Inverse problems exist in a wide variety of physical domains from aerospace engineering to medical imaging. The goal is to infer the underlying state from a set of observations. When the forward model that produced the observations is nonlinear and stochastic, solving the inverse problem is very challenging. Neural networks are an appealing solution for solving inverse problems as they can be trained from noisy data and once trained are computationally efficient to run. However, inverse model neural networks do not have guarantees of correctness built-in, which makes them unreliable for use in safety and accuracy-critical contexts. In this work we introduce a method for verifying the correctness of inverse model neural networks. Our approach is to overapproximate a nonlinear, stochastic forward model with piecewise linear constraints and encode both the overapproximate forward model and the neural network inverse model as a mixed-integer program. We demonstrate this verification procedure on a real-world airplane fuel gauge case study. The ability to verify and consequently trust inverse model neural networks allows their use in a wide variety of contexts, from aerospace to medicine.

As neural networks (NNs) become more prevalent in safety-critical applications such as control of vehicles, there is a growing need to certify that systems with NN components are safe. This paper presents a set of backward reachability approaches for safety certification of neural feedback loops (NFLs), i.e., closed-loop systems with NN control policies. While backward reachability strategies have been developed for systems without NN components, the nonlinearities in NN activation functions and general noninvertibility of NN weight matrices make backward reachability for NFLs a challenging problem. To avoid the difficulties associated with propagating sets backward through NNs, we introduce a framework that leverages standard forward NN analysis tools to efficiently find over-approximations to backprojection (BP) sets, i.e., sets of states for which an NN policy will lead a system to a given target set. We present frameworks for calculating BP over-approximations for both linear and nonlinear systems with control policies represented by feedforward NNs and propose computationally efficient strategies. We use numerical results from a variety of models to showcase the proposed algorithms, including a demonstration of safety certification for a 6D system.

Deep learning methods can be used to produce control policies, but certifying their safety is challenging. The resulting networks are nonlinear and often very large. In response to this challenge, we present OVERT: a sound algorithm for safety verification of nonlinear discrete-time closed loop dynamical systems with neural network control policies. The novelty of OVERT lies in combining ideas from the classical formal methods literature with ideas from the newer neural network verification literature. The central concept of OVERT is to abstract nonlinear functions with a set of optimally tight piecewise linear bounds. Such piecewise linear bounds are designed for seamless integration into ReLU neural network verification tools. OVERT can be used to prove bounded-time safety properties by either computing reachable sets or solving feasibility queries directly. We demonstrate various examples of safety verification for several classical benchmark examples. OVERT compares favorably to existing methods both in computation time and in tightness of the reachable set.

Flooding is a destructive and dangerous hazard and climate change appears to be increasing the frequency of catastrophic flooding events around the world. Physics-based flood models are costly to calibrate and are rarely generalizable across different river basins, as model outputs are sensitive to site-specific parameters and human-regulated infrastructure. In contrast, statistical models implicitly account for such factors through the data on which they are trained. Such models trained primarily from remotely-sensed Earth observation data could reduce the need for extensive in-situ measurements. In this work, we develop generalizable, multi-basin models of river flooding susceptibility using geographically-distributed data from the USGS stream gauge network. Machine learning models are trained in a supervised framework to predict two measures of flood susceptibility from a mix of river basin attributes, impervious surface cover information derived from satellite imagery, and historical records of rainfall and stream height. We report prediction performance of multiple models using precision-recall curves, and compare with performance of naive baselines. This work on multi-basin flood prediction represents a step in the direction of making flood prediction accessible to all at-risk communities.