XPPBE: PINN Solver for 3D Poisson-Boltzmann Equation

Physics-Informed Neural Network solver for the Poisson-Boltzmann equation applied to real macromolecules in polarizable media.

$$\nabla^2 \phi_m = -\frac{1}{\epsilon_m}\sum_k q_k\delta(x_k) \quad x \in \Omega_m $$

$$\nabla^2 \phi_w = \kappa^2_w\phi_w \quad x \in \Omega_w $$

Features

• Solves the electrostatic potential for the solute and solvent domain.
• Simple molecule definition by .pdb or .pqr file.
• Different loss terms can be added to the model.
• Use of different architectures is available, very customizable.
• Loss balancing algorithm implemented.
• Build in Python/Tensorflow.

Resources

• Papers: Check this folder for relevant papers and additional project documentation.
• Tutorials: Check this folder for notebooks tutorials.

Installation

To install and run this project locally, follow these steps:

1. Clone the repository to your local machine.

   git clone https://github.com/MartinAchondo/XPPBE

2. Navigate to the project directory

   cd XPPBE

3. Create a virtual environment

   conda create --name xppbe python=3.9

4. Activate the virtual environment

   conda activate xppbe

5. Install the project

   pip install .

Usage

To use this project, start by following the Tutorial.ipynb notebook. An explanation of this notebook is as follows:

1. Import the simulation object, the YAML file, and initialize it:

   from xppbe import Simulation
   simulation = Simulation(yaml_path, molecule_dir)

2. Run the simulation:

   simulation.create_simulation()
   simulation.adapt_model()
   simulation.solve_model()
   simulation.postprocessing(run_all=True)

The Simulation object import a YAML file with all the problem definitions. An explanation is as follows:

1. Define the molecule, the properties and the equation to solve:

   equation: regularized_scheme_2
   pbe_model: linear
   pinns_method: DCM
   
   domain_properties:
       molecule: methanol
       epsilon_1: 1
       epsilon_2: 80
       kappa: 0.125
       T: 300

2. Define the number of collocation points (mesh properties):

   mesh_properties:
       vol_max_interior: 0.04
       vol_max_exterior: 0.1
       density_mol: 10
       density_border: 0.5
       mesh_generator: msms
       dR_exterior: 3

3. Define the different loss terms (solute domain, solvent domain and combination of both)

   losses:
       - R1
       - R2
       - D2
       - Iu
       - Id

4. Define the architectures:

   num_networks: 2
   
   hyperparameters_in:
       architecture_Net: FCNN
       num_hidden_layers: 4
       num_neurons_per_layer: 200
       activation: tanh
       adaptive_activation: true
       fourier_features: true
       weight_factorization: false
       scale_input: true
       scale_output: true
   
   hyperparameters_out:
       architecture_Net: FCNN
       num_hidden_layers: 4
       num_neurons_per_layer: 200
       activation: tanh
       adaptive_activation: true
       fourier_features: true
       weight_factorization: false
       scale_input: true
       scale_output: true

5. Finally, specify the optimization algorithm, the weights algorithm, the batches/samples approach and the number of iterations.

   adapt_weights: true
   adapt_w_iter: 1000
   adapt_w_method: gradients
   alpha_w: 0.7         
   
   sample_method: random_sample
   
   optimizer: Adam
   lr:
       method: exponential_decay
       initial_learning_rate: 0.001
       decay_steps: 2000
       decay_rate: 0.9
       staircase: true
   
   N_iters: 20000

Recent Publication

Our recent work investigates the application of Physics-Informed Neural Networks (PINNs) to solve the Poisson-Boltzmann equation (PBE) using XPPBE. In this study, we highlight the impact of incorporating advanced neural network features, such as input and output scaling, random Fourier features, trainable activation functions, and a loss balancing algorithm.

• Title: An Investigation of Physics Informed Neural Networks to solve the Poisson-Boltzmann Equation in Molecular Electrostatics.
• Authors: Martín A. Achondo, Jehanzeb H. Chaudhry, Christopher D. Cooper.
• Journal/Conference: Under review.
• DOI: Pending.

All input files and scripts to reproduce the results are available in the Paper Folder.

Citing

If you find this project useful for your research or work, please consider citing it. Here is an example BibTeX entry:

@article{achondo2024investigation,
  title={An Investigation of Physics Informed Neural Networks to solve the Poisson-Boltzmann Equation in Molecular Electrostatics},
  author={Achondo, Martin A and Chaudhry, Jehanzeb H and Cooper, Christopher D},
  journal={arXiv preprint arXiv:2410.12810},
  year={2024}
}