This is a guide to reproducing the figures and data for the paper "Sharp estimates for target measure diffusion maps and applications to the committor problem." by Sule, Evans and Cameron.
Figures 4 & 5 for the 1D test system in Section 5.1 can be reproduced using this Jupyter notebook.
Figure 6 with the results of the experiemnts for measuring the bias error prefactor can be reproduced here: [https://github.com/ShashankSule/TMDmaps/blob/pub/data/1D/1d_potential_circular_errordriver.ipynb].
The simulation detailed in Section 5.1 is written in the run/1d_bias_error.py python script. To run this script, it is recommended to run the 1d_sim.sh bash script which iterates over the two choices of sampling density and test function. After running the bash script, move the produced data (i.e four .npy files) into the data/1D/ directory. Then change cell 7 of the 1d_potential_circular_errordriver.ipynb notebook to account for the file names of the new data. Finally, run the notebook to produce the figure!
The landscape of Muller's potential (Figure 7) can be regenerated here.
The landscape of the two well potential (Figure 10) is here.
Figures 8,9 for tracking the committor RMSE over the kernel bandwidth for Muller's potential: [https://github.com/ShashankSule/TMDmaps/blob/pub/data/Muller/error_data/Error%20driver.ipynb]
Figures 8,9 for tracking the committor RMSE over the kernel bandwidth for the two well potential: [https://github.com/ShashankSule/TMDmaps/blob/pub/data/Twowell/Error_analysis_twowell.ipynb]
The simulation detailed in section 5.2 is written in the run/error_analysis.py python script. To run this script, it is recommended to run the run_sim.sh bash script which iterates over the gibbs, metadynamics, and FEM choices of sampling density. In the run_sim.sh script you can change whether to run the simulation for Muller's potential or two well in the by either commenting out lines 5-7 or 11-13. After running the bash script, move the produced data (i.e three .npy files) into the data/POTENTIAL/error_data/ directory. Then run the file Error driver.ipynb in that directory to regenerate the figures.
The diffusion map is implemented in the src/diffusion_map.py module. Two sampling algorithms, Euler-Maruyama and Metadynamics are implemented in src/sampling.py. Finally, the FEM solutions for validation are generated using the code in the src/FEM folder. An example for generating the FEM solution for Muller's potential is provided in src/FEM/mueller_TPT_driver.ipynb.