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.
Unsupervised Adaptation of PDE Foundation Models
arXiv:2608. 07053v1 Announce Type: new Abstract: Pretrained partial differential equation (PDE) foundation models can generalize across different equations, but adapting them to unseen PDE systems typically requires dense solution data, which is often expensive or unavailable.
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arXiv Machine Learning
Jun 5
When Attention Beats Fourier: Multi-Scale Transformers for PDE Solving on Irregular Domains
arXiv:2605. 08318v2 Announce Type: replace Abstract: We study the problem of \emph{architecture selection} for deep learning models trained to solve partial differential equations (PDEs), asking when transformer-based architectures with learned attention outperform Fourier-domain neural operators.
arXiv Machine Learning
Jul 27
Latent PDE mapping for efficient physics-informed learning across geometries with limited data
arXiv:2607. 22215v1 Announce Type: new Abstract: In this study, we introduce latent PDE mapping, a broadly applicable physics-informed learning technique designed to enable efficient geometric generalization with sparse training data.
arXiv Machine Learning
5d ago
Physics-Informed Laplace Neural Operator for Solving Partial Differential Equations
arXiv:2602. 12706v2 Announce Type: replace Abstract: Neural operators have emerged as fast surrogate solvers for parametric partial differential equations (PDEs).
arXiv AI
Aug 5
PRISMA: Improving the Accuracy-Latency Frontier of Diffusion-based PDE Solvers Using Physics-Informed Spectral Attention
arXiv:2512. 01370v2 Announce Type: replace-cross Abstract: Diffusion-based solvers for partial differential equations (PDEs) are often bottle-necked by slow gradient-based test-time optimization routines that use PDE residuals for loss guidance.
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
Jun 5
DAS-PINNs for high-dimensional partial differential equations: extending deep adaptive sampling to spacetime domains
arXiv:2606. 06314v1 Announce Type: cross Abstract: Time-dependent high-dimensional partial differential equations (PDEs) with spatially localised and dynamically evolving solutions pose a fundamental challenge for physics-informed neural networks (PINNs), as uniform collocation sampling becomes increasingly ineffective in high-dimensional spatiotemporal domains.
arXiv AI
Jun 2
Towards a Physics Foundation Model
arXiv:2509. 13805v4 Announce Type: replace-cross Abstract: Foundation models have revolutionized natural language processing through a ``train once, deploy anywhere'' paradigm, where a single pre-trained model adapts to countless downstream tasks without retraining.
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 AI
Jul 14
RSLoRA: Training-free Rank Allocation for LoRA via Representational Sensitivity Probing
arXiv:2607. 09757v1 Announce Type: cross Abstract: Low-Rank Adaptation (LoRA) has become a cornerstone of parameter-efficient fine-tuning (PEFT); however, the conventional practice of uniform rank assignment ignores the functional heterogeneity of neural layers.
arXiv AI
Aug 11
MoNo: Multiscale Optimal Transport Neural Operator for Solving PDEs on General Geometries
arXiv:2608. 09764v1 Announce Type: cross Abstract: Transformer-based neural operators have achieved substantial progress in solving Partial Differential Equations (PDEs) by projecting spatial observations into compact latent tokens and learning physical interactions in latent spaces.
arXiv Machine Learning
Aug 11
Test-time Generalization for Physics through Neural Operator Splitting
arXiv:2602. 00884v2 Announce Type: replace Abstract: Neural operators have shown promise in learning solution maps of partial differential equations (PDEs), but they often struggle to generalize when test inputs lie outside the training distribution, such as novel initial conditions, unseen PDE coefficients or unseen physics.