Prediction

Model order reduction is a pervasive and necessary activity in materials research. However, even though reduced order models are never perfect, their “imperfection” is almost never accounted for. In this talk, I will give an example of how the quality of an inference in materials research may be improved by accounting for the imperfection of a reduced order model. The example will consider inference of the properties of a substrate based on the behavior of a phase separating thin film deposited on the substrate.

We are developing computational models to elucidate the injection, expansion, and dynamic filling process for polyurethane foam such as PMDI. The polyurethane is a chemically blown foam, where carbon dioxide is produced via reaction of water, the blowing agent, and isocyanate. In a competing reaction, the isocyanate reacts with polyol producing the polymer. A new kinetic model is implemented in a computational framework, which decouples these two reactions as extent of reactions equations.

In this presentation, we will discuss issues pertaining to the construction of prediction intervals in the presence of model biases or discrepancies. We will illustrate this in the context of models for smart material systems but the issues are relevant for a range of physical and biological models. In many cases, model discrepancies are neglected during Bayesian model calibration. However, this can yield nonphysical parameter values for applications in which the effects of unmodeled dynamics are significant.

Climate prediction may be defined as probabilistic forecasting of the state of the atmosphere-ocean system for lead times of a season or longer. Explicitly or implicitly, climate prediction forms the basis of all socio-economic planning, such as water resource allocation or insurance risk assessment. Climate prediction is carried out using dynamical and statistical models over a range of timescales, ranging from seasonal to centennial.

Motivated by the need to properly address near-term (i.e. interannual to interdecadal) climate prediction as an initial-value problem, intense interest has emerged on the development of data assimilation for coupled atmosphere--ocean global climate models. Basic research on this problem is challenging due to the large computational expense associated with ensemble simulation of coupled climate models over long periods of time. Here we apply an idealized atmosphere-ocean climate model and an ensemble Kalman filter to explore three basic questions on this problem:

We describe a novel approach to evaluate the performance of global atmospheric ensemble prediction systems. This approach is based on the observation that beyond a 2-3-day forecast time (i) the errors in the extratropics in a numerical weather prediction are dominated by synoptic scale structures (ii) the spatial error patterns in a 1000-km radius local neighborhood of location l can be described by a local linear space, S(l), and (iii) ensemble prediction systems usually provide a good representation of S(l).

Kriging response surfaces are now widely used to optimize design parameters in industrial applications where assessing a design's performance requires long computer simulations. The typical approach starts by running the computer simulations at points in an experiment design and then fitting kriging surfaces to the resulting data. One then proceeds iteratively: calculations are made on the surfaces to select new point(s); the simulations are run at these points; and the surfaces are updated to reflect the results.

In this talk, I will discuss the dynamic programming
methods for
simultaneously predicting secondary structure and alignment
for two
sequences. This approach was first suggested by Sankoff in
1985.
Recently, it has been implemented by several groups, using
one or more
heuristics to reduce the computational cost. Our
implementation,
Dynalign, finds the lowest free energy common secondary
structure. It
uses single sequence secondary structure prediction and
sequence