Publications by Michael John Willatt

Equivariant representations for molecular Hamiltonians and N-center atomic-scale properties

Michele Ceriotti, Jigyasa Nigam, Michael John Willatt

Symmetry considerations are at the core of the major frameworks used to provide an effective mathematical representation of atomic configurations that is then used in machine-learning models to predict the properties associated with each structure. In most ...

AIP Publishing2022

Comment on "Manifolds of quasi-constant SOAP and ACSF fingerprints and the resulting failure to machine learn four-body interactions" [J. Chem. Phys. 156, 034302 (2022)]

Michele Ceriotti, Sergey Pozdnyakov, Michael John Willatt

The "quasi-constant " smooth overlap of atomic position and atom-centered symmetry function fingerprint manifolds recently discovered by Parsaeifard and Goedecker [J. Chem. Phys. 156, 034302 (2022)] are closely related to the degenerate pairs of configurat ...

AIP Publishing2022

Efficient implementation of atom-density representations

Michele Ceriotti, Guillaume André Jean Fraux, Till Junge, Félix Benedito Clément Musil, Michael John Willatt, Max David Veit, Alexander Jan Goscinski

Physically motivated and mathematically robust atom-centered representations of molecular structures are key to the success of modern atomistic machine learning. They lie at the foundation of a wide range of methods to predict the properties of both materi ...

2021

Machine-Learning of Atomic-Scale Properties Based on Physical Principles

Michele Ceriotti, Michael John Willatt

We briefly summarize the kernel regression approach, as used recently in materials modelling, to fitting functions, particularly potential energy surfaces, and highlight how the linear algebra framework can be used to both predict and train from linear fun ...

Springer International Publishing2020

Incompleteness of Atomic Structure Representations

Michele Ceriotti, Sergey Pozdnyakov, Michael John Willatt

Many-body descriptors are widely used to represent atomic environments in the construction of machine-learned interatomic potentials and more broadly for fitting, classification, and embedding tasks on atomic structures. There is a widespread belief in the ...

AMER PHYSICAL SOC2020

Physics-based machine learning for materials and molecules

Michele Ceriotti, Michael John Willatt, Edgar Albert Engel

AMER CHEMICAL SOC2019

Path-integral dynamics of water using curvilinear centroids

Michael John Willatt

We develop a path-integral dynamics method for water that resembles centroid molecular dynamics (CMD), except that the centroids are averages of curvilinear, rather than Cartesian, bead coordinates. The curvilinear coordinates are used explicitly only when ...

2019

Atom-density representations for machine learning

Michele Ceriotti, Félix Benedito Clément Musil, Michael John Willatt

This has led to a proliferation of alternative ways to convert an atomic structure into an input for a machine-learning model. We introduce an abstract definition of chemical environments that is based on a smoothed atomic density, using a bra-ket notation ...

2019

Fast and Accurate Uncertainty Estimation in Chemical Machine Learning

Michele Ceriotti, Félix Benedito Clément Musil, Michael John Willatt, Mikhail Langovoy

We present a scheme to obtain an inexpensive and reliable estimate of the uncertainty associated with the predictions of a machine-learning model of atomic and molecular properties. The scheme is based on resampling, with multiple models being generated ba ...

2019

Approximating Matsubara dynamics using the planetary model: Tests on liquid water and ice

Michele Ceriotti, Michael John Willatt

Matsubara dynamics is the quantum-Boltzmann-conserving classical dynamics which remains when real-time coherences are taken out of the exact quantum Liouvillian [T. J. H. Hele et al., J. Chem. Phys. 142, 134103 (2015)]; because of a phase-term, it cannot b ...

2018