Accelerated and data-efficient flow prediction in stirred tanks via physics-informed learning

Turbulence is ubiquitous in engineering and science, yet direct simulation is prohibitively expensive. The Reynolds-averaged Navier-Stokes (RANS) equations provide savings exceeding ten orders of magnitude but introduce unclosed terms (the closure problem). Offline-trained machine-learning (ML) closures suffer distribution shift in predictive simulations, while ML methods that bypass the governing equations struggle to generalise from scarce high-fidelity data. We develop a physics-derived deep learning closure model for RANS, the Deep Algebraic Reynolds Stress Model (DARSM), which can be trained on small datasets and accurately generalise across Reynolds numbers, to unseen geometries, and to different flow regimes. A neural network maps flow invariants to empirical parameters in an implicit algebraic Reynolds stress equation, derived from the Reynolds stress transport equations under the weak-equilibrium assumption, imposing physics-based structure on the ML closure. End-to-end optimisation through the governing PDEs and the coupled implicit closure eliminates distribution shift, but both unrolled and implicit automatic differentiation fail on the stiff coupled solver. We derive adjoint equations that exploit the solver's implicit-explicit structure for efficient optimisation. On canonical square-duct and periodic-hill benchmarks, DARSM reduces average test velocity error over baseline RANS by $2$-$4\times$ across Reynolds number, geometries, and flow regimes, with peak case-level reductions of $12\times$. The model trained on attached, anisotropy-dominated flows (square duct) accurately generalises without retraining to separated flows (periodic hills), a regime change in the underlying physics. DARSM also outperforms five established ML methods: offline training, tensor-basis neural networks, field-inversion machine learning, DeepONets, and physics-informed neural networks.

Deep learning surrogates for CFD flow-field prediction often rely on large, complex models, which can be slow and fragile when data are noisy or incomplete. We introduce FlowForge, a staged local rollout engine that predicts future flow fields by compiling a locality-preserving update schedule and executing it with a shared lightweight local predictor. Rather than producing the next frame in a single global pass, FlowForge rewrites spatial sites stage by stage so that each update conditions only on bounded local context exposed by earlier stages. This compile-execute design aligns inference with short-range physical dependence, keeps latency predictable, and limits error amplification from global mixing. Across PDEBench, CFDBench, and BubbleML, FlowForge matches or improves upon strong baselines in pointwise accuracy, delivers consistently better robustness to noise and missing observations, and maintains stable multi-step rollout behavior while reducing per-step latency.

This work presents a high-fidelity computational fluid dynamics (CFD) and data-driven modeling framework for assembly-level flow characterization in a four-loop pressurized water reactor (PWR). A full lower-plenum and core-inlet domain was constructed using publicly available geometry and operating conditions, enabling transient simulations with pump-induced swirl boundary conditions. The results show that cold-leg swirl and lower-plenum transport generate strongly heterogeneous assembly-wise inlet flow distributions, particularly near the lower core region, while axial resistance and mixing progressively homogenize the flow at higher elevations. These physics-informed datasets were subsequently used to evaluate machine learning (ML) applications for partial field reconstruction and short-term autoregressive prediction. A 3D convolutional-based inpainting model successfully recon-structed missing assembly-level mass flow rates from partial observations, with errors concentrated in the highly turbulent base (bottom) layer and diminishing significantly in upper layers. Comparative analysis across multiple ML models demon-strates that spatially aware architectures, particularly ConvLSTM, significantly outperform sequence-based (LSTM) and operator-learning (DeepONet) approaches by effectively capturing coupled spatio-temporal dynamics. The study also high-lights key challenges, including the sensitivity of inlet flow predictions to turbulence and mesh resolution, as well as the absence of full-scale experimental validation data. Despite these limitations, the results remain consistent with expected physical behavior. Overall, this work establishes high-fidelity CFD as a critical foundation for developing data-driven surrogates, sparse sensing strategies, and future multiphysics coupling frameworks.