Uncertainty Quantification Module Overview
What Can the Uncertainty Quantification Module Do?
The Uncertainty Quantification Module can be used throughout the COMSOL product family. It provides a general interface for characterizing uncertainties, propagating input uncertainties in COMSOL Multiphysics models, and statistically analyzing output quantities of interest.
The Uncertainty Quantification Module can use any model parameters as inputs. The analyses performed are global in nature. In other words, the variations in the inputs need not be small. This ability makes the functionality very versatile for a number of investigation scenarios. A COMSOL model is, for most applications, a mathematical model of reality. Such a model will have inputs that are related to:
•
The physics — For example, boundary conditions, sources, and coupling terms, such as the velocity magnitude or direction, for an inflow boundary condition in a transport problem.
•
The materials — For example, material coefficients or details in their specification, such as Young’s modulus for a structural mechanics problem.
•
The geometry — For example, manufacturing specifications, such as a hole radius or plate thickness.
•
The discretization — For example, mesh properties such as the maximum and minimum mesh element sizes. Another example is the relative tolerance used to solve a time-dependent problem.
For a particular model, it is often expected that the variation of a few inputs will have a significant influence on the results. This can be a perfectly natural effect of the design of the model and the physics involved. This should lead to an expected sensitivity in the results to the variation in these inputs. At the same time, it is also expected that other inputs have a small or even negligible influence; that is, there is an expected insensitivity to the results. The Uncertainty Quantification Module can be used to test the validity of such expectation and verify that some key input variations affect the key outputs in the model while other input variations do not. Most experienced modelers routinely perform these types of exercises before they can trust their model. When there are just a few inputs, this can be done, for example, by performing a well-designed parametric sweep. In contrast, for more than a few parameters, this cannot be done in a simple and efficient way, and simply assuming that a model is correct can be dangerous. Uncertainty quantification is a convincing way to show the correctness of a model.
Furthermore, once you have verified the key parameters that account for most of the variations of the quantities of interest, you can take advantage of this knowledge to simplify further analysis by considering only those parameters.
The motivations for doing further, more rigorous uncertainty quantifications can be to answer questions like:
•
Which of the key parameters are more important than others for my quantities of interest? Remember that a high sensitivity to a variation can be both a desirable and an undesirable property. For example, a sensor is often designed to be sensitive to a certain input signal; sensitivity is thus desirable. A hi-fi amplifier’s characteristics should not be sensitive to the input frequency; sensitivity is here undesirable. How does a modification of the input uncertainties affect this? If the input uncertainty cannot be reduced (or increased), perhaps the underlying design can be altered to modify it to improve the sensitivity.
•
How does the uncertainty distribution of input parameters translate to the uncertainty distribution of a quantity of interest? What are the confidence intervals for the quantities of interest?
•
Given a nominal design and some specific uncertain inputs, what is the probability that the design fails? The failure can be a complete breakdown of the design, but it can also be phrased in terms of a quality criterion.
Given the available resources, these questions can be answered by performing different types of uncertainty quantification studies.