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A central concern of molecular dynamics simulations are the potential energy surfaces that govern atomic interactions. These hypersurfaces define the potential energy of the system, and have generally been calculated using either pre-defined analytical formulas (classical) or quantum mechanical simulations (ab initio). The former can Gaussian approximation potential models for tungsten. Physical Review B, 90 (10):104108, 2014. 30 XW Zhou and RE Jones. Effects of cutoff functions of Tersoff potentials on molecular dynamics simulations of thermal transport. Modelling , et al. Deep neural networks for acoustic modeling in speech recognition: The shared views of four research groups. IEEE Signal processing magazine, 29(6):82-97, 2012. 32 B Yegnanarayana. Artificial neural networks. PHI Learning Pvt. Ltd., 2009. 33 Yann LeCun, Yoshua Bengio, and Geoffrey Hinton. Deep learning. Nature, 521(7553):436, 2015. 34 Balázs Csanád Csáji. Approximation with artificial neural networks. Master's thesis, Etvs Lornd University, Hungary, 2001. 35 Ajeevsing Bholoa, Steven D Kenny, and Roger Smith. A new approach to potential fitting using neural networks. Nuclear instruments and methods in physics research section B: Beam interactions with materials and atoms, 255(1):1-7, 2007. 36 Sönke Lorenz, Axel Groß, and Matthias Scheffler. Representing high-dimensional potentialenergy surfaces for reactions at surfaces by neural networks. Chemical Physics Letters, 395 (4-6):210-215, 2004. 37 Thomas B Blank, Steven D Brown, August W Calhoun, and Douglas J Doren. Neural network models of potential energy surfaces. The Journal of chemical physics, 103(10): 4129-4137, 1995. 38 Frederico V Prudente and JJ Soares Neto. The fitting of potential energy surfaces using neural networks. Application to the study of the photodissociation processes. Chemical physics letters, 287(5-6):585-589, 1998. 39 Ana Carla P Bittencourt, Frederico V Prudente, and José David M Vianna. The fitting of potential energy and transition moment functions using neural networks: transition probabilities in OH (A2Σ+ X2Π). Michael Isard, et al. Tensorflow: a system for large-scale machine learning. In OSDI, volume 16, pages 265-283, 2016. 47 John-Anders Stende. Constructing high-dimensional neural network potentials for molecular dynamics. Master's thesis, University of Oslo, Norway, 2017. 48 Xavier Glorot and Yoshua Bengio. Understanding the difficulty of training deep feedforward neural networks. In Proceedings of the thirteenth international conference on artificial intelligence and statistics, pages 249-256, 2010.

Recently, machine learning potentials have been advanced as candidates to combine the high-accuracy of electronic structure methods with the speed of classical interatomic potentials. A crucial component of a machine learning potential is the description of local atomic environments by some set of descriptors. These should ideally be invariant to the symmetries of the physical system, twice-differentiable with respect to atomic positions (including when an atom leaves the environment), and complete to allow the atomic environment to be reconstructed up to symmetry.The stronger condition of optimal completeness requires that the condition for completeness be satisfied with the minimum possible number of descriptors. Evidence is provided that an updated version of the recently proposed Spherical Bessel (SB) descriptors satisfies the first two properties and a necessary condition for optimal completeness. The Smooth Overlap of Atomic Position (SOAP) descriptors and the Zernike descriptors are natural counterparts of the SB descriptors and are included for comparison. The standard construction of the SOAP descriptors is shown to not satisfy the condition for optimal completeness, and moreover is found to be an order of magnitude slower to compute than the SB descriptors.

Over the past few years, thermal design for cooling microprocessors has become increasingly challenging mainly because of an increase in both average power density and local power density, commonly referred to as “hot spots”. The current air cooling technologies present diminishing returns, thus it is strategically important for the microelectronics industry to establish the research and development focus for future non air-cooling technologies. This paper presents the thermal performance capability for enabling and package based cooling technologies using a range of “reasonable” boundary conditions. In the enabling area a few key main building blocks are considered: air cooling, high conductivity materials, liquid cooling (single and two-phase), thermoelectric modules integrated with heat pipes/vapor chambers, refrigeration based devices and the thermal interface materials performance. For package based technologies we present only the microchannel building block (cold plate in contact with the back-side of the die). It will be shown that as the hot spot density factor increases, package based cooling technologies should be considered for more significant cooling improvements. In addition to thermal performance, a summary of the key technical challenges are presented in the paper.   This paper was also originally published as part of the Proceedings of the ASME 2005 Heat Transfer Summer Conference.

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