Related papers: A Worked Example of the Bayesian Mechanics of Clas…
Closed-form, interpretable mathematical models have been instrumental for advancing our understanding of the world; with the data revolution, we may now be in a position to uncover new such models for many systems from physics to the social…
Bayesian optimization is used in many areas of AI for the optimization of black-box processes and has achieved impressive improvements of the state of the art for a lot of applications. It intelligently explores large and complex design…
Regarded as one of the most fundamental concepts of classical mechanics and thermodynamics, work has received well-grounded definitions within the quantum framework since the 1970s, having being successfully applied to many contexts. Recent…
The centuries-long practice of the teaching turned mechanics into an academic construct detached from its underlying science, the physics of macroscopic bodies. In particular, the regularities that delineate the scope of validity of…
We show that the classical mechanics of an algebraic model are implied by its quantizations. An algebraic model is defined, and the corresponding classical and quantum realizations are given in terms of a spectrum generating algebra.…
The quantum and classical dynamics of particles kicked by a gaussian attractive potential are studied. Classically, it is an open mixed system (the motion in some parts of the phase space is chaotic, and in some parts it is regular). The…
Novel gauge functions are introduced to non-relativistic classical mechanics and used to define forces. The obtained results show that the gauge functions directly affect the energy function and that they allow converting an undriven…
The notion of microscopic state of the system at a given moment of time as a point in the phase space as well as a notion of trajectory is widely used in classical mechanics. However, it does not have an immediate physical meaning, since…
We present a Bayesian method for the identification and classification of objects from sets of astronomical catalogs, given a predefined classification scheme. Identification refers here to the association of entries in different catalogs…
Interrelations between dynamical and statistical laws in physics, on the one hand, and between the classical and quantum mechanics, on the other hand, are discussed with emphasis on the new phenomenon of dynamical chaos. The principal…
We consider a 3-parametric linear deformation of the Poisson brackets in classical mechanics. This deformation can be thought of as the classical limit of dynamics in so-called "quantized spaces". Our main result is a description of the…
Classical mechanics is presented here in a unary operator form, constructed using the binary multiplication and Poisson bracket operations that are given in a phase space formalism, then a Gibbs equilibrium state over this unary operator…
The formulation of classical mechanics applicable to fermionic degrees of freedom is presented in mathematically rigorous terms, including a description of how the mathematical structure relates to the quantization of the theory. Canonical…
These lecture notes highlight the mathematical and computational structure relating to the formulation of, and development of algorithms for, the Bayesian approach to inverse problems in differential equations. This approach is fundamental…
It is shown that the equations of relativistic Bohmian mechanics for multiple bosonic particles have a dual description in terms of a classical theory of conformally "curved" space-time. This shows that it is possible to formulate quantum…
Explosive growth in data and availability of cheap computing resources have sparked increasing interest in Big learning, an emerging subfield that studies scalable machine learning algorithms, systems, and applications with Big Data.…
Bohmian mechanics is a realistic interpretation of quantum theory. It shares the same ontology of classical mechanics: particles following continuous trajectories in space through time. For this ontological continuity, it seems to be a good…
Bayesian Optimization using Gaussian Processes is a popular approach to deal with the optimization of expensive black-box functions. However, because of the a priori on the stationarity of the covariance matrix of classic Gaussian…
The relationship between chaos and quantum mechanics has been somewhat uneasy -- even stormy, in the minds of some people. However, much of the confusion may stem from inappropriate comparisons using formal analyses. In contrast, our…
A Bayesian approach is developed to determine quantum mechanical potentials from empirical data. Bayesian methods, combining empirical measurements and "a priori" information, provide flexible tools for such empirical learning problems. The…