Symmetric and antisymmetric kernels for machine learning problems in quantum physics and chemistry
arXiv:2103.17233 · doi:10.1088/2632-2153/ac14ad
Abstract
We derive symmetric and antisymmetric kernels by symmetrizing and antisymmetrizing conventional kernels and analyze their properties. In particular, we compute the feature space dimensions of the resulting polynomial kernels, prove that the reproducing kernel Hilbert spaces induced by symmetric and antisymmetric Gaussian kernels are dense in the space of symmetric and antisymmetric functions, and propose a Slater determinant representation of the antisymmetric Gaussian kernel, which allows for an efficient evaluation even if the state space is high-dimensional. Furthermore, we show that by exploiting symmetries or antisymmetries the size of the training data set can be significantly reduced. The results are illustrated with guiding examples and simple quantum physics and chemistry applications.
References in corpus (13)
- On representing chemical environments
- Deep neural network solution of the electronic Schrödinger equation
- Ab-Initio Solution of the Many-Electron Schrödinger Equation with Deep Neural Networks
- Fermionic neural-network states for ab-initio electronic structure
- Inhomogeneous backflow transformations in quantum Monte Carlo calculations
- Solving Many-Electron Schrödinger Equation Using Deep Neural Networks
- Kernel Flows: from learning kernels from data into the abyss
- Kernel-based approximation of the Koopman generator and Schrödinger operator
- Permutationally Invariant, Reproducing Kernel-Based Potential Energy Surfaces for Polyatomic Molecules: From Formaldehyde to Acetone
- Convergence to the fixed-node limit in deep variational Monte Carlo
- On Representing (Anti)Symmetric Functions
- Singular Value Decomposition of Operators on Reproducing Kernel Hilbert Spaces
- Approximating the Permanent by Sampling from Adaptive Partitions