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Neural Network Surrogates for Free Energy Computation of Complex Chemical Systems

Wasut Pornpatcharapong

TL;DR

This work addresses the bottleneck of requiring analytical Jacobians for CVs in GPR-based free energy reconstructions by introducing a neural-network surrogate that learns CVs directly from Cartesian coordinates and uses automatic differentiation to obtain Jacobians. The framework is validated on MgCl2 ion pairing with two CVs: a simple distance $d$ and a complex coordination-number $C$, demonstrating accurate CV predictions and Jacobians, with Jacobian errors following a near-Gaussian distribution favorable for GPR. The findings show that CVs can be learned without explicit analytic forms, enabling gradient-based free energy methods to incorporate complex or machine-learned CVs and scale to high-dimensional CV spaces, increasing applicability to biochemistry and materials simulations. The work lays the groundwork for integrating a full GPR pipeline with NN-derived CVs and applying it to large-scale, chemically important systems.

Abstract

Free energy reconstruction methods such as Gaussian Process Regression (GPR) require Jacobians of the collective variables (CVs), a bottleneck that restricts the use of complex or machine-learned CVs. We introduce a neural network surrogate framework that learns CVs directly from Cartesian coordinates and uses automatic differentiation to provide Jacobians, bypassing analytical forms. On an MgCl2 ion-pairing system, our method achieved high accuracy for both a simple distance CV and a complex coordination-number CV. Moreover, Jacobian errors also followed a near-Gaussian distribution, making them suitable for GPR pipelines. This framework enables gradient-based free energy methods to incorporate complex and machine-learned CVs, broadening the scope of biochemistry and materials simulations.

Neural Network Surrogates for Free Energy Computation of Complex Chemical Systems

TL;DR

This work addresses the bottleneck of requiring analytical Jacobians for CVs in GPR-based free energy reconstructions by introducing a neural-network surrogate that learns CVs directly from Cartesian coordinates and uses automatic differentiation to obtain Jacobians. The framework is validated on MgCl2 ion pairing with two CVs: a simple distance and a complex coordination-number , demonstrating accurate CV predictions and Jacobians, with Jacobian errors following a near-Gaussian distribution favorable for GPR. The findings show that CVs can be learned without explicit analytic forms, enabling gradient-based free energy methods to incorporate complex or machine-learned CVs and scale to high-dimensional CV spaces, increasing applicability to biochemistry and materials simulations. The work lays the groundwork for integrating a full GPR pipeline with NN-derived CVs and applying it to large-scale, chemically important systems.

Abstract

Free energy reconstruction methods such as Gaussian Process Regression (GPR) require Jacobians of the collective variables (CVs), a bottleneck that restricts the use of complex or machine-learned CVs. We introduce a neural network surrogate framework that learns CVs directly from Cartesian coordinates and uses automatic differentiation to provide Jacobians, bypassing analytical forms. On an MgCl2 ion-pairing system, our method achieved high accuracy for both a simple distance CV and a complex coordination-number CV. Moreover, Jacobian errors also followed a near-Gaussian distribution, making them suitable for GPR pipelines. This framework enables gradient-based free energy methods to incorporate complex and machine-learned CVs, broadening the scope of biochemistry and materials simulations.

Paper Structure

This paper contains 13 sections, 10 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Work
  3. Theoretical Background
  4. Machine Learning and Free Energy Computation
  5. Neural Networks and Autograd for Jacobian Computation
  6. Methodology
  7. Simulation Setup and CV Definitions
  8. Data Generation
  9. Neural Network Architecture and Training
  10. Results
  11. Prediction of $d$ and Its Jacobians
  12. Prediction of the $C$ and Its Jacobians
  13. Conclusion

Figures (4)

  • Figure 1: Prediction of $d$ for the randomized dataset (a) and simulation dataset (b) and distribution of prediction errors.
  • Figure 2: Prediction of the Jacobians (all dimensions) of $d$ for the randomized dataset (a) and simulation dataset (b) and distribution of prediction errors.
  • Figure 3: Prediction of $C$ for the randomized dataset (a) and simulation dataset (b) and distribution of prediction errors.
  • Figure 4: Prediction of the Jacobians (all dimensions) of $C$ for the randomized dataset (a) and simulation dataset (b) and distribution of prediction errors.