Towards extreme event prediction of turbulent flows with quantized local reduced-order models

TL;DR

This paper tackles the challenge of predicting extreme events in turbulent wall-bounded flows by developing a quantized local reduced-order modeling (ql-ROM) framework that combines cluster-based partitioning of the flow state space with local POD–Galerkin projections. By constructing a local ROM for each cluster and switching between them as the system traverses phase space, the approach captures the multiregime, nonlinear dynamics of the MFU with long-term stability and interpretability. A novel local modal energy-budget formulation quantifies intermodal energy transfers and dissipation within each cluster, linking dissipation bursts to energy transfer toward a few highly dissipative vortical modes driven by streak–traveling-wave interactions. The resulting framework provides a computationally efficient, reduced-space path toward detecting and potentially forecasting extreme events in turbulent flows, with clear physical interpretation and applicability to self-sustaining processes in near-wall turbulence.

Abstract

This work develops quantized local reduced-order models (ql-ROMs) of the turbulent Minimal Flow Unit (MFU) for the analysis and interpretation of intermittent dissipative dynamics and extreme events. The ql-ROM combines data-driven clustering of the flow state space with intrusive Galerkin projection on locally defined Proper Orthogonal Decomposition (POD) bases. This construction enables an accurate and stable low-dimensional representation of nonlinear flow dynamics whilst preserving the structure of the governing equations. The model is trained on direct numerical simulation data of the MFU. When deployed, the ql-ROM is numerically stable for long-term integration, and correctly infers the statistical behavior of the kinetic energy and dissipation observed of the full-order system. A local modal energy-budget formulation is employed to quantify intermodal energy transfer and viscous dissipation within each region of the attractor. The analysis reveals that dissipation bursts correspond to localized energy transfer from streamwise streaks and travelling-wave modes toward highly dissipative vortical structures, consistent with the self-sustaining process of near-wall turbulence. Beyond reduced modeling, the ql-ROM framework provides a pathway for the reduced-space characterization and potential prediction of extreme events. ql-ROM offer an interpretable and computationally efficient framework for the analysis and prediction of extreme events in turbulent flows.

Figures (5)

• Figure 1: Minimal Flow Unit. Computational setup. The left panel shows the computational domain. The right panel displays a representative snapshot of the simulated flow field, including the iso-surface of the $Q$-criterion ($Q = 0.05$) and the axial velocity distribution on the mid-plane $z=0$.
• Figure 2: Intermittent dynamics of the MFU. The upper panel shows the temporal evolution of the domain-averaged dissipation $D(t)$, highlighting intense dissipative bursts (extreme events). Dashed lines mark high-dissipation peaks and pre-burst states, illustrated below, where partial relaminarization is followed by rapid regeneration and energy transfer leading to dissipation bursts.
• Figure 3: Schematic overview of the quantized local reduced-order modeling (ql-ROM) framework. The manifold schematically represents the high-dimensional attractor on which the system dynamics evolve. The approach consists of four main stages: (1) data collection, where trajectories in the state space are sampled; (2) phase-space quantization, where the manifold is partitioned into clusters; (3) local basis construction, where a reduced-order model is built around each cluster centroid (illustrated by local 2D patches); and (4) model deployment, which includes (4.1) prediction using the active local ROM and (4.2) cluster transition through coordinate transformations between local bases.
• Figure 4: Performance of the ql-ROM for the Minimal Flow Unit (MFU). (a) Prediction error $\varepsilon(t)$, eq. \ref{['eq:error']}, for the test dataset. (b) Temporal evolution and PDFs of the total kinetic energy $E(t)$ for the FOM and the ql-ROM. (c) PDFs of $E(t)$ for FOM and ql-ROM. (d) Temporal evolution of the total dissipation $D(t)$, eq. \ref{['eq:dissipU']}, for both models. (e) Corresponding PDFs of $D(t)$ for FOM and ql-ROM. The PDFs distributions are estimated using kernel density estimation (KDE) Scott1992. The ql-ROM exhibits stable and accurate predictions, preserving the main energetic features of the FOM.
• Figure 5: Local modal energy budget analysis of the MFU. (a) Cluster-averaged dissipation normalized by its maximum value; cluster $k=3$ shows the highest dissipation. (b) Modal dissipation $\langle D_i^{\,k} \rangle_k$ for $k=3$, which shows that modes 5 and 6 are the most dissipative. (c) Selected intermodal energy transfer terms showing the main nonlinear couplings. (d) Axial velocity structures of selected modes.