetic force fluctuated with time and in-homogeneously distributed in space. Two flow circles formed in the upper and lower zones of bulk melt were caused by the PMO induced electromagnetic force. The numerical results about the temperature field presented that the induced flow could reduce the temperature gradient in axial direction of billet, giving rise to a more uniform internal temperature distribution.

Density functional theory (DFT) makes computational materials science into a practical tool for materials discovery. This contribution will examine the question of the best method to quantify “model form” error in DFT due to the functional form of the exchange correlation energy – that is, error due to its inherent physical approximations. Model-based Bayesian calibration in both intrusive and non-intrusive modes will be discussed. Intrusive methods locate the uncertainty within the DFT model itself, leading to stochastic predictions across chemistries and structures, but are challenging to implement. Recent results that speak to the feasibility of intrusive UQ for DFT will be presented.

Computer simulations are increasingly being used to inform decision making in both industrial and public policy settings. While this strategy saves time, money, and allows for efficient exploration of alternative scenarios, such use of models and simulations requires that their outputs be carefully assessed for their assumptions and accuracy so as to promote stability and confidence in the decision making process. Uncertainty quantification (UQ) is the field of study providing the foundation for such assessment techniques in scientific computing. In this talk I will present recent results in development of uncertainty quantification applied to estimates of the glass-transition temperature derived from molecular dynamics simulations of aerospace polymers. Elements of this uncertainty analysis---non-linear regression, and analysis of mixed effects---will be familiar to statisticians working in measurement sciences. However, the application of these tools to molecular dynamics "measurements" represents a new avenue for their use.

The Fisher Information Matrix (FIM) is a foundational concept in statistics quantifying how much information data carries about model parameters. For models with many parameters, parametric uncertainty is often very large as revealed by the FIM eigenvalues. The FIM also acts as a Riemannian metric on the manifold of parameterized models. For many models in a variety of fields, the model manifold is bounded with a hierarchy of widths (as measured by the FIM) so that the model behavior exhibits a low effective dimensionality. This low effective dimensionality implies an absolute limit on the range of possible model predictions so that models with large (even infinite) parametric uncertainty may be predictive. I discuss implications of this observation for predictive modeling. I also show how this approach motivates new methods of model reduction (the Manifold Boundary Approximation Method) and a new framework for understanding the structure of models called Information Topology.

Tailorability of transformation temperature (MS) due to Ni partitioning during precipitation of secondary phases makes NiTi shape memory alloys attractive in a number of applications. Therefore, the hard task of implementing and calibrating a physical precipitation model has been performed for this binary system in MatCalc©. Sensitive parameters have been found in this model through forward analysis. A Bayesian approach based on MCMC-Metropolis-Hastings algorithm has been selected to calibrate these model parameters. A relationship has been proposed for matrix/precipitate interfacial energy versus aging temperature and nominal composition, using the calibrations of interfacial energy besides the other parameters with each experimental data individually. After inserting this equation in the model, the other parameters have been calibrated with all experimental data together. Although the model results do not fit the data exactly, the data is located in model's 95% Bayesian confidence intervals.