A Fast and Generic Energy-Shifting Transformer for Hybrid Monte Carlo Radiotherapy Calculation

To enable accurate and rapid photon control point and proton beamlet dose calculation in the DoseRAD2026 challenge, we present BEAM3R, a dose estimation framework operating in beam's-eye-view (BEV). Our core innovation combines a Mamba-3 state-space depth-sequence core with physics-based transport conditioning to model long-range depth transport without expensive 3D convolutions. BEAM3R shares a 2D CNN encoder-decoder architecture for photon and proton dose tasks, processing per-plane BEV slices. Proton beamlets are conditioned on water equivalent thickness and remaining range, encoding the parameters determining Bragg peak position. Photon models use a bidirectional Mamba-3 core to capture dose contributions from materials downstream of the calculation point, while the proton model uses a forward core with learned energy-prefix tokens and a Bragg-peak refinement module. To reduce interpolation artifacts and support high spatial resolution, we introduce axial grid alignment of BEV lattices with CT slices and an implicit super-resolution representation via sub-pixel phase packing, evaluated by a differentiable Triton-accelerated resampler that reconstructs packed cubic B-spline coefficients directly in CT space. For MRI-based tasks, synthetic CTs (sCT) are generated by a patch-based conditional GAN with a SwinUNETR backbone. On the preliminary DoseRAD2026 test set, CT-to-photon and CT-to-proton models achieved 1%/1 mm local gamma pass rates of 96.8% and 96.0%, with stratified plan-level MAEs of 0.0041 and 0.0079. Substituting sCT reduced gamma pass rates to 89.7% for photon and 75.4% proton plan level doses, with stratified plan-level MAEs of 0.0093 and 0.0336. Standardised runtimes were 23.4 s and 18.4 s for CT-to-photon and CT-to-proton prediction, increasing to 39.7 s and 42.8 s for the corresponding MRI-based pipelines.

Architecture category. Hybrid method: a physics-based analytical pencil-beam (PB) dose engine followed by a 3-D convolutional residual-correction network (RepVGG-U-Net). We addressed the DoseRAD2026 proton dose-prediction task with PyDoseRT Proton, a GPU-accelerated engine implemented in PyTorch and augmented by a learned residual toward Monte Carlo (MC) accuracy. A double-Gaussian PB kernel was calibrated to GATE/Geant4 integrated depth doses in water in two stages: a classical per-energy curve fit, then a gradient-based fit of the full 3-D dose through the PyTorch physics engine as it retains a differentiable execution path for gradient-based optimization of dose-dependent objectives. The engine computes each beamlet on a beam's-eye-view (BEV) lattice with variance-preserving Gaussian splitting, an analytic nuclear halo, and a Fermi-Eyges heterogeneity term, then rotates the result into the patient frame. Additionally, a compact residual U-Net predicts an additive correction in BEV space. It is conditioned on voxelwise material-label embeddings, a discrete energy embedding and spot size. The same model was used for all anatomical sites (thoracic and abdominal). It was trained with a patient-space L1 objective emphasizing the scored high-dose region and multi-scale BEV deep supervision. The submitted CT configuration obtained preliminary-test beamlet MAE 0.0066, image-z IDD distance 0.0025, plan MAE 0.0049, 98.30% gamma pass rate (1%/1 mm), and DVH error 0.460.

Learning-based fluence map prediction offers a fast alternative to iterative inverse planning in intensity-modulated radiation therapy (IMRT), but its robustness under realistic distribution shifts remains unclear. We study a two-stage transformer pipeline that maps anatomy (CT and contours) to dose and then to beamlet fluence maps. We compare fluence-stage transformer backbones with hierarchical, global, and hybrid attention, trained with a physics-informed loss enforcing energy consistency. Robustness is evaluated under geometric perturbations, radiometric noise, reduced training data, and domain shifts using a prostate IMRT dataset, with additional evaluation of the dose stage on public datasets. Results show smooth degradation under moderate perturbations but sharp failures under severe rotations and noise. Hierarchical transformers (e.g., SwinUNETR) exhibit slower growth in upper-quartile energy error, indicating improved robustness. We further show that SSIM alone fails to capture clinically relevant errors, highlighting the need for physics-informed evaluation.