Speaker
Description
Electrostatic interactions play a fundamental role in biomolecular recognition, binding affinity, conformational stability, and enzymatic activity. These effects are commonly modeled using the linearized Poisson–Boltzmann equation (LPBE), which provides a continuum description of electrostatics in implicit solvent environments. However, obtaining systematically converged high-resolution numerical solutions requires extremely fine spatial discretizations, resulting in substantial computational costs, particularly in multi-query and parametric settings.
In this work, we propose a neural surrogate framework for data-driven resolution enhancement of electrostatic potentials computed with NextGenPB. Rather than approximating the LPBE solution operator itself, we formulate the problem as the learning of a correction operator acting on coarse-grid numerical solutions. Given a coarse discretization of the LPBE solution, the neural network is trained to approximate the resolution-dependent correction that maps the coarse solution to its fine-grid counterpart on the molecular surface.
More precisely, the network learns a parametric representation of the discretization error, approximating the difference between fine- and coarse-grid solutions. The training process relies on analytically generated LPBE configurations, which provide exact reference solutions and ensure physics-consistent supervision. This construction allows the model to preserve the linear operator structure of the underlying equation while focusing on the approximation of resolution-induced discrepancies.
The surrogate is subsequently evaluated on realistic biomolecular geometries, where it provides a data-driven correction to coarse numerical solutions, enabling the recovery of refined electrostatic features without explicitly solving the LPBE on highly refined grids. This work contributes to the development of physically grounded neural surrogate models for PDE-based electrostatics, with emphasis on operator-consistent correction learning, cross-geometry transferability, and scalability in biomolecular simulation workflows.