Nathan Lee

Dougal Stewart, Nathan Lee, Kenneth Duru

Robust and convergent high-order numerical methods for solving partial differential equations are highly attractive due to their efficiency on modern and next-generation hardware architectures. However, designing such methods for nonlinear hyperbolic conservation laws remains a significant challenge. In this work, we introduce a framework based on dual-pairing (DP) and upwind summation-by-parts (SBP) finite difference (FD) and discontinuous Galerkin (DG) finite element methods, aimed at achieving accurate and robust numerical approximations of nonlinear conservation laws. The framework ensures entropy consistency and features an intrinsic high-order accurate filter designed to detect and resolve regions where the solution is poorly captured or discontinuities are present. The DP SBP FD/DG operators form a dual pair of discrete derivative operators that collectively preserve the SBP property. Furthermore, these operators are constructed to be upwind, allowing them to incorporate dissipation within the elements themselves.This contrasts with traditional SBP and collocated DG spectral element methods, which typically induce dissipation solely through numerical fluxes at element interfaces. Our framework facilitates the systematic combination of DP SBP FD/DG operators with skew-symmetric and upwind flux splitting techniques. This integration enables the development of robust, high-order accurate schemes for nonlinear hyperbolic conservation laws.

Viet K. Nguyen, Nathan Lee, Mohammad Husain

Deep learning-based perception pipelines in autonomous ground vehicles are vulnerable to both adversarial manipulation and network-layer disruption. We present a systematic, on-hardware experimental evaluation of five attack classes: FGSM, PGD, man-in-the-middle (MitM), denial-of-service (DoS), and phantom attacks on low-cost autonomous vehicle platforms (JetRacer and Yahboom). Using a standardized 13-second experimental protocol and comprehensive automated logging, we systematically characterize three dimensions of attack behavior:(i) control deviation, (ii) computational cost, and (iii) runtime responsiveness. Our analysis reveals that distinct attack classes produce consistent and separable "fingerprints" across these dimensions: perception attacks (MitM output manipulation and phantom projection) generate high steering deviation signatures with nominal computational overhead, PGD produces combined steering perturbation and computational load signatures across multiple dimensions, and DoS exhibits frame rate and latency degradation signatures with minimal control-plane perturbation. We demonstrate that our fingerprinting framework generalizes across both digital attacks (adversarial perturbations, network manipulation) and environmental attacks (projected false features), providing a foundation for attack-aware monitoring systems and targeted, signature-based defense mechanisms.