A Data-Free Physics-Informed Neural Operator for Level-Set Interface Advection
Read the original on arXiv Machine Learning →The Flow has not summarised this story yet — read it at arXiv Machine Learning.
The Flow has not summarised this story yet — read it at arXiv Machine Learning.
arXiv:2608. 08322v1 Announce Type: cross Abstract: Physics-informed neural networks applied to the level-set formulation of interface advection commonly augment the residual and initial-condition losses with an eikonal regulariser, penalising the deviation of $\|\nabla\phi\|$ from unity.
arXiv:2605. 24651v2 Announce Type: replace-cross Abstract: We propose a Weak-form Physics-Informed Neural Operator (WINO), a data-free framework that combines the efficiency of neural operators with the geometric flexibility of the $\varphi$-finite element method ($\varphi$-FEM).
arXiv:2608. 08608v1 Announce Type: cross Abstract: Fourier neural operators (FNOs) provide efficient nonlocal spectral learning, but varying geometries and independently chosen discretizations remain difficult to accommodate.
arXiv:2609.24947v1 Announce Type: new Abstract: Neural operators evaluate parametric partial differential equations cheaply but degrade sharply outside their training distribution. Physics-informed n...
The paper introduces the Spatiotemporal Conditional Operator (STCO), a framework for learning neural operators that can incorporate prescribed target‑time condition fields—such as body motion, inflow disturbances, or body‑force actuation—into time‑dependent PDE simulations. STCO combines a Flow‑Aware Graph Leaf (FAGL) partitioning scheme with Dual‑Site Feature‑wise Linear Modulation (DSFiLM) to inject these conditions before and after the core operator computation. Evaluated on twelve backbone architectures across an immersed‑boundary CFD benchmark, STCO achieves significant reductions in relative‑L2 field error (31.1%) and pressure‑derived load error (24.7%) while improving long‑lead predictions for most backbones.
arXiv:2606. 06171v1 Announce Type: cross Abstract: Physics-Informed Neural Networks inherently suffer from task interference because they rely on a shared parameter space to satisfy both governing differential equations and boundary conditions.