Jun-Yi Wu

Junyi Wu, Guang Lin

We propose PO-CKAN, a physics-informed deep operator framework based on Chunkwise Rational Kolmogorov--Arnold Networks (KANs), for approximating the solution operators of partial differential equations. This framework leverages a Deep Operator Network (DeepONet) architecture that incorporates Chunkwise Rational Kolmogorov-Arnold Network (CKAN) sub-networks for enhanced function approximation. The principles of Physics-Informed Neural Networks (PINNs) are integrated into the operator learning framework to enforce physical consistency. This design enables the efficient learning of physically consistent spatio-temporal solution operators and allows for rapid prediction for parametric time-dependent PDEs with varying inputs (e.g., parameters, initial/boundary conditions) after training. Validated on challenging benchmark problems, PO-CKAN demonstrates accurate operator learning with results closely matching high-fidelity solutions. PO-CKAN adopts a DeepONet-style branch--trunk architecture with its sub-networks instantiated as rational KAN modules, and enforces physical consistency via a PDE residual (PINN-style) loss. On Burgers' equation with $ν=0.01$, PO-CKAN reduces the mean relative $L^2$ error by approximately 48\% compared to PI-DeepONet, and achieves competitive accuracy on the Eikonal and diffusion--reaction benchmarks.

Feiran Wang, Jiachen Tao, Junyi Wu et al.

X-ray imaging is indispensable in medical diagnostics, yet its use is tightly regulated due to potential health risks. To mitigate radiation exposure, recent research focuses on generating novel views from sparse inputs and reconstructing Computed Tomography (CT) volumes, borrowing representations from the 3D reconstruction area. However, these representations originally target visible light imaging that emphasizes reflection and scattering effects, while neglecting penetration and attenuation properties of X-ray imaging. In this paper, we introduce X-Field, the first 3D representation specifically designed for X-ray imaging, rooted in the energy absorption rates across different materials. To accurately model diverse materials within internal structures, we employ 3D ellipsoids with distinct attenuation coefficients. To estimate each material's energy absorption of X-rays, we devise an efficient path partitioning algorithm accounting for complex ellipsoid intersections. We further propose hybrid progressive initialization to refine the geometric accuracy of X-Filed and incorporate material-based optimization to enhance model fitting along material boundaries. Experiments show that X-Field achieves superior visual fidelity on both real-world human organ and synthetic object datasets, outperforming state-of-the-art methods in X-ray Novel View Synthesis and CT Reconstruction.