Extending learned closure models to complex fluid physics (compressible shocks, irregular domains, reactive flows, high Reynolds numbers)

Develop closure models based on scientific machine learning that are applicable to complex fluid-physics regimes, specifically for compressible flows with shock waves, flows in irregular geometries, reactive flows, and high-Reynolds-number conditions, thereby extending beyond simplified benchmarks to these sparsely explored but practically important cases.

Background

In the outlook, the authors emphasize that most existing demonstrations of learned closures focus on simplified PDEs or idealized flow settings, and note concerted efforts to build datasets and benchmarks. They state explicitly that moving beyond such testbeds to more complex physics remains unresolved.

They list specific fluid-mechanics regimes—compressible flows with shocks, irregular domains, reactive flows, and high-Reynolds-number flows—as sparsely explored but important targets for closure modeling with scientific machine learning.

References

Extension to more complex physics is still an open topic---in fluid flows, closure models for compressible flows with shock waves, for irregular domains, for reactive flows, and for high Reynolds number flows are a sparsely explored but important territory [shankar2023differentiable,sirignano2020dpm].

— Scientific machine learning for closure models in multiscale problems: a review  (2403.02913 - Sanderse et al., 2024) in Section 9.5 (Benchmarking, test cases, and datasets)

Despite these advances, developing a unified and computationally efficient correction strategy that reduces spurious oscillations while preserving sharp transport features remains a challenging open problem.

— Physics-Informed Learning of Probabilistic Gegenbauer Reconstruction for Transport-Dominated Problems  (2608.18001 - Yan et al., 18 Aug 2026) in Section 1, Introduction

How well do the findings of this thesis on simple PDEs and structured grids translate to more complex physics and unstructured domains?

— From Numerical Simulators of PDEs to Neural Emulators and Back  (2608.24547 - Koehler, 25 Aug 2026) in Section 11.3, “Beyond Structured Grids”

Thus, the deeper question is what these AI models are missing because coarse-graining has removed physics from their training data. Is this absence part of why AIWP models struggle with gray swans ? What does it imply for probabilistic forecasts, especially at subseasonal-to-seasonal lead times, which rely on perturbation growth and must be well calibrated ? The question might be even more pressing for long-term climate emulators: AI models of the emerging global km-scale, physics-based simulations are typically trained on output first heavily coarse-grained, e.g., to \sim$100~km , to $\Delta t$ of hours to a day, and even to daily-averaged state variables , which can discard significant physics.

— Missing the Butterfly and Predicting the Past: Features or Bugs of Accurate AI Weather Models?  (2608.25835 - Hassanzadeh et al., 26 Aug 2026) in Discussion, paragraph beginning “Growing efforts focus on identifying the physics that AI models miss”

One remaining question is whether the model may have been able to learn the constraints we identified as beneficial.

— A physics-constrained machine-learning sub-grid-scale modeling approach for turbulent premixed flames  (2608.28525 - Suh et al., 28 Aug 2026) in Section 5, Conclusion (final section)