Linear-Radiation-Transport

Dataset Description: A surrogate-modeling dataset for the 2-D linear Radiation Transport Equation (RTE)**, covering two canonical benchmarks that vary along complementary axes: **Lattice** (707 samples, 494 train / 106 val / 107 test) — fixed `7 × 7` block geometry; per-sample variation in the white-background scattering coefficient \\(\sigma_s^W\\) and the blue-absorber cross- section \\(\sigma_a^B\\) drawn from a discrete design grid (see § Data generation). QoI: final-time absorption integral \\(\int_B \sigma_a\, \phi\, dx\\) over the absorbing blocks. **Hohlraum** (846 samples, 592 train / 126 val / 128 test) — fixed per-region cross-sections; per-sample variation in 8 geometry parameters (`ulr, llr, urr, lrr, hlr, hrr, cx, cy`) controlling the inner edges and y-extents of two wall-anchored red strips and the (x, y) offset of a center insert (see § Data generation). QoI: final-time absorption integral \\(\int_S \sigma_a\, \phi\, dx\\) evaluated over three material regions \\(S \in \{\text{center insert},\ \text{vertical strip},\ \text{horizontal strip}\}\\). The dataset contains initial and final timesteps. Data generation Simulations were produced with KiT-RT using a discrete-ordinate (S_N) angular discretization, a finite-volume scheme on an unstructured mesh, and an explicit SSP Runge-Kutta time integrator, then curated into the PhysicsNeMo `Mesh` memmap format. Both benchmarks sweep their per-sample parameters over a **discrete design grid** rather than continuous uniform random sampling. Lattice.** The design set is the full Cartesian product of \\(\sigma_a^B \in \{5, 7.5, \ldots, 102.5\}\\) and \\(\sigma_s^W \in \{0.1, 0.6, \ldots, 9.6\}\\), with spacings 2.5 and 0.5 respectively, giving **800** unique parameter configurations. Of these, 707** yielded complete and valid simulations. Hohlraum.** The full design set contains \\(3^8 = 6561\\) configurations formed from three prescribed values for each of the eight geometry parameters: | Parameter family | Val