upb-sciml/mhd_control

MHD Control Experiments

Results of all experiments in our MHD control paper: solver validation, solver benchmarks, inverse design, and the training and test runs of the controllers. The simulations use FluidGym with the phiPICT solver. The initial domains of the RBCMHD3D environments live in the FluidGym data repository.

Scripts: all scripts that produce and evaluate these results are in the mhd_control branch of FluidGym. See experiments.md for the commands and the directory structure.

Every run was launched with Hydra and has its own directory. That directory holds the resolved config (config.yaml), the Hydra settings (hydra.yaml) and the command-line overrides (overrides.yaml), so any run can be reproduced from its directory. Sweep directories also contain a multirun.yaml.

File structure

validation/                              # solver validation against analytic/reference solutions
├── hartmann/<Ha>/<nx>x<ny>/             #   Hartmann flow, per Hartmann number and grid
├── hartmann_rot/<Ha>/<nx>x<ny>/         #   Hartmann flow on a rotated grid
├── shercliff/<Ha>/<nx>x<ny>/            #   Shercliff flow (insulating duct walls)
├── hunt/<Ha>/<nx>x<ny>/                 #   Hunt flow (conducting Hartmann walls)
├── temp1/<Ha>_<Cw>/<nx>x<ny>x<nz>/      #   magnetoconvection, case 1
├── temp2/<Ha>_<Cw>/<nx>x<ny>x<nz>/      #   magnetoconvection, case 2 (varying wall conductance)
├── duct/<Ha>/<nx>x<ny>x<nz>_<duct>/     #   turbulent MHD duct flow
└── optim/{hartmann,shercliff,hunt}/     #   gradient-based recovery of the Stuart number
optim/                                   # duplicate of validation/optim
benchmark/                               # solver throughput, PICT vs. phiPICT
├── <env_id>/benchmark.csv               #   steps/s and memory per solver variant and batch size
├── speedup.csv                          #   speedup per environment and solver ablation
└── speedup.tex                          #   the same as a LaTeX table
optimize_cw_inverse/                     # inverse design of the wall conductance ratios
└── {lbfgs,cma_es}/<seed>/
training/marl/                           # multi-agent RL / BPTT controllers
└── <env_id>/<algorithm>/<seed>/         #   env_id: RBCMHD3D-{easy,medium}-v0
    ├── training_log.csv                 #   training curve
    ├── <checkpoints>                    #   see below
    └── test/<domain_idx>/               #   evaluation on the test initial domains

Contents

validation/

Simulations of MHD flows with known analytic or reference solutions. They check the solver for increasing Hartmann numbers Ha, wall conductance ratios Cw and grid resolutions. A run directory contains the simulation setup (simulation.json, domain.json), logs (logs.csv where available) and sometimes the final domain (final_domain.json). It also has plots of the computed against the reference profiles (velocity and current density profiles, Hartmann layers, Nusselt numbers, grids).

validation/optim/ holds the gradient-based recovery of the Stuart number through the differentiable solver. optim_log.csv logs the loss and the learned value N_learn against the target target_N per step.

benchmark/

Throughput of the original PICT solver against phiPICT for all FluidGym environments. benchmark.csv lists environment steps per second (mean and std) and peak GPU memory per solver variant and number of batched environments. speedup.csv gives the speedup over PICT for each solver ablation (no fused Krylov solver, no batching, no warm start, no intermediate tolerances, full phiPICT) and the best batch size.

optimize_cw_inverse/

Inverse design: recovering the wall conductance ratios Cw of a target flow, with L-BFGS through the differentiable solver (lbfgs) and gradient-free CMA-ES (cma_es). There are 5 seeds per method. Each run contains:

• optimization_log.csv: objective, field error, Cw error, gradient norm, and forward/backward step counts per evaluation.
• log*_cw_history.csv: the history of the optimized Cw values.
• target_domain.* / best_domain.*: the target and best found domains. Each is saved as .json + .npz, plus best_domain_info.json and maps.json.

training/marl/

Multi-agent controllers for RBCMHD3D-easy-v0 and RBCMHD3D-medium-v0, with 5 seeds each:

• SAC/<seed>/: SAC (Stable-Baselines3). The checkpoint is ckpt_latest.zip, with its replay buffer in ckpt_latest_replay_buffer.pkl.
• BPTT10_mlp/<seed>/: an MLP policy trained by backpropagation through time over 10-step horizons. The policies are bptt_policy.pth (last) and bptt_policy_best.pth (best), each with its observation normalization *_obs_norm.pth.

training_log.csv contains the training curve (reward, Nusselt number, buoyancy and electrical power, ...). test/<domain_idx>/test_results.csv contains the per-step metrics and actions of one test episode per test initial domain. The final flow state of that episode is saved as test_eval_episode_*_final_domain.{json,npz}.

Reproduction

Check out the mhd_control branch and follow experiments.md. The scripts are in runscripts/. To place this data in output/, run runscripts/evaluation/download_experimental_results.py.