Iterative Power Algorithm for Global Optimization with Quantics Tensor Trains.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Optimization Theory

Background:

• Optimization is fundamental to molecular and electronic structure calculations in chemistry.
• Existing methods face challenges with high-dimensional and complex potential energy surfaces.
• The curse of dimensionality hinders efficient evaluation of potential energy surfaces.

Purpose of the Study:

• Introduce the iterative power algorithm (IPA) for global optimization.
• Provide a formal proof of convergence for discrete and continuous problems.
• Demonstrate IPA's applicability to molecular geometry optimization and other chemical calculations.

Main Methods:

• IPA utilizes the power iteration method within quantics tensor train (QTT) representations.
• It iteratively refines a probability distribution based on the potential energy surface (PES).
• Fast adaptive interpolation of multidimensional arrays bypasses the curse of dimensionality.

Main Results:

• IPA converges to a delta function at the global minimum of the PES.
• Successfully optimized multidimensional PESs, including a 50 base-pair DNA model and a prime factorization problem.
• Resolved multiple degenerate global minima even across large energy barriers in rugged landscapes.

Conclusions:

• IPA provides a robust and efficient method for global optimization in computational chemistry.
• The algorithm's ability to handle complex, high-dimensional problems is demonstrated.
• IPA is expected to be valuable for a wide range of molecular and electronic structure calculations.