Uncertainty Quantification and Complex Systems

Uncertainty is ubiquitous in modeling complex systems in various scientific and engineering problems that involve stochastic processes, random parameters, unknown physics, or noise. Uncertainty Quantification (UQ) is the science of quantitative characterization and reduction of uncertainties in real world problems. The behavior of such problems can be described using mathematical modeling and computer simulations. UQ methods aim to predict system responses against uncertain inputs, quantify confidence of the predictions, obtain optimized solutions that are stable across a wide range of inputs, and reduce computational or experiment cost in engineering design.

UQ lies at the intersection of applied mathematics, statistics, and engineering. Most practical real world UQ problems are quite challenging because they are high-dimensional and therefore, computationally expensive to solve, e.g., the stochastic optimal control of complex industrial engineering systems. Therefore, there is the need to develop systems solvers which are efficient for stochastic forward, inverse, or control problems. Efficient numerical algorithms are also aimed at breaking the so-called curse of dimensionality associated with UQ problems.

At Lehigh ISE, we tackle the challenges of real-world large-scale complex engineering problems with uncertainty and investigate a broad range of methods relevant to optimization, control, and decision-making under uncertainty. Our contributions span areas such as stochastic processes, queueing systems, experimental design, sensitivity analysis, optimization under uncertainty, statistical Bayesian inverse problems, multifidelity methods, among others.

Lehigh's research groups / institutes / programs:

Lehigh Uncertainty Quantification Research Group