
Quantum steampunk: Quantum information, thermodynamics, their intersection, and applications thereof across physics
Combining quantum information theory with thermodynamics unites 21stcen...
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Unreasonable effectiveness of Monte Carlo
This is a comment on the article "Probabilistic Integration: A Role in S...
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Opening the black box of deep learning
The great success of deep learning shows that its technology contains pr...
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A Numerical Example on the Principles of Stochastic Discrimination
Studies on ensemble methods for classification suffer from the difficult...
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Probabilistic Models with Deep Neural Networks
Recent advances in statistical inference have significantly expanded the...
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Computer Algebra and Material Design
This article is intended to an introductory lecture in material physics,...
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Probabilistic Integration: A Role in Statistical Computation?
A research frontier has emerged in scientific computation, wherein numer...
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Emulating the First Principles of Matter: A Probabilistic Roadmap
This chapter provides a tutorial overview of first principles methods to describe the properties of matter at the ground state or equilibrium. It begins with a brief introduction to quantum and statistical mechanics for predicting the electronic structure and diverse static properties of of manyparticle systems useful for practical applications. Pedagogical examples are given to illustrate the basic concepts and simple applications of quantum Monte Carlo and density functional theory – two representative methods commonly used in the literature of first principles modeling. In addition, this chapter highlights the practical needs for the integration of physicsbased modeling and datascience approaches to reduce the computational cost and expand the scope of applicability. A special emphasis is placed on recent developments of statistical surrogate models to emulate first principles calculation from a probabilistic point of view. The probabilistic approach provides an internal assessment of the approximation accuracy of emulation that quantifies the uncertainty in predictions. Various recent advances toward this direction establish a new marriage between Gaussian processes and first principles calculation, with physical properties, such as translational, rotational, and permutation symmetry, naturally encoded in new kernel functions. Finally, it concludes with some prospects on future advances in the field toward faster yet more accurate computation leveraging a synergetic combination of novel theoretical concepts and efficient numerical algorithms.
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