Energy-Stable Parametric Operator Inference across Regime Transitions: Application to Unconfined Buoyant Plumes in Stratified Ambients
Abstract
Buoyant plumes in stratified ambients arise in wildfire smoke transport, ventilation, and pollutant dispersion, where many-query prediction requires models that stay accurate and stable as the dynamics transition from free rise to internal-wave trapping. Operator Inference (OpInf) learns polynomial reduced models from snapshots, and the Boussinesq plume depends affinely on the squared buoyancy frequency N2. However, this compatibility masks two stability gaps: a single affine operator family can distort the per-parameter dynamics into unstable spectra, and for quadratic OpInf models, finite-time blowup is governed by a cubic energy injection channel from the inferred quadratic operator. To address these gaps, we develop cyclic-skew regime-bridged OpInf (CR-OpInf). We derive an affine-inadequacy diagnostic that links the departure from a shared affine family to destabilizing spectral drift before integration. In place of the shared affine fit, we interpolate per-parameter operators with a Gaussian kernel. We also extend the cyclic-skew quadratic constraint to the buoyancy-source-forced parametric setting, closing the cubic energy channel and isolating this closure as the boundedness mechanism. We further introduce a regime-bridging basis split that resolves free rise and trapped intrusion structures while preserving the cyclic-skew structure under convex interpolation. Applied to an unconfined Boussinesq plume and a viscous Burgers problem spanning a smooth-to-shock transition, CR-OpInf remains bounded for five training horizons, avoids the divergence of affine and unconstrained variants, tracks the plume rise, and recovers stratification-dependent rise scaling at moderate horizons. To our knowledge, this is the first parametric OpInf study of an unconfined stratified plume.
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BibTeX
@misc{kwon2026energystable,
title = {{Energy-Stable Parametric Operator Inference across Regime Transitions: Application to Unconfined Buoyant Plumes in Stratified Ambients}},
author = {Youngjun Kwon and Abdollah Shafieezadeh},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20626},
eprint = {2610.20626},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20626},
}
RIS
TY - UNPB
TI - Energy-Stable Parametric Operator Inference across Regime Transitions: Application to Unconfined Buoyant Plumes in Stratified Ambients
AU - Youngjun Kwon
AU - Abdollah Shafieezadeh
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.20626
UR - https://arxiv.org/abs/2610.20626
AB - Buoyant plumes in stratified ambients arise in wildfire smoke transport, ventilation, and pollutant dispersion, where many-query prediction requires models that stay accurate and stable as the dynamics transition from free rise to internal-wave trapping. Operator Inference (OpInf) learns polynomial reduced models from snapshots, and the Boussinesq plume depends affinely on the squared buoyancy frequency N^2. However, this compatibility masks two stability gaps: a single affine operator family can distort the per-parameter dynamics into unstable spectra, and for quadratic OpInf models, finite-time blowup is governed by a cubic energy injection channel from the inferred quadratic operator. To address these gaps, we develop cyclic-skew regime-bridged OpInf (CR-OpInf). We derive an affine-inadequacy diagnostic that links the departure from a shared affine family to destabilizing spectral drift before integration. In place of the shared affine fit, we interpolate per-parameter operators with a Gaussian kernel. We also extend the cyclic-skew quadratic constraint to the buoyancy-source-forced parametric setting, closing the cubic energy channel and isolating this closure as the boundedness mechanism. We further introduce a regime-bridging basis split that resolves free rise and trapped intrusion structures while preserving the cyclic-skew structure under convex interpolation. Applied to an unconfined Boussinesq plume and a viscous Burgers problem spanning a smooth-to-shock transition, CR-OpInf remains bounded for five training horizons, avoids the divergence of affine and unconstrained variants, tracks the plume rise, and recovers stratification-dependent rise scaling at moderate horizons. To our knowledge, this is the first parametric OpInf study of an unconfined stratified plume.
ER -