Bridgmanite Thermoelastic Eval

---
name: bridgmanite-thermoelastic-eval
description: Evaluates the accuracy of deep-learning molecular dynamics potentials in predicting the structural, thermodynamic, and elastic properties of bridgmanite (MgSiO3-perovskite) under high-pressure and high-temperature conditions relevant to Earth's lower mantle. Use when the user wants to benchmark on DFT reference dataset, Experimental benchmarks, PREM seismic model, or asks about evaluating this task. Reports RMSE.
metadata:
  skill_kind: dataset_eval
  source_arxiv: 2307.07127
  bibtex_key: wan2023thermoelastic
  confidence: high
---

# bridgmanite-thermoelastic-eval

> Thermoelastic properties of bridgmanite using Deep Potential Molecular Dynamics — Wan et al. (2023) (arXiv:2307.07127, 2023)

## What this evaluates

Evaluates the accuracy of deep-learning molecular dynamics potentials in predicting the structural, thermodynamic, and elastic properties of bridgmanite (MgSiO3-perovskite) under high-pressure and high-temperature conditions relevant to Earth's lower mantle.

## Datasets

- **DFT reference dataset** — total ?; splits: train (-1), val (-1)
- **Experimental benchmarks** — total ?; splits: test (-1)
- **PREM seismic model** — total ?; splits: reference (-1)

## Metrics

- `RMSE` **(primary)** — range: other
  - Root-mean-square error computed between deep potential predictions and DFT reference values for potential energy (meV/atom) and atomic forces (eV/Å).
- `EOS & Elastic Moduli Accuracy` — range: other
  - Quantitative comparison of predicted equation of state (Birch-Murnaghan fit), elastic coefficients (c_ij), bulk/shear moduli, and wave velocities against experimental measurements and PREM seismic data.

## Input / output format

**Input**: Atomic coordinates, simulation cell parameters, and target pressure-temperature conditions for MgSiO3 bridgmanite.

**Output**: Predicted potential energies, atomic forces, radial distribution functions, phonon dispersions, equation of state parameters, elastic stiffness tensor (c_ij), and derived macroscopic moduli/velocities.

## Scoring recipe

```python
def evaluate(dp_model, config, gold):
    # 1. Compute RMSE for energy and forces
    rmse_e = np.sqrt(np.mean((dp_model.predict_energy(config) - gold['energy'])**2))
    rmse_f = np.sqrt(np.mean((dp_model.predict_force(config) - gold['force'])**2))
    # 2. Structural & Phonon validation
    g_r = compute_radial_distribution(dp_model.run_md(config))
    phonons = compute_phonon_dispersion(dp_model.run_md(config))
    # 3. Thermodynamic & Elastic properties
    eos_params = fit_birch_murnaghan(dp_model.compute_PV(config))
    elastic_tensor = compute_elastic_tensor(dp_model.compute_stress_strain(config))
    K_S, G = voigt_reuss_hill(elastic_tensor)
    V_p = np.sqrt((K_S + 4*G/3) / dp_model.density)
    V_s = np.sqrt(G / dp_model.density)
    return {'rmse_energy': rmse_e, 'rmse_force': rmse_f, 'eos': eos_params, 'moduli': (K_S, G), 'velocities': (V_p, V_s)}
```

## Common pitfalls

- Classical MD neglects zero-point motion (ZPM), causing systematic underestimation of pressure and volume at low temperatures (e.g., 300 K).
- Isothermal elastic coefficients are reported, but adiabatic corrections may be required for direct comparison with seismic data at high temperatures.
- PBE and PBEsol functionals systematically overestimate volume and deviate ~12.5% from experimental elastic data, making them unsuitable for this system.

## Evidence (verbatim from paper)

> We quantified the root-mean-square error (RMSE) for the DP's predictions on the validation sets. Fig. 1 shows the outcomes of this analysis for the DP-LDA calculation. The RMSE for potential energies amounted to approximately 0.82meV / atom, while the RMSE for atomic force prediction errors was around 0.07eV / A.

## Citation

```bibtex
@misc{wan2023thermoelastic,
  title={Thermoelastic properties of bridgmanite using Deep Potential Molecular Dynamics},
  author={Wan et al. (2023)},
  year={2023},
  note={arXiv:2307.07127}
}
```

- arXiv: 2307.07127