As noted in my Research Page, one of my main areas of interest is sensitivity analysis. This includes computational techniques as well as exploring the applicability of this information.

*Sensitivity analysis* refers to quantifying the dependence of
solutions on problem parameters. Typically, the solutions are those
of a mathematical model (eg. a partial differential equation, PDE)
and parameters may include equation coefficients (usually material
properties such as conductivity, viscosity, etc.), initial and
boundary conditions, or the shape of the domain/length of a time
interval.

For example, consider the following skematic of heat conduction in a composite rod.

The temperature at any position (x) of the rod and at any time (t): will also depend on these other parameters. Thus, we can write to highlight these dependencies. The sensitivity

- Gradients for Optimization
- Nearby Solutions
- Reduced-Order Modeling
- Relative Importance of Parameters
- Turbulence Modeling
- Uncertainty Analysis

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