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Lecture

Machine Learning in Molecular Dynamics

In course

PHYS-754: Lecture series on scientific machine learning

This lecture presents ongoing work on how scientific questions can be tackled using machine learning. Machine learning enables extracting knowledge from data computationally and in an automatized way. We will learn on examples how this is influencing the v ...

Description

This lecture presents examples of research on the application of machine learning in molecular dynamics, materials, and chemistry. Starting with linear regression and polynomial regression, it progresses to kernel regression and neural networks. The focus is on creating meaningful features that capture relevant information and symmetries in the system. The lecture discusses a paper on using neural networks to model potential energy surfaces efficiently, emphasizing the importance of generalizability. It then delves into another paper that unifies the modeling of materials and molecules using atomic neighbor densities and Gaussian functions. The lecture concludes with a discussion on kernel regression and structured kernels in relation to molecular energy prediction.

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Instructors (10)

Anne-Clémence Corminboeuf

David Richard Harvey

Alexander Mathis

Alexander studied pure mathematics with a minor in logic and theory of science at the Ludwig Maximilians University in Munich. For his PhD also at LMU, he worked on optimal coding approaches to elucidate the properties of grid cells. As a postdoctoral fellow with Prof. Venkatesh N. Murthy at Harvard University and Prof. Matthias Bethge at Tuebingen AI, he decided to study olfactory behaviors such as odor-guided navigation, social behaviors and the cocktail party problem in mice. During this time, he increasingly got interested sensorimotor behaviors beyond olfaction and started working on proprioception, motor adaption, as well as computer vision tools for measuring animal behavior. In his group, he is interested in elucidating how the brain gives rise to adaptive behavior. One of the major goals is to synthesize large datasets into computationally useful information. For those purposes, he develops algorithms and systems to analyze animal behavior (e.g. DeepLabCut), neural data, as well as creates experimentally testable computational models.

Philippe Schwaller

Matthieu Wyart

Giuseppe Carleo

Giuseppe Carleo is a computational quantum physicist, whose main focus is the development of advanced numerical algorithms tostudy challenging problems involving strongly interacting quantum systems.He is best known for the introduction of machine learning techniques to study both equilibrium and dynamical properties,based on a neural-network representations of quantum states, as well for the time-dependent variational Monte Carlo method.He earned a Ph.D. in Condensed Matter Theory from the International School for Advanced Studies (SISSA) in Italy in 2011.He held postdoctoral positions at the Institut d’Optique in France and ETH Zurich in Switzerland, where he alsoserved as a lecturer in computational quantum physics.In 2018, he joined the Flatiron Institute in New York City in 2018 at the Center for Computational Quantum Physics (CCQ), working as a Research Scientist and project leader, and also leading the development of the open-source project NetKet.Since September 2020 he is an assistant professor at EPFL, in Switzerland, leading the Computational Quantum Science Laboratory (CQSL).

Official source

Ontological neighbourhood

Statistics

Data analysis: Regression analysis

Related concepts (32)

Linear regression

In statistics, linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables). The case of one explanatory variable is called simple linear regression; for more than one, the process is called multiple linear regression. This term is distinct from multivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable.

Symmetry

Symmetry () in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, the term has a more precise definition and is usually used to refer to an object that is invariant under some transformations, such as translation, reflection, rotation, or scaling. Although these two meanings of the word can sometimes be told apart, they are intricately related, and hence are discussed together in this article.

Polynomial regression

In statistics, polynomial regression is a form of regression analysis in which the relationship between the independent variable x and the dependent variable y is modelled as an nth degree polynomial in x. Polynomial regression fits a nonlinear relationship between the value of x and the corresponding conditional mean of y, denoted E(y |x). Although polynomial regression fits a nonlinear model to the data, as a statistical estimation problem it is linear, in the sense that the regression function E(y | x) is linear in the unknown parameters that are estimated from the data.

Simple linear regression

In statistics, simple linear regression is a linear regression model with a single explanatory variable. That is, it concerns two-dimensional sample points with one independent variable and one dependent variable (conventionally, the x and y coordinates in a Cartesian coordinate system) and finds a linear function (a non-vertical straight line) that, as accurately as possible, predicts the dependent variable values as a function of the independent variable. The adjective simple refers to the fact that the outcome variable is related to a single predictor.

Symmetry group

In group theory, the symmetry group of a geometric object is the group of all transformations under which the object is invariant, endowed with the group operation of composition. Such a transformation is an invertible mapping of the ambient space which takes the object to itself, and which preserves all the relevant structure of the object. A frequent notation for the symmetry group of an object X is G = Sym(X). For an object in a metric space, its symmetries form a subgroup of the isometry group of the ambient space.

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