TellusPM: a GPU-accelerated material point method for large-deformation geomechanics driven by an AI agent, calibrated against analytical, numerical and experimental benchmarks

TellusPM is a material point method (MPM) program for geotechnical large deformation, written in Rust, whichruns one explicit algorithm in 2D and 3D on a CPU or, through a run-time compiled CUDA engine, on an NVIDIAGPU, and which an engineer, an embedded AI agent or any Model Context Protocol client can drive through thesame 28 tools. We verified it against closed-form solutions and calibrated it against other programs and experimentsin a campaign of about 120 runs on one RTX 4090. The code converges at second order on the vibrating bar, matchesthe logarithmic-strain oedometer within 0.6 % and Terzaghi consolidation within 3.9 % of the initial pore pressure,and gives a factor of safety of 1.34 to 1.40 for the Griffiths and Lane slope, against 1.35 to 1.40 from finite elements.The calibration showed that a per-step FLIP/PIC blend, local damping under displacement control and the absenceof volumetric averaging each changed answers by up to a third, and that the remaining errors in granular runout, a 25% short runout of aluminium rods and a 1.3 to 1.7 times long runout of tall columns, belong to the rate-independentMohr-Coulomb model. On the 2026 Patong debris flow, a single-source back-analysis matches a coupled DEM–SPH model on the deposition along Nanai Road, and releasing every cell whose saturated infinite-slope factor ofsafety is below 1, with the strength reduced by γ𝑠𝑎𝑡/γ’ = 1.96, reproduces the 99th-percentile travel of a finiteelement and DEM–SPH chain on the same release within 6 %, although the median travel is 38 % longer. The GPUengine reproduces the CPU engine at about 40 times its speed, and a whole-hillside scenario of 546,738 points on9.4 × 107 cells ran in 12 min.