Determining anomalies in data using classical machine learning techniques typically requires characterizing the notion of what is "normal" or "expected" in the instance space. Upon doing so, one would then utilize this profile to identify points that do not coincide with this description of normal. However, this process tends to be costly computationally, thus limiting…

Often in large numerical simulations decisions are made to reduce the fidelity of particular features in order to simulate the event duration. One common method is the application of shell formulations instead of 3D continuum, especially for objects with large aspect ratios of extent to thickness. While these reductions allow for longer duration events to…

Many large computational problems depend on solutions to systems of linear equations. One widely used method of solving systems of linear equations is the Conjugate Gradient method (CG). Terminating CG after only a few iterations can save computational resources but can also cause an error in the solution to the system of linear equations, and…

By their very nature, rare event probabilities are expensive to compute; they are also delicate to estimate as their value strongly depends on distributional assumptions on the model parameters. Hence, understanding the sensitivity of the computed rare event probabilities to the hyperparameters that define the distribution law of the model parameters is crucial. We show…

We consider the shallow water magnetohydrodynamic (SWMHD) equations, in which multiscale phenomena appear in geophysics, astrophysics, and energy production applications. However, capturing both large and small scales numerically requires an exact treatment of the physically-observed divergence-free condition of the magnetic field and typically a very fine spatial grid. An alternative to requiring a fine spatial…

There are several challenges associated with inverse problems in which the unknown parameters can be modeled as piecewise constant functions. We model the unknown parameter using multiple level sets to represent the piecewise constant function. Adopting a Bayesian approach, we impose prior distributions on both the level set functions that determine the piecewise constant regions…

When dealing with large compartment models it can often be challenging to track how a small component of the model affects the overall system. This is an issue when trying to determine if a model is in its "simplest form" or if there are components that can be removed without significantly affecting the model's behavior.…