Enforcing Constraints in Molecular and Crystalline Generative Models via Physics-Constrained Flow Matching

Pengfei Cai, Utkarsh Utkarsh, Nofit Segal, Akshay Subramanian, Katharina Jager, Elton Pan, Alan Edelman, Christopher Vincent Rackauckas, Rafael Gomez-Bombarelli

Keywords: Generative models, flow matching, constraints, molecular conformer generation, crystal structure prediction

TL;DR: We enforce pretrained flow-based generative models to generate molecular and crystalline structures that satisfy hard geometric and physical constraints at inference time.

Abstract: Pretrained flow-based generative models for molecules and crystals often violate hard geometric constraints at inference time, despite being trained on valid data. Herein, we extend Physics-Constrained Flow Matching (PCFM) to atomistic generative models and demonstrate it in two representative settings: (i) enforcing bond length, aromatic planarity, E/Z double bond stereochemistry, and R/S tetrahedral chirality constraints for conformer sampling, and (ii) enforcing lattice system constraints in crystal structure prediction. On GEOM-DRUGS, PCFM enforces bond length bounds and aromatic planarity while preserving ET-Flow recall and precision, and improves stereochemical pass rates by up to $14.5$%. On MP-20, conditional lattice correction with PCFM reduces unit cell mismatches and increases FlowMM's crystal structure match rate to $74.3$%. Overall, PCFM turns pretrained flow matching models into constrained samplers for molecular and crystalline generation, without finetuning or architectural changes, with broader applications to molecular and materials design currently underway.

Submission Track: Paper Track (Tiny Paper)

Submission Category: AI-Guided Design

Submission Number: 69