arXiv Machine Learning By Pengfei Zhu, Julien Lecompagnon, Mathias Ziegler

Can Deep Learning Achieve Cross-Physics Mapping?

Read the original on arXiv Machine Learning →

The paper introduces Cross-Physics Mapping (CPM), an operator-learning framework that enables deep learning to translate physical fields governed by different equations. By aligning latent representations and applying a dimensionless scaling principle, CPM maps between heterogeneous domains such as diffusion and wave fields. Experiments with seven neural operator architectures show directional asymmetry: diffusion-to-wave mapping is harder, while wave-to-diffusion mapping is more stable, with neural operators outperforming conventional convolutional baselines.

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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.

By Brandon Yee, Pairie Koh, Jack Rodriguez, Mihir Tekal
arXiv Machine Learning
Sep 7

Disentangling Attention in Deep Operator Learning: A Controlled Study of Data-Driven and Physics-Informed Architectures

The paper investigates how different attention mechanisms affect the performance of DeepONet neural operators. Five variants—varying in cross‑attention, self‑attention, tokenization, and attention depth—are trained in both data‑driven and physics‑informed settings on one‑ and two‑dimensional PDE benchmarks. Results show that per‑sensor tokenization with cross‑attention consistently reduces error, while branch self‑attention helps only in complex spatial problems, and deeper cross‑attention yields diminishing returns with higher cost.

By Amar Alem Koric, Qibang Liu, Seid Koric