论文库

Neural surrogates for computational fluid dynamics (CFD) are trained and ranked on datasets that each vary one design family in one flow domain. Such datasets cannot test the least that an aerodynamic foundation model must do: predict CFD-quality incompressible flow in seconds for new shapes in new enclosures. On DrivAerML, larger models and longer training barely lower Transolver's error; doubling the training cases cuts it by about 12% up to 400 cases, exhausting the dataset. We introduce AeroZoo, a benchmark and training corpus of 3,815 time-mean solutions to the unsteady Reynolds-averaged Navier--Stokes (RANS) equations with a transition model, across seven geometry families, eight enclosure configurations and Reynolds numbers from $10^3$ to $10^8$. Each sample poses a well-posed PDE problem in the form a solver receives it: the boundary meshes grouped by condition type, the prescribed values and the fluid properties. The 2,816 samples with a stable time mean form the canonical benchmark: two tasks, engineering metrics and 22 frozen splits, disjoint in geometry, that hold out geometry families, enclosures, boundary-condition layouts and Reynolds ranges. On the random split, boundary-condition tokens cut GeoTransolver's median velocity error from 76.9% to 8.4% of the inlet speed in single-seed runs (uniform inlet flow: 11.0%). ISLA, a transformer for boundary-driven PDEs, reaches 5.3% over four seeds, about 4 times the change from a finer mesh. On the same test samples, a held-out geometry family barely changes ISLA's error relative to uniform flow, and a held-out enclosure or boundary-condition layout raises it 2.4 to 9.2 times. The data and the scoring code will be released.

A foundational principle of physics is that all coordinate systems are equally valid: the behavior of a PDE-governed system does not depend on the origin or orientation of the frame, nor on the units or mesh used to write it down, and neither should a surrogate model. Yet the neural surrogates with the lowest errors on today's aerodynamics benchmarks lack these invariances and fail under simple transformations of the same problem: for models trained on PDEs of cars in one pose (i.e., translation and rotation) and from one mesher, rotating the full PDE raises the surface-pressure error from 4% to more than 100%, and re-sampling its boundary raises it to about 30%. We introduce ISLA (Invariant Slice Attention), a slice-attention transformer for steady, boundary-driven PDEs in which no learned operation receives a coordinate and every sum over the boundary is a quadrature. Positions enter only as distances and relative angles to learned slice anchors, lengths are measured in a unit computed from the boundary, and interior points query the boundary through a tree-accelerated learned kernel without influencing one another. With every boundary cell a token and an exact boundary read, ISLA is equivariant to rigid motions and reflections, invariant to the units of its declared data, and consistent under mesh refinement, while at every setting each query is independent of all other queries. On AeroZoo, 2,816 flows that vary in shape, size, speed, and boundary conditions, its mean reference-scaled velocity and pressure errors are at least 3.1 and 3.3 times lower than any baseline's. On AirfRANS its errors are second only to those of a boundary-integral model (GLOBE) and at least 1.6 times lower than those of Transolver and GeoTransolver.

Pore-space evolution and fluid displacement influence how rocks transmit and store fluids, affecting geological carbon storage, underground hydrogen storage and groundwater contaminant transport. A single time-resolved micro-CT experiment may produce tens to hundreds of three-dimensional images, and segmentation is required to quantify physical properties and run image-based simulations. Traditional methods such as thresholding perform poorly on noisy, low-contrast images and need manual adjustment per image; 3D deep learning networks segment each image without temporal information, so their errors vary between images and could be mistaken for physical change. Here we introduce a transformer-based 4D segmentation framework combining spatial and temporal information. It uses sequential images to resolve ambiguous phase assignments and separate physical change from segmentation error. The method is tested on images of mineral dissolution: it measures pore-volume growth and rock boundaries more accurately than an equivalent 3D model that ignores temporal information. It also captures the increase in permeability verified against reference segmentations and flow simulations. The advantage transfers to another dissolution sample without retraining. On two other datasets of fluid displacement, it reduces spurious changes in predicted rock and porosity fluctuations and accurately identifies filling events. Spatiotemporal segmentation turns sequences of hundreds of three-dimensional images into more reliable quantitative measurements of pore-space evolution and fluid displacement without per-image parameter adjustment to support the analysis of time-resolved CT imaging.

Reconstructing full flow fields from sparse sensors requires prior assumptions about unmeasured regions and physical variables. Yet it remains unclear when learned models outperform classical estimators and which aspects of their predictions can be trusted. FlowReconBench evaluates ten learned and five classical methods on three regimes: a laminar cylinder wake across Reynolds numbers, two-dimensional Kolmogorov turbulence and a large-scale three-dimensional (3D) isotropic turbulence. Methods share leakage-controlled splits and sensor draws and are scored on per-channel error, ensemble spread, calibration, spectra and cost. The leading method changes for each regime. Classical methods perform strongly in low-order and dense-sensing regimes. On the cylinder wake, linear stochastic estimation and gappy proper orthogonal decomposition lead, including for unobserved pressure. In 3D, inverse-distance weighting matches the best learned methods on observed channels. Data-driven methods become superior at decreasing sensor density or poor sensor observability. On Kolmogorov flow, continuous ranked probability score and error yield different method rankings: generative models offer broader but underdispersed ensembles, while deterministic models prioritize pointwise error. Generative models balance this tradeoff through their sampler budget, with a larger budget improving ensemble quality at higher computational cost. In 3D, scaling tests demonstrate that queryable methods are flat in memory, while full-grid construction methods run out of memory. Observing only 2 of 4 fields leaves the problem kinematically underconstrained, yet a latent model can reproduce structural similarities to the ground truth.