Residual-guided AI-CFD hybrid method enables stable and scalable simulations: from 2D benchmarks to 3D applications

TL;DR

This work tackles the instability of purely data-driven CFD surrogates by introducing XRePIT, a residual-guided, automated hybrid framework that couples ML acceleration with solver-based corrections. The method stabilizes long-term MPC-like rollouts (≥$10^4$ timesteps), generalizes to unseen boundary conditions via online transfer learning, and scales to 3D flows with substantial speedups (up to $4.98\times$) while preserving high fidelity (temperature errors ∼$10^{-3}$ and velocity errors < $10^{-2}$ m s$^{-1}$). The authors demonstrate architecture-agnostic stability through adversarial benchmarking between FVMN and FVFNO, revealing a practical trade-off between model complexity and speed. The 3D buoyancy-driven case confirms the approach’s utility for real-world simulations, suggesting broad applicability to engineering design and real-time monitoring, supported by an open-source framework and comprehensive supplementary material for reproducibility.

Abstract

Purely data-driven surrogates for fluid dynamics often fail catastrophically from error accumulation, while existing hybrid methods have lacked the automation and robustness for practical use. To solve this, we developed XRePIT, a novel hybrid simulation strategy that synergizes machine learning (ML) acceleration with solver-based correction. We specifically designed our method to be fully automated and physics-aware, ensuring the stability and practical applicability that previous approaches lacked. We demonstrate that this new design overcomes long-standing barriers, achieving the first stable, accelerated rollouts for over 10,000 timesteps. The method also generalizes robustly to unseen boundary conditions and, crucially, scales to 3D flows. Our approach delivers speedups up to 4.98$\times$ while maintaining high physical fidelity, resolving thermal fields with relative errors of ~1E-3 and capturing low magnitude velocity dynamics with errors below 1E-2 ms-1. This work thus establishes a mature and scalable hybrid method, paving the way for its use in real-world engineering.

Figures (11)

• Figure 1: From costly traditional numerical method to stable, accelerated hybrid simulation.(a) A representative high-fidelity 3D CFD simulation, which is computationally expensive and time-consuming. (b) The failure of a conventional data-driven surrogate. The relative residual of a FVMN-based model grows exponentially during an autoregressive rollout, leading to a distorted, non-physical temperature field at 1,000 timesteps as shown in inset. (c) A schematic of the proposed hybrid simulation concept, where acceleration is provided by a neural network and long-term stability is ensured by a traditional numerical solver. (d) The stability claim of the proposed method which is brought by the constant monitoring of the residual mass as the flow evolves. The strategy for using residual threshold to quantify the error accumulation made the temperature field stabilize even after 1000 timesteps. (e) A summary of the wall-clock time comparison between the proposed framework (blue) and the traditional CFD solver (gray) for all cases investigated throughout the study.
• Figure 2: XRePIT performance and long-term stability analysis. (a) The relationship between the acceleration factor, MSE for temperature, the relative residual threshold, and the number of transfer learning epochs. It illustrates how the hyperparameters can be tuned to balance computational speed against predictive accuracy. (b) The relative L2 error over time for temperature (right) and velocity magnitude (left) under different physical boundary conditions. This demonstrates the framework's robustness, as the prediction errors for both quantities are consistently maintained at a minimal level (less than 1% for temperature and around 10% for low magnitude velocity). (c) A diagram indicating the six monitoring points placed along the vertical centerline of the domain. Three points are located near the top boundary and three near the bottom to capture the temporal evolution of the flow for quantitative comparison. (d) Line plots comparing the values predicted by XRePIT against the ground truth at the probe locations defined in (c). The results show that the hybrid simulation accurately follows the same physical trends as the ground truth solver, even during very long-term simulations, confirming the stability. (e) A visual comparison between the velocity magnitude fields predicted by XRePIT and the ground truth solver at t = 40s and t = 110s. The corresponding absolute error fields remain low (in the range of 1e-2), demonstrating high fidelity even after 10,000 timesteps in the hybrid regime.
• Figure 3: Architectural extensibility and performance benchmarking in XRePIT. (a) The architecture features a tier-input system, distinct processing pathways for different physical variables, and a combined derivative loss function to ensure physical consistency. This modular design allows for the FNO block to be replaced with fully connected layers to constitute the baseline FVMN model. (b) Relative L2 error for velocity magnitude (dotted lines) and temperature (solid lines) over 10,000 timesteps for both the FVMN (blue) and FVFNO (orange) models. Both architectures maintain low, stable error profiles, demonstrating the framework's ability to support different neural network designs without sacrificing physical fidelity. (c) The number of consecutive timesteps predicted by each neural network per switch. The plot shows that for both models, the framework intelligently adapts to flow complexity, taking fewer ML steps during transient phases and increasing the prediction horizon as the flow stabilizes. This highlights the robustness of the residual-guided switching mechanism.
• Figure 4: Scalability and performance of the XRePIT framework in a 3D simulation. (a) Schematic of probe locations within the 3D computational domain used for quantitative temporal analysis. (b) Comparison of the temporal evolution of a flow variable at a representative probe point between the ground truth (blue) and the XRePIT hybrid prediction (orange), demonstrating long-term trend agreement. (c) Domain-wide MSE for the three velocity components (left) and temperature (right) over 10,000 timesteps, showing error stabilization after an initial transient period. (d,e) Qualitative comparison of the 3D flow field at t = 110s. The visualization shows streamlines colored by velocity magnitude for the ground truth OpenFOAM simulation (d) and the XRePIT hybrid simulation (e), confirming that the complex flow structures are accurately reproduced.
• Figure 5: The automated workflow and physics-informed components of the hybrid methodology.(a) Schematic of the automated, timestep-coupled hybrid workflow. The loop alternates between rapid, auto-regressive prediction by the machine learning (ML) surrogate and on-demand, single-step correction by the computational fluid dynamics (CFD) solver, triggered by a residual-guided switching logic. (b) The physics-inspired tiered stencil input structure. The input for each cell is a feature vector containing its own value and the values of its immediate neighbors, providing the neural network with local spatial context analogous to a finite volume discretization. (c) A priori boundary condition enforcement. Before being passed to the ML model, the domain is padded with an extra layer of cells that are filled with the appropriate physical boundary conditions, making the surrogate inherently aware of the domain constraints. (d) Importance of the a posteriori mass flux correction. The plot demonstrates that applying the adjustPhiML utility to enforce mass conservation on the ML-predicted velocity field significantly stabilizes the simulation, enabling longer ML rollouts.