Data-Driven Forecasting of Turbulent Flows via Space-Time Projection

We present Space-Time Projection (STP), a data-driven forecasting method tailored for high-dimensional, transient datasets. STP builds on space-time Proper Orthogonal Decomposition (POD) to derive orthogonal modes capturing both past (hindcast) and future (forecast) dynamics. Forecasting involves projecting new observations onto these modes, exploiting their inherent spatiotemporal correlations. The method combines dimensionality reduction and time-delay embedding, requiring only the truncation rank as a tunable parameter. Hindcast performance reliably predicts short-term forecasting accuracy, setting a practical lower bound on expected errors. We illustrate STP's effectiveness using two cases: simulations of anisotropic turbulence from supernova explosions and experimental velocity measurements of a turbulent, high-subsonic flow. In comparisons with standard Long Short-Term Memory (LSTM) neural networks—while acknowledging possible enhancements from alternative configurations—STP consistently delivers better forecasting accuracy.