Can Deep Learning Achieve Cross-Physics Mapping?
Abstract
Can deep learning translate physical fields governed by fundamentally different equations? We address this question by introducing Cross-Physics Mapping (CPM), an operator-learning framework for mappings between heterogeneous physical domains. We formulate sufficient conditions for such mappings through compatible latent representations and propose a dimensionless scaling principle that aligns the characteristic evolution scales of the source and target systems without assuming their dynamical equivalence. As a representative test, paired diffusion and wave fields are generated independently from their respective parabolic and hyperbolic equations while sharing the same latent geometry, material heterogeneity, excitation, and dimensionless scale. Seven architectures-ResUNet, DeepONet, Fourier, latent, wavelet, U-shaped, and Galerkin neural operators-are evaluated for both diffusion-to-wave and wave-to-diffusion mappings. The results reveal a strong directional asymmetry. Diffusion-to-wave reconstruction is more challenging because it requires recovering wavefront, phase, and time-of-flight information attenuated by diffusion; U-NO performs best in this direction, achieving a relative ℓ2 error of $0.307$ and an R2 of $0.905$. Wave-to-diffusion mapping is considerably more stable, with GNO attaining a relative ℓ2 error of $0.154$ and an R2 of $0.935$. Neural operators generally outperform the conventional convolutional baseline, highlighting the nonlocal nature of cross-physics transformations. These findings demonstrate that deep learning can establish useful mappings between distinct physical modalities on a shared latent manifold, while the achievable accuracy remains fundamentally constrained by the direction-dependent information content of the governing physics.
Related
- Retrospective macromolecular pool fraction mapping from conventional clinical MRI: a physics-guided self-supervised deep learning framework
- Physics-Informed GPR with Deep Kernel Learning for Femtosecond Laser Machining of Fused Silica Microchannels
- Physics-Assisted Deep Learning Denoising for Stabilized IMPULSED dMRI Microenvironment Parameter Fitting
- NuPaD: A Generative AI Framework for Fostering Deep Learning in Subatomic Physics
- Physics-Constrained Deep Learning Model for Contactless Blood Pressure Monitoring from Triaxial Bodyseismography
BibTeX
@misc{zhu2026deep,
title = {{Can Deep Learning Achieve Cross-Physics Mapping?}},
author = {Pengfei Zhu and Julien Lecompagnon and Mathias Ziegler},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.16853},
eprint = {2609.16853},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.16853},
}
RIS
TY - UNPB
TI - Can Deep Learning Achieve Cross-Physics Mapping?
AU - Pengfei Zhu
AU - Julien Lecompagnon
AU - Mathias Ziegler
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.16853
UR - https://arxiv.org/abs/2609.16853
AB - Can deep learning translate physical fields governed by fundamentally different equations? We address this question by introducing Cross-Physics Mapping (CPM), an operator-learning framework for mappings between heterogeneous physical domains. We formulate sufficient conditions for such mappings through compatible latent representations and propose a dimensionless scaling principle that aligns the characteristic evolution scales of the source and target systems without assuming their dynamical equivalence. As a representative test, paired diffusion and wave fields are generated independently from their respective parabolic and hyperbolic equations while sharing the same latent geometry, material heterogeneity, excitation, and dimensionless scale. Seven architectures-ResUNet, DeepONet, Fourier, latent, wavelet, U-shaped, and Galerkin neural operators-are evaluated for both diffusion-to-wave and wave-to-diffusion mappings. The results reveal a strong directional asymmetry. Diffusion-to-wave reconstruction is more challenging because it requires recovering wavefront, phase, and time-of-flight information attenuated by diffusion; U-NO performs best in this direction, achieving a relative ℓ_2 error of $0.307$ and an R^2 of $0.905$. Wave-to-diffusion mapping is considerably more stable, with GNO attaining a relative ℓ_2 error of $0.154$ and an R^2 of $0.935$. Neural operators generally outperform the conventional convolutional baseline, highlighting the nonlocal nature of cross-physics transformations. These findings demonstrate that deep learning can establish useful mappings between distinct physical modalities on a shared latent manifold, while the achievable accuracy remains fundamentally constrained by the direction-dependent information content of the governing physics.
ER -