Numerical Approaches for Developing Predictive Models

We present an approach to uncertainty propagation in dynamic systems, exploiting information provided by related experimental results along with their models. The approach relies on a solution mapping technique to approximate mathematical models by polynomial surrogate models. We use these surrogate models to formulate prediction bounds in terms of polynomial optimizations. Recent results on polynomial optimizations are then applied to solve the prediction problem. Two examples which illustrate the key aspects of the proposed algorithm are given. The proposed algorithm offers a framework for collaborative data processing among researchers.