Physics-Grounded Machine Learning Force Fields for Biomolecular Modelling: Variational, Renormalization and Effective Field Theory Approaches

Machine learning is rapidly reshaping how we model molecules, and a growing body of work suggests that neural networks are not merely statistical approximators but effective representations of complex many-body systems. From this perspective, neural network training shows a natural correspondence with variational principles in physics: the stationarity of the action in the Principle of Least Action mirrors the stationarity of the training loss, and the hierarchical compositions a deep network learns can be read as truncated power-series expansions, where higher-order contributions are suppressed much as they are by renormalization in effective field theories.

Recent advances such as SE(3)-equivariant graph neural networks, geometric transformers, and symmetry-preserving molecular foundation models have successfully encoded rotational and translational equivariance. Yet these capture only part of the mathematical structure of molecular systems: variational principles, renormalization, scale separation, effective interactions, thermodynamic consistency, gauge invariance, and emergent many-body behavior remain only indirectly represented.

The goal of this Research Topic is to advance the fundamental understanding and predictive power of physically grounded machine learning for biomolecular systems such as proteins, nucleic acids, membranes, and other soft-matter assemblies. We seek to bring together biophysicists, computational and structural biologists, and researchers in statistical and soft-matter physics, machine learning, and computational chemistry to address a central question: can machine learning force fields and molecular foundation models be built on mathematical foundations inspired by variational mechanics, renormalization, effective field theories, and statistical physics?

Specific objectives include:
• formulating machine learning through variational and least-action principles
• developing gauge-symmetry-aware and gauge-fixed neural architectures
• suppressing divergence causing higher-order interactions through renormalization- and power-law-inspired regularization
• building force fields that capture beyond-pairwise and higher-order many-body effects across scales
• ensuring thermodynamic consistency and effective representations for soft-matter and biomolecular systems

By achieving these goals, this collection aims to bridge machine learning and theoretical physics, moving beyond geometric equivariance toward models that learn physically meaningful representations, force fields, and potentials across multiple spatial and temporal scales.

This Research Topic welcomes contributions that establish the next generation of physically grounded machine learning frameworks for biomolecular modeling. Themes of interest include but are not limited to:
• Variational and least-action formulations of machine learning
• Gauge-fixed neural architectures and gauge-symmetry-aware models
• Orthogonal basis learning and neural-network spectral decomposition methods
• Power-law regularization, implicit self-regularization, and renormalization-group-inspired machine learning
• Neural-network force fields for beyond-pairwise and higher-order many-body interactions in soft matter and biomolecular systems
• Manifold-constrained optimization and thermodynamically consistent effective representations across scales

We invite Original Research, Methods, Review, Perspective, Dataset, and Benchmark articles. All contributions must advance the physical understanding of machine-learned force fields and molecular foundation models, and demonstrate clear relevance to soft-matter or biomolecular systems.