Physics-Aware Adaptive Checkpointing with Shadow Systems for Nonlinear PDE Simulations

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Abstract
Large-scale simulations of nonlinear partial differential equations (PDEs) that exhibit strongly transient behavior and pattern-forming dynamics produce enormous amount of data, which, even with modern storage system, cannot be stored for later curation. Current I/O strategies either write dense time series of snapshots, which is often prohibitive in I/O and storage, or store a few checkpoints that enable restart but incur expensive recomputation cost and provide no control on post-restart error growth, especially when lossy compression is used. Moreover, most if not all existing strategies take no account of the actual physical state of the system. Here, we present a simple physics-aware I/O framework in which a lowcost shadow system adaptively triggers lossy checkpoints when the shadow system deviates from the fine-scale simulation. The shadow system can be a coarsened replica of the fine-scale simulation that evolves concurrently. This means that checkpoints are taken based on the physical state of the system: fewer checkpoints are triggered when the system is quiescent while more are taken when the system undergoes a rapid change. This type of behavior is observed in many systems such as Brusselator and FitzHugh-Nagumo. We illustrate that our framework maintains stable restarts, keeps fine-scale restart errors bounded by shadow errors, and reconstructs the time history with significantly lower error and storage than interpolating fixed-interval snapshots, at only modest additional runtime overhead.

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