PhysDiT: A Physics-Informed Linear Diffusion Transformer for Real-Time 4-D Geophysical Electromagnetic Inversion
Abstract
Real-time 4-D geophysical electromagnetic (EM) monitoring is critical for dynamic geo-energy applications such as geologic CO2 sequestration, but traditional inversion methods are computationally expensive and severely ill-posed. While deep learning (DL) accelerates inference, purely data-driven models can fail to resolve deep geological structures because geophysical EM fields undergo rapid, depth-dependent attenuation in conductive mediaand generally do not quantify reconstruction stability. Furthermore, applying a Diffusion Transformer (DiT) to volumetric data is constrained by the <inline-formula> <tex-math notation="LaTeX">$\mathcal {O}(N^{2})$ </tex-math></inline-formula> complexity of standard attention. To address these limitations, we propose a physics-informed linear DiT (PhysDiT) for fast, generative 4-D geophysical EM reconstruction. Its skin-effect spectral linear attention (SE-SLA) module applies a learnable, nonnegative spectral decay gate to value features before linear attention. The resulting cost is <inline-formula> <tex-math notation="LaTeX">$\mathcal {O}(Nd^{2}+Nd\log N)$ </tex-math></inline-formula> and is quasi-linear in token count for fixed head width <inline-formula> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula>. In the reported setup, a 50-step <inline-formula> <tex-math notation="LaTeX">$64^{3}$ </tex-math></inline-formula> reconstruction requires 10.66 s on one GPU, corresponding to approximately <inline-formula> <tex-math notation="LaTeX">$675\times $ </tex-math></inline-formula> the stated traditional-solver reference time. Repeated data-guided sampling provides a local ensemble-stability map, while new out-of-distribution (OOD) tests show that the present learned prior can suppress elongated or disconnected structures. PhysDiT is therefore effective for familiar compact geometries but requires broader training support and separate OOD checks for risk-sensitive use.