Zero-shot super-resolution is information-theoretically impossible for some simple operators but possible under Hölder smoothness of outputs, accompanied by generalization bounds.
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Recent advances on machine learning for computational fluid dynamics: A survey.arXiv preprint arXiv:2408.12171, 2024a
13 Pith papers cite this work. Polarity classification is still indexing.
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FD-Bench supplies the first modular, reproducible benchmark and leaderboard for comparing neural PDE solvers on fluid dynamics tasks with direct numerical solver baselines.
PINS combines an outer proximal-point loop over shifted entropic OT problems with inner Sinkhorn warm-up and sparse-Newton refinement to reach unregularized OT solutions with global convergence and lower error than Sinkhorn baselines.
A physics-informed Fourier-wavelet transformer model reports the lowest normalized mean-squared error on cylinder-wake and fluid-structure interaction velocity-field benchmarks compared with spectral, transformer, operator-learning, and PINN baselines.
DW-Net improves the accuracy versus computational cost Pareto front over standard U-Nets for 2D and 3D multi-scale flow benchmarks by stacking multiple waves while keeping training settings identical.
SINO learns PDE operators from limited data using spectral features from frequency indices, a Pi-block for nonlinearities, and a low-pass filter, achieving 1-2 orders of magnitude better accuracy than prior methods on 2D/3D benchmarks.
DeepPropNet predicts thermal plasma properties with relative L2 errors of 10^{-3} to 10^{-2} for SF6-N2 and C4F7N-CO2-O2 mixtures using single-property and mixture-of-experts architectures trained on high-fidelity data.
A conditional diffusion model trained on partitioned incomplete samples for physical dynamics achieves asymptotic convergence to the true generative process under mild conditions and outperforms baselines in imputation.
PINNs and DeepONets solve Newtonian plane Couette flow with dynamic wall slip; DeepONet achieves 0.36% mean relative error on unseen cases and 540X speedup over numerical methods.
A survey organizing AI methods for inverse PDE problems into inverse problems, inverse design, and control categories, covering applications and future challenges like physics-informed models and uncertainty quantification.
PnP-Corrector decouples pre-trained physics engines from a correction agent to mitigate reciprocal error amplification in coupled spatiotemporal forecasting, cutting error by 28% on a 300-day ocean-atmosphere task.
Encoding strategies for quantum fluid simulations trade off compactness against practicality in state preparation, measurement, boundary conditions, and nonlinear operations, with no single approach being universally optimal.
A survey of variational quantum algorithms, quantum neural networks, and tensor networks for addressing scalability challenges in computational fluid dynamics.
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Deep Wave Network for Modeling Multi-Scale Physical Dynamics
DW-Net improves the accuracy versus computational cost Pareto front over standard U-Nets for 2D and 3D multi-scale flow benchmarks by stacking multiple waves while keeping training settings identical.
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Spectral-inspired Operator Learning with Limited Data and Unknown Physics
SINO learns PDE operators from limited data using spectral features from frequency indices, a Pi-block for nonlinearities, and a low-pass filter, achieving 1-2 orders of magnitude better accuracy than prior methods on 2D/3D benchmarks.
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Incomplete Data, Complete Dynamics: A Diffusion Approach
A conditional diffusion model trained on partitioned incomplete samples for physical dynamics achieves asymptotic convergence to the true generative process under mild conditions and outperforms baselines in imputation.