Simulating many-engine spacecraft: Exceeding 1 quadrillion degrees of freedom via information geometric regularization

TL;DR

The paper introduces information geometric regularization (IGR) to enable unprecedentedly large and scalable compressible CFD simulations for many-engine spacecraft plumes, replacing traditional viscous shock-capturing with a well-conditioned, inviscid-like regularization. By combining IGR with unified memory architectures and mixed-precision computation, the authors achieve over 200 trillion grid points (1 quadrillion DOF), with substantial reductions in time-to-solution and energy-to-solution across flagship systems. The work reports near-ideal weak scaling and strong scaling on El Capitan, Frontier, and Alps, as well as substantial memory-footprint reductions (~25×) and notable energy savings, enabling design-optimization workflows at exascale. The approach is generalizable to other compressible-flow problems and potentially broader PDE contexts, offering a path to predictive, simulation-driven engineering for aerospace and beyond.

Abstract

We present an optimized implementation of the recently proposed information geometric regularization (IGR) for unprecedented scale simulation of compressible fluid flows applied to multi-engine spacecraft boosters. We improve upon state-of-the-art computational fluid dynamics (CFD) techniques along computational cost, memory footprint, and energy-to-solution metrics. Unified memory on coupled CPU--GPU or APU platforms increases problem size with negligible overhead. Mixed half/single-precision storage and computation on well-conditioned numerics is used. We simulate flow at 200 trillion grid points and 1 quadrillion degrees of freedom, exceeding the current record by a factor of 20. A factor of 4 wall-time speedup is achieved over optimized baselines. Ideal weak scaling is seen on OLCF Frontier, LLNL El Capitan, and CSCS Alps using the full systems. Strong scaling is near ideal at extreme conditions, including 80% efficiency on CSCS Alps with an 8-node baseline and stretching to the full system.

Figures (8)

• Figure 1: Simulation results showing the interacting plumes from an array of 33 thrusters in a configuration inspired by the SpaceX Super Heavy with 16.5 trillion degrees of freedom. (The thrusters themselves are for visualization purposes. We model them through inflow boundary conditions.)
• Figure 2: Inviscid regularization: Localized artificial diffusion (LAD) spreads shocks over a user-defined width (a,i). The resulting curve is not high-order smooth. This can cause methods with a high order of accuracy to develop oscillations and, ultimately, fail. Increasing the width for coarser discretizations yields unphysical and significant dissipation of oscillatory solution profiles (b,i). Information geometric regularization replaces shocks with smooth profiles (a,ii) at the grid scale and preserves oscillatory features (b,ii).
• Figure 3: Information geometric regularization modifies shocks by changing the geometry according to which the flow map $\phi_t$ evolves in time. In the modified geometry, the trajectories of two tracer particles $t \mapsto \phi_t(x_1), \phi_t(x_2)$ converge in $t$ rather than cross. The regularization strength $\alpha$ determines the rate of convergence. The vanishing viscosity solution is recovered in the $\alpha \rightarrow 0$ limit. Figure adapted from Cao and Schäfer cao2023information with author permission.
• Figure 4: Schematic of the chip-to-chip (C2C) transfers of intermediate time-step variables between the on-node CPU and GPU devices. The time sub-steps are $q_{1,2}$ and the full step integration is stored in $q_1$.
• Figure 5: Visualization of a three-engine configuration and its plumes using (a) FP16, (b) FP32, (c) FP64 storage, and (d) the baseline numerics. The contours indicate where the velocity exceeds the free stream flow, and the initial state is seeded with smooth, random noise in all cases. FP32 and FP64 yield visually indistinguishable results. Visual differences in the FP16 case are solely due to the earlier onset of physical flow instabilities, yet they remain faithfully representative of the flow features. The grid-dependent nature of the baseline shock-capturing approach results in spurious grid-alignment artifacts.