FD-Bench supplies the first modular, reproducible benchmark and leaderboard for comparing neural PDE solvers on fluid dynamics tasks with direct numerical solver baselines.
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arXiv preprint arXiv:2408.12171 , year=
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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.
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.
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.
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.
citing papers explorer
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FD-Bench: A Modular and Fair Benchmark for Data-driven Fluid Simulation
FD-Bench supplies the first modular, reproducible benchmark and leaderboard for comparing neural PDE solvers on fluid dynamics tasks with direct numerical solver baselines.
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PINS: Proximal Iterations with Sparse Newton and Sinkhorn for Optimal Transport
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.
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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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DeepPropNet: an operator learning-based predictor for thermal plasma properties
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.
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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.
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Harnessing AI for Inverse Partial Differential Equation Problems: Past, Present, and Prospects
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.
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Encoding strategies for quantum enhanced fluid simulations: opportunities and challenges
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.
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A review of quantum machine learning and quantum-inspired applied methods to computational fluid dynamics
A survey of variational quantum algorithms, quantum neural networks, and tensor networks for addressing scalability challenges in computational fluid dynamics.
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