Approximating net interactions among rigid domains.

Area of Science:

• Computational physics
• Biomolecular simulations
• Materials science

Background:

• Evaluating net interactions between rigid bodies is crucial for biomolecular applications like protein folding, drug design, and nanoparticle self-assembly.
• Traditional brute-force methods require computationally expensive quadratic evaluations for each relative body pose.
• Existing simplifying assumptions can lead to a collapse in computational complexity, limiting their applicability.

Purpose of the Study:

• To develop a computationally efficient approximation for pairwise interaction functions between rigid bodies.
• To reduce the quadratic complexity of interaction evaluations in physical simulations.
• To maintain reasonable precision while achieving significant speed-up in calculations.

Main Methods:

• Approximating pairwise interaction functions using a linear predictor with separated basis functions.
• Splitting variables describing local geometries and relative poses within basis functions.
• Performing a one-time quadratic computation of characteristic parameters in a preprocessing step.
• Evaluating a constant number of pose functions for each relative pose.

Main Results:

• The proposed method replaces quadratic interaction evaluations with a preprocessing step and constant pose function evaluations.
• The standard deviation of the net interaction error is linearly proportional to the regression error under normal distribution assumptions.
• The approximation offers a computationally superior alternative to existing methods while preserving reasonable precision.

Conclusions:

• The linear predictor with separated basis functions provides an efficient approximation for rigid body interactions.
• This method offers a favorable trade-off between accuracy and speed-up for complex simulations.
• The approach has broad applicability in biomolecular and materials science simulations.