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: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:2509. 15236v2 Announce Type: replace-cross Abstract: Data-driven surrogate models are increasingly used in computational fluid dynamics, and their reliability depends on the quality of the training data.
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.
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.
arXiv:2512. 17534v2 Announce Type: replace-cross Abstract: Modeling and controlling fluids is critical across science and engineering.
arXiv:2511. 15684v2 Announce Type: replace-cross Abstract: Foundation models have transformed machine learning for language and vision, but achieving comparable impact in physical simulation remains a challenge.
arXiv:2602. 22188v2 Announce Type: replace Abstract: Modelling rock-fluid interaction requires solving a set of partial differential equations (PDEs) to predict the flow behaviour and the reactions of the fluid with the rock on the interfaces.
Generative AI emulators are increasingly used in scientific domains where we already have strong theory, benchmarks, and physical intuition. This raises a central evaluation and interpretability question: when a foundation-style model can reproduce known continuum dynamics, what internal mechanism supports that behavior, is the internal behaviour consistent with known physics, and how does it relate to where the emulator succeeds or fails?