Neural SHAKE: geometric constraints in neural differential equations

Area of Science:

• Computational chemistry
• Machine learning for science
• Molecular modeling

Background:

• Generating accurate molecular conformations is challenging due to high-dimensional spaces.
• Physics-based information can be incorporated as geometric constraints to improve conformation generation.
• Existing methods often use soft constraints, which may not guarantee physical validity.

Purpose of the Study:

• To develop a method for generating accurate and physically valid molecular conformations.
• To embed strict geometric constraints into neural differential equations within a diffusion framework.
• To improve the efficiency of exploring low-energy molecular conformations.

Main Methods:

• Proposed Neural SHAKE, a method integrating denoising diffusion with neural differential equations.
• Recasted physics-based information as nonlinear geometric constraints.
• Projected stochastic generative dynamics onto a manifold defined by constraint sets, enforcing exact feasibility.
• Utilized manifold-projected score-based diffusion with Lagrange multipliers for orthogonal projection onto constraint surfaces.

Main Results:

• Generated lower-energy molecular conformations with exact feasibility at each step.
• Enabled more efficient exploration of conformational subspaces.
• Formally subsumed classifier-guidance methods by treating geometric constraints as strict algebraic conditions.
• Preserved global SE(3) symmetry and enforced constraints to solver tolerance.

Conclusions:

• Neural SHAKE provides a robust framework for generating accurate molecular conformations by enforcing strict geometric constraints.
• The method offers significant improvements in efficiency and physical validity compared to existing approaches.
• This work advances the application of diffusion models and neural differential equations in molecular modeling.