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Can Deep Learning Achieve Cross-Physics Mapping?
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arXiv Machine Learning
Sep 16
Can Deep Learning Achieve Cross-Physics Mapping?
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.
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
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.
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
Jun 11
HAMNO: A Hierarchical Adaptive Multi-scale Neural Operator with Physics-Informed Learning for Dynamical Systems
arXiv:2606. 11963v1 Announce Type: new Abstract: Neural operators provide a powerful framework for learning solution mappings of partial differential equations directly in function space.
arXiv Machine Learning
Jul 22
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics
arXiv:2510. 25306v3 Announce Type: replace Abstract: Partial physical knowledge--governing structures known, constitutive relations or their combinations not--pervades spatiotemporal systems.