Scott Moe

Donsub Rim, Scott Moe, Randall J. LeVeque

Snapshot matrices built from solutions to hyperbolic partial differential equations exhibit slow decay in singular values, whereas fast decay is crucial for the success of projection- based model reduction methods. To overcome this problem, we build on previous work in symmetry reduction [Rowley and Marsden, Physica D (2000), pp. 1-19] and propose an iterative algorithm that decomposes the snapshot matrix into multiple shifting profiles, each with a corresponding speed. Its applicability to typical hyperbolic problems is demonstrated through numerical examples, and other natural extensions that modify the shift operator are considered. Finally, we give a geometric interpretation of the algorithm.

Naman Maheshwari, Nicholas Malaya, Scott Moe et al.

For Deep Neural Networks (DNNs) to become useful in safety-critical applications, such as self-driving cars and disease diagnosis, they must be stable to perturbations in input and model parameters. Characterizing the sensitivity of a DNN to perturbations is necessary to determine minimal bit-width precision that may be used to safely represent the network. However, no general result exists that is capable of predicting the sensitivity of a given DNN to round-off error, noise, or other perturbations in input. This paper derives an estimator that can predict such quantities. The estimator is derived via inequalities and matrix norms, and the resulting quantity is roughly analogous to a condition number for the entire neural network. An approximation of the estimator is tested on two Convolutional Neural Networks, AlexNet and VGG-19, using the ImageNet dataset. For each of these networks, the tightness of the estimator is explored via random perturbations and adversarial attacks.