This minisymposium brings together researchers advancing high-order discretizations for large-scale simulations of hyperbolic and multi-physics PDEs. The focus is on structure-preserving numerics (conservation, positivity, entropy stability, kinetic-energy preservation), robust shock capturing, fast time integration, and scalable preconditioning on heterogeneous hardware (CPUs, GPUs, and emerging accelerators). We emphasize rigorous verification and validation through manufactured solutions, benchmark suites, uncertainty quantification, and practical algorithm-hardware co-design that reduces memory traffic and enables mixed-precision performance. A central theme is the careful use of scientific machine learning (SciML) to augment (not entirely replace) classical solvers. Topics include learned multigrid and preconditioner components, surrogate Jacobian actions for implicit solves, conservative reduced-order models and operator-inference surrogates with certified error control, ML-guided sensors/limiters and hp-adaptivity/AMR that respect discrete invariants, and data-assisted closure or parameter inference integrated with adjoints and ensemble methods. We explicitly invite talks that clarify when ML effectively encodes physics and when it fails or requires remedies to ensure reliability and generalization. Target applications span compressible aerodynamics and hypersonics, magnetohydrodynamics and space physics, acoustics and electromagnetics, multiphase and reacting flows, and coupled multi-physics in complex geometries. The minisymposium aims to chart practical routes for deploying high-order, structure-preserving and SciML-augmented methods in routine simulation workflows.