A Stability Analysis of Neural Networks and Its Application to Tsunami Early Warning

Abstract Neural networks (NNs) enable precise modeling of complicated geophysical phenomena but can be sensitive to small input changes. In this work, we present a new method for analyzing this instability in NNs. We focus our analysis on adversarial examples, test‐time inputs with carefully crafted human‐imperceptible perturbations that expose the worst‐case instability in a model's predictions. Our stability analysis is based on a low‐rank expansion of NNs on a fixed input, and we apply our analysis to a NN model for tsunami early warning which takes geodetic measurements as the input and forecasts tsunami waveforms. The result is an improved description of local stability that explains adversarial examples generated by a standard gradient‐based algorithm, and allows the generation of other comparable examples. Our analysis can predict whether noise in the geodetic input will produce an unstable output, and identifies a potential approach to filtering the input that enable more robust forecasting.