GP-STACF: Gaussian Process Surrogate Modeling for Viscosity Prediction

A computational workflow implementing Gaussian Process (GP) regression as surrogate models for the Stress Tensor Autocorrelation Function (STACF)—to accelerate and refine shear viscosity calculations from Molecular Dynamics (MD) simulations using the Green-Kubo (GK) formalism.

---

Overview

Calculating transport properties such as shear viscosity via equilibrium Molecular Dynamics (MD) relies on integrating the time correlation function of the off-diagonal elements of the stress/pressure tensor:

$$\eta = \frac{V}{k_B T} \int_{0}^{\infty} \langle P_{\alpha\beta}(0) P_{\alpha\beta}(t) \rangle , dt$$

Because the raw correlation tail suffers from statistical noise at long correlation times, this repository applies Gaussian Process (GP) regression to fit and filter the averaged autocorrelation curves, providing robust functional representations and quantifiable uncertainty estimates for numerical integration.

---

Repository Structure

• GP_PACF.ipynb: Jupyter Notebook containing Gaussian Process (GP) model training, validation, and integration
• PACF_average.csv.zip: Compressed Comma-Separated Values (CSV) dataset of ensemble-averaged Pressure Autocorrelation Function (PACF) trajectories
• README.md: Project documentation

---

Getting Started

Prerequisites

Ensure you have Python installed alongside the standard scientific computing environment:

• Python 3.9+
• NumPy
• SciPy
• Pandas
• Scikit-Learn
• Matplotlib

Setup

1. Clone the repository:

   git clone https://github.com/Fadeshola/GP-STACF.git
   cd GP-STACF

2. Extract the dataset: Unzip the ensemble data file directly within the repository root directory:

   unzip PACF_average.csv.zip

3. Run the analysis: Launch Jupyter Notebook to execute the regression workflow:

   jupyter notebook GP_PACF.ipynb

---

Workflow Details

• Data Preprocessing: Ingestion and formatting of averaged correlation profiles from PACF_average.csv.
• Surrogate Fitting: Optimizing kernel hyper-parameters for Gaussian Process (GP) regressors (such as Radial Basis Function (RBF) or Matérn kernels) against early- and mid-time autocorrelation behavior.
• Integration & Error Estimation: Numerical integration of the predictive posterior mean and calculation of confidence bounds for the resulting Green-Kubo (GK) running viscosity.

---

License

This project is licensed under the Massachusetts Institute of Technology (MIT) License - see the LICENSE file for details.