arXiv subjects

Matthew Eagon

Publications and source records attributed to Matthew Eagon.

3 recordsLinked to original sources

arXiv2023

A Survey on Solving and Discovering Differential Equations Using Deep Neural Networks

Ordinary and partial differential equations (DE) are used extensively in scientific and mathematical domains to model physical systems. Current literature has focused primarily on deep neural network (DNN) based methods for solving a specific DE or a family of DEs. Research communities with a history of using DE models may view DNN-based differential equation solvers (DNN-DEs) as a faster and transferable alternative to current numerical methods. However, there is a lack of systematic surveys detailing the use of DNN-DE methods across physical application domains and a generalized taxonomy to guide future research. This paper surveys and classifies previous works and provides an educational tutorial for senior practitioners, professionals, and graduate students in engineering and computer science. First, we propose a taxonomy to navigate domains of DE systems studied under the umbrella of DNN-DE. Second, we examine the theory and performance of the Physics Informed Neural Network (PINN) to demonstrate how the influential DNN-DE architecture mathematically solves a system of equations. Third, to reinforce the key ideas of solving and discovery of DEs using DNN, we provide a tutorial using DeepXDE, a Python package for developing PINNs, to develop DNN-DEs for solving and discovering a classic DE, the linear transport equation.

cs.NE↗

arXiv2023

Eco-PiNN: A Physics-informed Neural Network for Eco-toll Estimation

The eco-toll estimation problem quantifies the expected environmental cost (e.g., energy consumption, exhaust emissions) for a vehicle to travel along a path. This problem is important for societal applications such as eco-routing, which aims to find paths with the lowest exhaust emissions or energy need. The challenges of this problem are three-fold: (1) the dependence of a vehicle's eco-toll on its physical parameters; (2) the lack of access to data with eco-toll information; and (3) the influence of contextual information (i.e. the connections of adjacent segments in the path) on the eco-toll of road segments. Prior work on eco-toll estimation has mostly relied on pure data-driven approaches and has high estimation errors given the limited training data. To address these limitations, we propose a novel Eco-toll estimation Physics-informed Neural Network framework (Eco-PiNN) using three novel ideas, namely, (1) a physics-informed decoder that integrates the physical laws of the vehicle engine into the network, (2) an attention-based contextual information encoder, and (3) a physics-informed regularization to reduce overfitting. Experiments on real-world heavy-duty truck data show that the proposed method can greatly improve the accuracy of eco-toll estimation compared with state-of-the-art methods.

cs.LG↗

arXiv2019

Flight Recovery of MAVs with Compromised IMU

Micro Aerial Vehicles (MAVs) rely on onboard attitude and position sensors for autonomous flight. Due to their size, weight, and power (SWaP) constraints, most modern MAVs use miniaturized inertial measurement units (IMUs) to provide attitude feedback, which is critical for flight stabilization and control. However, recent adversarial attack studies have demonstrated that many commonly used IMUs are vulnerable to attacks exploiting their physical characteristics. Conventional redundancy-based approaches are not effective against such attacks because redundant IMUs have the same or similar physical vulnerabilities. In this paper, we present a novel fault-tolerant solution for IMU compromised scenarios, using separate position and heading information to restore the failed attitude states. Rather than adding more IMU alternatives for recovery, the proposed method is intended to minimize any modifications to the existing system and control program. Thus, it is particularly useful for vehicles that have tight SWaP constraints while requiring simultaneous high performance and safety demands. To execute the recovery logic properly, a robust estimator was designed for fine-grained detection and isolation of the faulty sensors. The effectiveness of the proposed approach was validated on a quadcopter MAV through both simulation and experimental flight tests.

cs.RO↗