Jax Mpm Geophysical Benchmarks Eval

jax-mpm-geophysical-benchmarks-eval

JAX-MPM: A Learning-Augmented Differentiable Meshfree Framework for GPU-Accelerated Lagrangian Simulation and Geophysical Inverse Modeling — Du et al. (2025) (arXiv:2507.04192, 2025)

What this evaluates

Tests the accuracy and computational efficiency of a differentiable Material Point Method (MPM) simulator on geophysical flow benchmarks. It probes the framework's ability to reproduce free-surface dynamics, granular collapse rheology, and rigid-body contact against analytical or experimental ground truth, while measuring GPU acceleration speedups.

Datasets

• JAX-MPM Geophysical Benchmarks — total ?; splits: test (-1)

Metrics

• normalized_runout (primary) — range: dimensionless
  • Computed as $d_n = (L_f - L_0) / L_0$, where $L_f$ is the final runout distance and $L_0$ is the initial base length of the granular column. Used to quantify scaling behavior with aspect ratio.
• wall_clock_time_s_per_1000_steps — range: seconds
  • Wall-clock time in seconds required to complete 1000 simulation time steps, measured on specific hardware (NVIDIA A100 GPU or AMD EPYC CPU). Reported for float32 and float64 precision.

Input / output format

Input: Simulation setup parameters including domain dimensions, grid resolution ($\Delta h$), particle count, material properties (density, viscosity, friction angle, etc.), boundary conditions, and time step size ($\Delta t$).

Output: Time-evolving particle positions and velocities, free surface profiles, equivalent plastic strain contours, and final deposit geometry (runout distance).

Scoring recipe

def compute_normalized_runout(final_deposit_x, initial_base_length):
    L_f = max(final_deposit_x) - min(final_deposit_x)
    L_0 = initial_base_length
    return (L_f - L_0) / L_0

def compute_wall_clock_time(sim_function, num_steps=1000):
    start = time.perf_counter()
    sim_function(num_steps)
    end = time.perf_counter()
    return end - start

Common pitfalls

• Early-time dam-break simulations ($t<0.3$ s) violate shallow-water assumptions due to finite-depth effects, causing discrepancies with analytical solutions that are often misinterpreted as solver errors.
• Comparing computational scaling against solvers using different constitutive models (e.g., Mohr–Coulomb vs. Drucker–Prager) can confound performance benchmarks, as non-smooth yield surfaces increase computational cost independently of implementation efficiency.

Evidence (verbatim from paper)

Moreover, the final runout distances $L_{f}$ are compared by defining the normalized runout as $d_{n}=(L_{f}-L_{0})/L_{0}$. The results show a clear increase in $d_{n}$ with aspect ratio: 2.05 ($a=0.5$), 3.97 ($a=1.0$), 7.76 ($a=2.0$), and 10.65 ($a=3.0$). Wall-clock times are recorded for every 1000 simulation steps under the following hardware configurations: (1) CB-Geo on an AMD EPYC 7763 CPU with 128 threads, and (2) JAX-MPM on an NVIDIA A100 GPU.

Citation

@misc{du2025jaxmpm,
  title={JAX-MPM: A Learning-Augmented Differentiable Meshfree Framework for GPU-Accelerated Lagrangian Simulation and Geophysical Inverse Modeling},
  author={Du et al. (2025)},
  year={2025},
  note={arXiv:2507.04192}
}

• arXiv: 2507.04192