arXiv Machine Learning
Jun 2
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.
A Robust In-Context Model for Conservation Laws: Injecting Context into Flux Neural Operators via Recurrent Vision Transformers
arXiv:2605. 05488v2 Announce Type: replace Abstract: We propose an architecture that augments the Flux Neural Operator (Flux NO), which combines the classical finite volume method (FVM) with neural operators, with ViT-based context injection.
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arXiv AI
Jun 10
Structure-Preserving Learning Improves Geometry Generalization in Neural PDEs
arXiv:2602. 02788v2 Announce Type: replace-cross Abstract: We aim to develop physics foundation models for science and engineering that provide real-time solutions to Partial Differential Equations (PDEs) which preserve structure and accuracy under adaptation to unseen geometries.
arXiv Machine Learning
Aug 20
Flux-form spatiotemporal neural operators for coarse-grained dynamics of multiscale PDEs
The paper introduces flux‑form spatiotemporal neural operators for predicting coarse‑grained dynamics of multiscale PDEs without relying on closure models. It learns a surrogate evolution operator from filtered high‑fidelity data, using Fourier convolution for spatial mixing and a causal kernel with time‑lag attention for temporal mixing. The method incorporates a flux‑form inductive bias to maintain conservation and provides a data‑driven rule for selecting memory length, achieving stable, accurate long‑horizon rollouts on benchmark equations and turbulent flow simulations.
arXiv AI
Jun 17
Conservation Laws for Modern Neural Architectures
arXiv:2606. 17816v1 Announce Type: cross Abstract: Understanding gradient descent dynamics is key to explaining the success of over-parameterized models, where implicit bias manifests through conservation laws in gradient flow.
arXiv Machine Learning
Jul 15
MUSA-PINN: Multi-scale Weak-form Physics-Informed Neural Networks for Fluid Flow in Complex Geometries
arXiv:2603. 08465v3 Announce Type: replace Abstract: While Physics-Informed Neural Networks (PINNs) offer a mesh-free approach to solving fluid-flow PDEs, standard point-wise residual minimization suffers from convergence pathologies in topologically complex domains like Triply Periodic Minimal Surfaces (TPMS).
arXiv Machine Learning
Aug 12
Efficient Weak-Entropy PINN for Solving Hyperbolic Conservation Laws
arXiv:2608. 10389v1 Announce Type: cross Abstract: In recent years, neural networks have significantly advanced numerical solutions of partial differential equations (PDEs).
arXiv AI
Jul 24
HypNO: A Graph-Based Neural Operator with Physics-Informed Message Passing for Hyperbolic Conservation Laws
arXiv:2607. 20541v1 Announce Type: cross Abstract: We introduce HypNO, a graph-based neural operator for scalar hyperbolic conservation laws.
arXiv Machine Learning
Aug 3
Feature Interaction Modeling for Physics-Informed Neural Networks and Neural Operators
arXiv:2607. 28762v1 Announce Type: new Abstract: This work embeds feature interaction modules derived from factorization machines (FMs) into physics-informed neural networks (PINNs) and neural operator learning, to enhance model expressiveness for solution manifolds of parameterized partial differential equations (PDEs).
arXiv Machine Learning
Jun 3
Flow Learners for PDEs: Toward a Physics-to-Physics Paradigm for Scientific Computing
arXiv:2604. 07366v2 Announce Type: replace Abstract: Partial differential equations (PDEs) govern nearly every physical process in science and engineering, but solving them at scale remains prohibitively expensive.
arXiv AI
Jul 9
Physics-guided spatiotemporal neural models for fuel density prediction
arXiv:2607. 06999v1 Announce Type: cross Abstract: This paper presents a physics-guided machine learning (PGML) framework for fuel density prediction, integrating physics constraints and domain knowledge into deep learning models to enhance model accuracy and stability.
arXiv AI
Jul 2
A Multi-Resolution Finite-Volume Inspired Deep Learning Framework for Spatiotemporal Dynamics Prediction
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 Machine Learning
Jun 11
Structure-Preserving Neural Surrogates with Tractable Uncertainty Quantification
arXiv:2606. 11650v1 Announce Type: new Abstract: Recent advances in scientific machine learning provide a means of near-real-time solution to partial differential equations (PDEs), but lack the theoretical underpinnings of conventional simulators that support contemporary verification and validation.