Non-intrusive Learning of Physics-Informed Spatio-temporal Surrogate for Accelerating Design

Reservoir simulation workflows face a fundamental data asymmetry: input parameter fields (geostatistical permeability realizations, porosity distributions) are free to generate in arbitrary quantities, yet existing neural operator surrogates require large corpora of expensive labeled simulation trajectories and cannot exploit this unlabeled structure. We introduce PI-JEPA (Physics-Informed Joint Embedding Predictive Architecture), a surrogate pretraining framework that trains without any completed PDE solves, using masked latent prediction on unlabeled parameter fields under per-sub-operator PDE residual regularization. The predictor bank is structurally aligned with the Lie--Trotter operator-splitting decomposition of the governing equations, dedicating a separate physics-constrained latent module to each sub-process (pressure, saturation transport, reaction), enabling fine-tuning with as few as 100 labeled simulation runs. On single-phase Darcy flow, PI-JEPA achieves $1.9\times$ lower error than FNO and $2.4\times$ lower error than DeepONet at $N_\ell{=}100$, with 24% improvement over supervised-only training at $N_\ell{=}500$, demonstrating that label-free surrogate pretraining substantially reduces the simulation budget required for multiphysics surrogate deployment.

We test whether an architecture that succeeds on a simple flow regime also succeeds on a richer one, with each trained separately on each regime. We explore two transient flows under time-varying boundary conditions: the three-dimensional slurry film in chemical-mechanical planarisation (CMP), central to semiconductor manufacturing, and the two-dimensional Kármán vortex street (KVS). Eight surrogate models on one shared pipeline differ in whether they learn the full field or a latent representation, and in whether they predict in one shot or step by step. No single architecture wins both regimes. On the film, a one-shot full-field model reconstructs the cumulative wall shear stress to 2.7% relative error. On the wake, a latent autoregressive DeepONet retains 90% of the shedding power that direct and one-shot models damp to almost zero. The treatment of time decides the outcome. The self-sustained wake calls for autoregressive feedback and the boundary-driven film for a direct map. Pointwise RMSE hides the damped oscillation on the wake, compresses the sixfold lead on the film's process target, and picks the damped model under wake extrapolation. The evaluation scores five physical questions. Trained surrogates answer queries 10^3 to 10^4 times faster than the finite-element solver and pay off from the first query beyond the training set on the film and from the third on the wake. Neither the winning architecture nor its validation holds across regimes. The choice of surrogate should follow the dynamical character of the target flow, and its validation should resolve the failure modes.

Physics-informed surrogate models can accelerate computational fluid dynamics simulations. However, many existing methods reproduce global flow patterns more reliably than localized multiscale structures. This study presents a physics-informed Fourier-wavelet transformer for next-step velocity-field reconstruction in real-world flow benchmarks. The proposed formulation combines hybrid Fourier-wavelet spectral encoding with physics-biased self-attention based on partial differential equation residual diagnostics. It also uses self-supervised pretraining through Masked Physics Prediction and Equation Consistency Prediction. The experiments are conducted on two real benchmark cases: cylinder-wake flow and fluid-structure interaction. All approaches are evaluated under a shared local protocol and compared with spectral, transformer-based, operator-learning, and physics-informed neural-network baselines. On the cylinder-wake benchmark, the proposed model achieves the best aggregate accuracy, with an all-channel normalized mean-squared error of 0.05875 and an all-channel Pearson correlation coefficient of 0.97019. On the fluid-structure-interaction benchmark, it gives the lowest all-channel normalized mean-squared error of $2.70 \times 10^{-4}$, compared with $4.02 \times 10^{-4}$ for the strongest baseline. Component-wise field comparisons and scale-separated diagnostics further show stronger recovery of localized wake structures, including near-body, wake-core, and far-wake features. The results demonstrate improved real-world flow reconstruction while maintaining a practical accuracy-cost tradeoff.