Higher-order triplet interaction in energy-level modeling of excited-state absorption for an expanded porphyrin cadmium complex

Recent measurements of transmission versus fluence for a methanol-solvated asymmetric pentaazadentate porphyrin-like (APPC) cadmium complex, [(C6H4-APPC)Cd]Cl, showed the limitations of current energy-level models in predicting the transmission behavior of organic reverse saturable absorbers at fluences greater than 1 J/cm². A new model has been developed that incorporates higher-order triplet processes and accurately fits both nanosecond and picosecond transmission-versus-fluence data. This model has provided the first known determination of a higher triplet excited-state absorption cross section and lifetime for an APPC complex and also described a previously unreported feature in the transmission-versus-fluence data. The intersystem crossing rate and the previously neglected higher triplet excited-state absorption cross section are shown to govern the excited-state population dynamics of methanol-solvated [(C6H4-APPC)Cd]Cl most strongly at more-practical device energies

The Optimal Uncertainty Algorithm in the Mystic Framework

We have recently proposed a rigorous framework for Uncertainty Quantification (UQ) in which UQ objectives and assumption/information set are brought into the forefront, providing a framework for the communication and comparison of UQ results. In particular, this framework does not implicitly impose inappropriate assumptions nor does it repudiate relevant information. This framework, which we call Optimal Uncertainty Quantification (OUQ), is based on the observation that given a set of assumptions and information, there exist bounds on uncertainties obtained as values of optimization problems and that these bounds are optimal. It provides a uniform environment for the optimal solution of the problems of validation, certification, experimental design, reduced order modeling, prediction, extrapolation, all under aleatoric and epistemic uncertainties. OUQ optimization problems are extremely large, and even though under general conditions they have finite-dimensional reductions, they must often be solved numerically. This general algorithmic framework for OUQ has been implemented in the mystic optimization framework. We describe this implementation, and demonstrate its use in the context of the Caltech surrogate model for hypervelocity impact

Optimal Uncertainty Quantification

We propose a rigorous framework for Uncertainty Quantification (UQ) in which the UQ objectives and the assumptions/information set are brought to the forefront. This framework, which we call Optimal Uncertainty Quantification (OUQ), is based on the observation that, given a set of assumptions and information about the problem, there exist optimal bounds on uncertainties: these are obtained as extreme values of well-defined optimization problems corresponding to extremizing probabilities of failure, or of deviations, subject to the constraints imposed by the scenarios compatible with the assumptions and information. In particular, this framework does not implicitly impose inappropriate assumptions, nor does it repudiate relevant information. Although OUQ optimization problems are extremely large, we show that under general conditions, they have finite-dimensional reductions. As an application, we develop Optimal Concentration Inequalities (OCI) of Hoeffding and McDiarmid type. Surprisingly, contrary to the classical sensitivity analysis paradigm, these results show that uncertainties in input parameters do not necessarily propagate to output uncertainties. In addition, a general algorithmic framework is developed for OUQ and is tested on the Caltech surrogate model for hypervelocity impact, suggesting the feasibility of the framework for important complex systems

Optimal uncertainty quantification for legacy data observations of Lipschitz functions

We consider the problem of providing optimal uncertainty quantification (UQ) --- and hence rigorous certification --- for partially-observed functions. We present a UQ framework within which the observations may be small or large in number, and need not carry information about the probability distribution of the system in operation. The UQ objectives are posed as optimization problems, the solutions of which are optimal bounds on the quantities of interest; we consider two typical settings, namely parameter sensitivities (McDiarmid diameters) and output deviation (or failure) probabilities. The solutions of these optimization problems depend non-trivially (even non-monotonically and discontinuously) upon the specified legacy data. Furthermore, the extreme values are often determined by only a few members of the data set; in our principal physically-motivated example, the bounds are determined by just 2 out of 32 data points, and the remainder carry no information and could be neglected without changing the final answer. We propose an analogue of the simplex algorithm from linear programming that uses these observations to offer efficient and rigorous UQ for high-dimensional systems with high-cardinality legacy data. These findings suggest natural methods for selecting optimal (maximally informative) next experiments.Comment: 38 page

Raman spectrometry study of phonon anharmonicity of hafnia at elevated temperatures

Raman spectra of monoclinic hafnium oxide (HfO_2) were measured at temperatures up to 1100 K. Raman peak shifts and broadenings are reported. Phonon dynamics calculations were performed with the shell model to obtain the total and partial phonon density of states, and to identify the individual motions of Hf and O atoms in the Raman modes. Correlating these motions to the thermal peak shifts and broadenings, it was found that modes involving changes in oxygen-oxygen bond length were the most anharmonic. The hafnium-dominated modes were more quasiharmonic and showed less broadening with temperature. Comparatively, the oxygen-dominated modes were more influenced by the cubic term in the interatomic potential than the hafnium-dominated modes. An approximately quadratic correlation was found between phonon-line broadening and softening

Efficient Learning of Accurate Surrogates for Simulations of Complex Systems

Machine learning methods are increasingly used to build computationally inexpensive surrogates for complex physical models. The predictive capability of these surrogates suffers when data are noisy, sparse, or time-dependent. As we are interested in finding a surrogate that provides valid predictions of any potential future model evaluations, we introduce an online learning method empowered by optimizer-driven sampling. The method has two advantages over current approaches. First, it ensures that all turning points on the model response surface are included in the training data. Second, after any new model evaluations, surrogates are tested and "retrained" (updated) if the "score" drops below a validity threshold. Tests on benchmark functions reveal that optimizer-directed sampling generally outperforms traditional sampling methods in terms of accuracy around local extrema, even when the scoring metric favors overall accuracy. We apply our method to simulations of nuclear matter to demonstrate that highly accurate surrogates for the nuclear equation of state can be reliably auto-generated from expensive calculations using a few model evaluations.Comment: 13 pages, 6 figures, submitted to Nature Machine Intelligenc

AtomSim: web-deployed atomistic dynamics simulator

AtomSim, a collection of interfaces for computational crystallography simulations, has been developed. It uses forcefield-based dynamics through physics engines such as the General Utility Lattice Program, and can be integrated into larger computational frameworks such as the Virtual Neutron Facility for processing its dynamics into scattering functions, dynamical functions etc. It is also available as a Google App Engine-hosted web-deployed interface. Examples of a quartz molecular dynamics run and a hafnium dioxide phonon calculation are presented

Optimal Uncertainty Quantification

We propose a rigorous framework for Uncertainty Quantification (UQ) in which the UQ objectives and the assumptions/information set are brought to the forefront. This framework, which we call \emph{Optimal Uncertainty Quantification} (OUQ), is based on the observation that, given a set of assumptions and information about the problem, there exist optimal bounds on uncertainties: these are obtained as values of well-defined optimization problems corresponding to extremizing probabilities of failure, or of deviations, subject to the constraints imposed by the scenarios compatible with the assumptions and information. In particular, this framework does not implicitly impose inappropriate assumptions, nor does it repudiate relevant information. Although OUQ optimization problems are extremely large, we show that under general conditions they have finite-dimensional reductions. As an application, we develop \emph{Optimal Concentration Inequalities} (OCI) of Hoeffding and McDiarmid type. Surprisingly, these results show that uncertainties in input parameters, which propagate to output uncertainties in the classical sensitivity analysis paradigm, may fail to do so if the transfer functions (or probability distributions) are imperfectly known. We show how, for hierarchical structures, this phenomenon may lead to the non-propagation of uncertainties or information across scales. In addition, a general algorithmic framework is developed for OUQ and is tested on the Caltech surrogate model for hypervelocity impact and on the seismic safety assessment of truss structures, suggesting the feasibility of the framework for important complex systems. The introduction of this paper provides both an overview of the paper and a self-contained mini-tutorial about basic concepts and issues of UQ.Comment: 90 pages. Accepted for publication in SIAM Review (Expository Research Papers). See SIAM Review for higher quality figure

Self-Powered Dynamic Systems in the Framework of Optimal Uncertainty Quantification

The energy that is needed for operating a self-powered device is provided by the energy excess in the system in the form of kinetic energy, or a combination of regenerative and renewable energy. This paper addresses the energy exchange issues pertaining to regenerative and renewable energy in the development of a self-powered dynamic system. A rigorous framework that explores the supply and demand of energy for self-powered systems is developed, which considers uncertainties and optimal bounds, in the context of optimal uncertainty quantification. Examples of regenerative and solar-powered systems are given, and the analysis of self-powered feedback control for developing a fully self-powered dynamic system is discussed