Learning-Augmented FEM–BEM Solvers for Biomolecular Simulations Kingston University in United Kingdom

This PhD project at Kingston University focuses on developing learning-augmented FEM–BEM solvers for biomolecular simulations, targeting the accurate and efficient modeling of electrostatic interactions in complex molecular systems. Electrostatics are fundamental to processes such as protein–ligand binding, RNA folding, and vaccine design, and the Poisson–Boltzmann equation (PBE) is a key tool for their study. However, computational challenges—especially for non-linear PBE and intricate biomolecular geometries—limit the practical application of existing solvers.

Recent advances have shown that coupling the finite element method (FEM) with the boundary element method (BEM) can significantly enhance solver stability and accuracy. This approach leverages the volumetric flexibility of FEM and the precise boundary representation of BEM, resulting in improved solvation free energy estimates for challenging molecular systems. Despite these improvements, issues such as solver convergence, preconditioning, and adaptivity remain, particularly as system complexity increases.

Parallel developments in machine learning, especially physics-informed neural networks (PINNs), offer new opportunities to augment traditional PDE solvers. PINNs can learn electrostatic potentials directly from molecular geometries and charge distributions, potentially bypassing the need for full mesh-based discretization. However, current ML approaches face difficulties with high-dimensional problems, scaling to large molecular systems, and enforcing the strict physical constraints required in charged solvation environments.

This project proposes a novel research direction: integrating machine learning techniques with FEM–BEM solvers to create a learning-augmented framework for solving the Poisson–Boltzmann equation. The goal is to combine the rigor and reliability of established numerical methods with the efficiency and adaptivity of modern ML, enabling accurate biomolecular simulations even for highly complex systems.

The successful candidate will join the Faculty of Engineering, Computing and the Environment at Kingston University, working under the supervision of Dr M Bosy. The project is part of the Graduate School studentships competition for October 2026 entry, offering full funding opportunities. Applicants should have a strong background in computer science, mathematics, chemistry, physics, or engineering, with experience in numerical methods, scientific computing, or machine learning highly desirable. The application deadline is March 4, 2026.

For more information and to apply, visit the Kingston University PhD Studentships page and the Faculty research webpage. This is an excellent opportunity for students interested in computational science, biomolecular modeling, and interdisciplinary research at the intersection of numerical analysis and artificial intelligence.