No Free Lunch in Flow Surrogates under Time-Varying Boundary Conditions: A Two-Regime Study

This study investigates the performance of eight different surrogate modeling architectures across two distinct transient flow regimes: the three-dimensional slurry film in chemical-mechanical planarization (CMP) and the two-dimensional Kármán vortex street (KVS) behind a cylinder. The researchers evaluate models based on their ability to handle time-varying boundary conditions, comparing architectures that learn either full-field or latent representations and those that predict trajectories either in one shot or via autoregressive, step-by-step updates.

The researchers demonstrate a clear "no free lunch" result: no single architecture performs best across both regimes. For the boundary-driven CMP film, a one-shot full-field model is superior, achieving a 3.2% relative error in cumulative wall shear stress. Conversely, the KVS wake, which features self-sustained oscillations, requires the phase memory provided by autoregressive feedback; in this regime, a latent autoregressive DeepONet retains 96% of the shedding power, while other models fail by damping the motion to near zero.

Crucially, the study finds that standard metrics like pointwise RMSE are misleading. They often favor models that produce damped or unphysical results, failing to capture critical physical features such as onset latency or structural integrity. The authors propose a specialized evaluation suite that scores five distinct physical dimensions: the field, its structure, invented motion, amplitude, and timing.

Surrogate models offer significant speedups—often $10^3$ to $10^4$ times faster than finite-element solvers—making them attractive for high-dimensional parameter sweeps. However, this study highlights that the "break-even" point, where the surrogate becomes more efficient than direct simulation, is dictated by the offline cost of generating training data. Furthermore, the results warn researchers against assuming that a model validated on a simple regime will remain reliable when applied to more complex, dynamic physics.