Flowers: A Warp Drive for Neural PDE Solvers
arXiv:2603. 04430v2 Announce Type: replace Abstract: We introduce Flowers, a neural architecture for learning PDE solution operators built entirely from multihead warps.
arXiv:2607. 22280v2 Announce Type: replace-cross Abstract: Compressible multiphase flows involving shocks and material interfaces arise in applications such as bubble collapse and droplet breakup, where strong nonlinear interactions produce complex interface deformation, mixing, and multiscale dynamics.
arXiv:2603. 04430v2 Announce Type: replace Abstract: We introduce Flowers, a neural architecture for learning PDE solution operators built entirely from multihead warps.
arXiv:2510.01365v2 Announce Type: replace Abstract: The ability to model mechanics of soft materials under flowing conditions is key in designing and engineering processes and materials with targeted...
arXiv:2608. 04222v1 Announce Type: cross Abstract: Turbulence is a central testbed for machine learning on physical dynamics because its governing laws are known exactly.
arXiv:2606. 17460v1 Announce Type: new Abstract: Neural operators are widely used as surrogate solution maps for partial differential equations (PDEs), but full-size models can be costly to store, deploy, and evaluate in many-query scientific workflows.
arXiv:2512. 07847v2 Announce Type: replace Abstract: Benchmarking has been the cornerstone of progress in computer vision, natural language processing, and the broader deep learning domain, driving algorithmic innovation through standardized datasets and reproducible evaluation protocols.
ChannelFlow-Tools is an open‑source, configuration‑driven pipeline that generates machine‑learning‑ready datasets for three‑dimensional obstructed channel flows. It combines procedural obstacle geometry generation across six shape families, signed‑distance‑field voxelisation, lattice‑Boltzmann simulation, and packaging into ML‑ready tensors, all driven by reproducible configuration files. The pipeline is validated through mesh‑integrity audits, SDF representation checks, solver benchmarks, and data‑integrity audits, and it has been used to train surrogate models (3D U‑Net, FNO, U‑FNO) that learn geometry‑to‑flow mappings and exhibit physically interpretable behaviour on out‑of‑distribution splits.
arXiv:2609. 19039v1 Announce Type: cross Abstract: We introduce the Long-Short-Range Neural Network (LSR-Net), a novel neural operator architecture designed for data-driven forward evolution modeling, and extends it to the prediction of nonlinear fluid dynamics.
arXiv:2607. 03809v1 Announce Type: new Abstract: Normalising flows provide a powerful variational family for approximate inference, yet individual architectures often fail to generalise across heterogeneous posterior geometries.
arXiv:2602. 00072v2 Announce Type: replace Abstract: The performance of machine learning surrogates is critically dependent on data quality and quantity.
FlowMoDL is an unrolled neural network designed for highly accelerated 4D flow MRI reconstruction, optimizing both anatomical magnitude and phase-derived velocity accuracy. It alternates a learned (3+1)D spatiotemporal denoiser with conjugate‑gradient data‑consistency updates, using a dual‑pathway conditioning scheme to handle acceleration factors from 10× to 50×. Trained with a deep‑supervision composite loss that penalizes velocity magnitude and angular errors, FlowMoDL outperforms classical and deep‑learning baselines on the multi‑center CMRx4DFlow dataset, achieving superior gradient‑step efficiency and robust convergence across all acceleration factors.
arXiv:2606. 16050v1 Announce Type: cross Abstract: Robust deep learning under heavy-tailed and impulsive noise remains challenging because conventional losses such as mean squared error (MSE) exhibit unbounded sensitivity to outliers.
arXiv:2607. 00460v1 Announce Type: cross Abstract: Predicting complex spatiotemporal dynamics in physical processes often demands computationally expensive numerical methods or data-driven neural networks that suffer from high training costs, error accumulation, and limited generalizability to unseen parameters.