Reconstructing Kernel-Based Machine Learning Force Fields with Superlinear Convergence.

Area of Science:

• Quantum Chemistry
• Machine Learning

Background:

• Kernel machines show promise in quantum chemistry, particularly for force field reconstruction with limited data.
• Physical symmetries can be incorporated into kernel functions to enhance performance in low-data scenarios.

Purpose of the Study:

• To address the scalability limitations of kernel machines, specifically their quadratic memory and cubical runtime complexity.
• To develop effective preconditioners for Krylov subspace solvers, crucial for overcoming computational burdens.

Main Methods:

• Investigated Nyström-type methods for constructing preconditioners.
• Employed low-rank approximations of kernel matrices to identify representative inducing columns.
• Aimed to approximate the dominant kernel spectrum.

Main Results:

• Nyström-type methods offer a class of approaches for preconditioner construction.
• These methods provide various computational trade-offs.
• The core strategy involves selecting a subset of kernel columns to approximate the kernel spectrum.

Conclusions:

• Nyström-type methods present a viable strategy for enhancing the scalability of kernel machines in quantum chemistry.
• Effective preconditioners are key to enabling efficient use of Krylov subspace solvers.
• Approximating the kernel spectrum through low-rank methods is central to this approach.