Computational Methods and Experimental Approaches for Uncertainty Quantification and Propagation, Model Validation, and Stochastic Predictions: Uncertainty Quantification in Density Functional Theory (DFT)
Sponsored by: TMS: Computational Materials Science and Engineering Committee, TMS: Chemistry and Physics of Materials Committee, TMS: Integrated Computational Materials Engineering Committee
Program Organizers: Francesca Tavazza, National Institute of Standards and Technology; Richard Hennig, University of Florida; Li Ma, NIST; Shawn Coleman, ARL; Jeff Doak, QuesTek Innovations, LLC; Fadi Abdeljawad, Sandia naional Laboratory
Wednesday 2:00 PM
March 1, 2017
Location: San Diego Convention Ctr
Session Chair: Francesca Tavazza, National Institute of Standards and Technology; Richard Hennig, University of Florida
Automatized Convergence and Error Analyses for High Precision Density Functional Theory Calculations: Jan Janßen1; Tilmann Hickel1; Joerg Neugebauer1; 1Max-Planck-Institut für Eisenforschung GmbH
Over the last years methodological and computational progress in atomistic simulations has substantially improved the predictive power in materials design. However to compare the simulation results with experimental data, it is necessary to quantify the various sources of uncertainty. We therefore leverage the capabilities of our recently developed Python based workbench PyIron, to implement an automatized stochastic sensitivity analyses with the aim to determine and differentiate model errors, statistical errors and systematical errors. For each error type the convergence gradient based on our sensitivity analyses is determined and combined with the individual cost function of the parameters. Based on this function we derive an algorithm for automated convergence which allows to quantify the precision of the energy of an individual ab initio calculation as well as for derived quantities of huge sets of ab initio calculations. The efficiencey of the approach will be demonstrated for determining structural and thermodynamic quantities.
2:20 PM Invited
Peierls Barrier in Ta-W Alloys: Estimating Aleatory Variability: Stephen Foiles1; 1Sandia National Laboratories
The deformation of body-centered-cubic (BCC) metals depends strongly on the motion of screw dislocations. Due to lattice resistance, the Peierls barrier, screw dislocation motion is thermally activated leading to temperature and rate dependent flow. Thus, the Peierls barrier is an important consideration in alloy design. The most common first-principles computational approach to predict this dependence invokes the virtual crystal approximation which treats all atoms as equivalent and focuses on the changes in bonding due to alloying but does not account for the detailed local distribution of substitutional atoms. Here we employ density functional theory calculations for the case of W additions in Ta to develop a model for the interaction of substitutional atoms with screw dislocations and the modification of the local barriers due to the substitutional atom. This model is then used to estimate the local variability in the Peierls barrier due to the stochastic distribution of substitutional atoms.
2:55 PM Invited
Density Functionals and the Finite Temperature Properties of Ferroelectric Oxides: Valentino Cooper1; 1Oak Ridge National Laboratory
Density functional theory (DFT) is routinely used to explore groundstate properties of ferroelectric oxides. However, evaluating finite-temperature behavior is not straightforward; requiring Monte Carlo or molecular dynamics simulations employing DFT-trained models. Unfortunately, these methods often deviate from experiments due to uncertainties in the phenomenological models and the DFT functionals used to parameterize them. Using DFT-based Wang-Landau Monte Carlo simulations, we explore how exchange-correlation functional choices affect both groundstate properties predictions and phase transitions in three prototypical perovskites. We reduce the number of costly DFT energy evaluations by employing machine learning techniques to reject unfavorable moves. This approach allows us to identify the best density functional for these materials and can be used in a diverse set of systems. Supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Science and Engineering Division through the Office of Science Early Career Research Program, using resources at NERSC.
3:30 PM Break
3:50 PM Invited
Quantifying Uncertainty from (Pseudo)potentials for First Principles and Classical Atomistic Simulations: Mark Tschopp1; Efrain Hernandez1; Shawn Coleman1; Decarlos Taylor1; Jennifer Synowczynski-Dunn1; 1Army Research Laboratory
How do we quantify uncertainty in first principles or atomistic simulations? In this work, we used different approaches to quantify the influence of the (pseudo)potential (and other parameters) on the structure of boron-based ceramics. One example focuses on coupling different similarity/distance measures with virtual x-ray diffraction profiles to quantify the structural uncertainty due to different (pseudo)potentials for first principles and atomistic simulations. The diffraction profiles highlight subtle structural changes that occur when modeling complex materials using different first-principles techniques, basis-sets, pseudopotentials, and classical interatomic potentials. The ability to quantify the difference between these profiles involved the use of approximately 50 distance and similarity metrics. Other examples focus on uncertainty in the parameterization of classical potentials. The significance of this work is that this methodology can highlight the uncertainty associated with various computational approaches and help to validate structure and quantify the fidelity of various classical potentials in atomistic simulations.
Validation and Uncertainty Assessment of Bond-order Potentials for Transition Metals: Matous Mrovec1; Thomas Hammerschmidt1; Yi-Shen Lin2; Vaclav Vitek2; Ralf Drautz1; 1ICAMS, Ruhr University Bochum, Germany; 2Department of Materials Science and Engineering, University of Pennsylvania
Bond-order potentials (BOPs) present a bridge between electronic and atomistic modeling. They are based on the tight-binding (TB) approximation, but the exact diagonalization of the Hamiltonian is replaced by an approximate evaluation of the local densities of states, which leads to a real-space formalism and linear-scaling computation of the energy and forces for a system of interacting atoms. The BOP formalism can be carried out using either a numerical integration or an analytical expansion of the response functions. In this work we present a detailed comparison of the k-space TB with the numerical and analytic BOPs for several transition metals, and assess the differences of the three approaches. The tests are carried out not only for properties of bulk phases but also crystal defects. Particular focus is given to dislocation behavior, which is often used to validate the accuracy and reliability of interatmoic potentials for transition metals.