Numerical Accuracy Matters: Applications of Machine Learned Potential Energy Surfaces

Area of Science:

• Computational Chemistry
• Machine Learning in Science
• Quantum Mechanics

Background:

• Neural network-based potential energy surfaces (PES) are increasingly used in computational chemistry.
• The numerical precision of calculations can impact the accuracy of these PES.
• Different experimental observables may have varying sensitivities to the accuracy of PES derivatives.

Purpose of the Study:

• To investigate the impact of numerical accuracy on training and evaluating neural network-based PES.
• To determine the required precision for different types of calculations and observables.
• To assess the suitability of single-precision versus double-precision arithmetic for PES development.

Main Methods:

• Training neural network-based PES using both single-precision and double-precision arithmetic.
• Evaluating PES accuracy by examining third- and fourth-order derivatives.
• Calculating anharmonic frequencies and tunneling splitting for benchmark molecules (H2CO, malonaldehyde).
• Assessing PES suitability for molecular dynamics simulations requiring first-order derivatives.

Main Results:

• Single-precision arithmetic leads to rough PES and inaccurate higher-order derivatives, unsuitable for observables requiring them.
• Double-precision arithmetic yields smooth PES with numerically stable higher-order derivatives.
• Double-precision enables accurate prediction of anharmonic frequencies and tunneling splitting.
• Single-precision is sufficient for molecular dynamics simulations that only require first-order derivatives.

Conclusions:

• Double-precision arithmetic is essential for developing accurate neural network-based PES when higher-order derivatives are needed.
• Careful consideration of numerical precision is vital for reliable predictions in computational chemistry.
• The choice of numerical precision should be guided by the specific requirements of the intended application and observables.