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DOE OSTI2019

Identification of stable adsorption sites and diffusion paths on nanocluster surfaces: an automated scanning algorithm

The diverse coordination environments on the surfaces of discrete, three-dimensional (3D) nanoclusters contribute significantly to their unique catalytic properties. Identifying the numerous adsorption sites and diffusion paths on these clusters is however tedious and time-consuming, especially for large, asymmetric nanoclusters. Here, we present a simple, automated method for constructing approximate 2D potential energy surfaces for the adsorption of atomic species on the surfaces of 3D nanoclusters with minimal human intervention. These potential energy surfaces fully characterize the important adsorption sites and diffusion paths on the nanocluster surfaces with accuracies similar to current approaches and at comparable computational cost. Our method can treat complex nanoclusters, such as alloy nanoclusters, and accounts for cluster relaxation and adsorbate-induced reconstruction, important for obtaining accurate energetics. Moreover, its highly parallelizable nature is ideal for modern supercomputer architectures. We showcase our method using two clusters: Au 18 and Pt 55 . For Au 18 , diffusion of atomic hydrogen between the most stable sites occurs via non-intuitive paths, underlining the necessity of exploring the complete potential energy surface. By enabling the rapid and unbiased assessment of adsorption and diffusion on large, complex nanoclusters, which are particularly difficult to handle manually, our method will help advance materials discovery and the rational design of catalysts.

36 MATERIALS SCIENCE↗

DOE OSTI2025

A comparative study of calibration techniques for finite strain elastoplasticity: Numerically-exact sensitivities for FEMU and VFM

Accurate identification of material parameters is crucial for predictive modeling in computational mechanics. Here, the two primary approaches in the experimental mechanics community for calibration from full-field digital image correlation data are known as finite element model updating (FEMU) and the virtual fields method (VFM). In VFM, the objective function is a squared mismatch between internal and external virtual work or power. In FEMU, the objective function quantifies the weighted mismatch between model predictions and corresponding experimentally measured quantities of interest. It is minimized by iteratively updating the parameters of an FE model. While FEMU is seen as more flexible, VFM is commonly used instead of FEMU due to its considerably greater computational expense. However, comparisons between the two methods usually involve approximations of gradients or sensitivities with finite difference schemes, thereby making direct assessments difficult. Hence, in this study, we compare VFM and FEMU in the context of numerically-exact sensitivities obtained through local sensitivity analyses and the application of automatic differentiation software. To this end, we conduct a series of test cases to assess both methods under practical challenges using a finite strain elastoplasticity model.

Automatic differentiation↗

DOE OSTI2018

Estimating the joint distribution of rate parameters across multiple reactions in the absence of experimental data

Here, a procedure for determining the joint uncertainty of Arrhenius parameters across multiple combustion reactions of interest is demonstrated. This approach is capable of constructing the joint distribution of the Arrhenius parameters arising from the uncertain measurements performed in specific target experiments without having direct access to the underlying experimental data. The method involves constructing an ensemble of hypothetical data sets with summary statistics consistent with the available information reported by the experimentalists, followed by a fitting procedure that learns the structure of the joint parameter density across reactions using this consistent hypothetical data as evidence. The procedure is formalized in a Bayesian statistical framework, employing maximum-entropy and approximate Bayesian computation methods and utilizing efficient Markov chain Monte Carlo techniques to explore data and parameter spaces in a nested algorithm. We demonstrate the application of the method in the context of experiments designed to measure the rates of selected chain reactions in the H 2 -O 2 system and highlight the utility of this approach for revealing the critical correlations between the parameters within a single reaction and across reactions, as well as for maximizing consistency when utilizing rate parameter information in predictive combustion modeling of systems of interest.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Enhanced multiscale restriction-smoothed basis (MsRSB) preconditioning with applications to porous media flow and geomechanics

A novel method to enable application of the Multiscale Restricted Smoothed Basis (MsRSB) method to non M-matrices is presented. The original MsRSB method is enhanced with a filtering strategy enforcing M-matrix properties to enable the robust application of MsRSB as a preconditioner. Through applications to porous media flow and linear elastic geomechanics, the method is proven to be effective for scalar and vector problems with multipoint finite volume (FV) and finite element (FE) discretization schemes, respectively. Realistic complex (un)structured two- and three-dimensional test cases are considered to illustrate the method's performance.

58 GEOSCIENCES↗

DOE OSTI2018

Sliced-Inverse-Regression--Aided Rotated Compressive Sensing Method for Uncertainty Quantification

Compressive-sensing-based uncertainty quantification methods have become a pow- erful tool for problems with limited data. In this paper, we use the sliced inverse regression (SIR) method to provide an initial guess for the alternating direction method, which is used to enhance sparsity of the Hermite polynomial expansion of stochastic state variables. The sparsity improvement increases both the efficiency and accuracy of the compressive-sensing-based uncertainty quantification method. We demonstrate that the initial guess from SIR is more suitable for the cases when the available data is very limited (Algorithm 4). We also propose another algorithm (Algorithm 5) that performs dimension reduction first with sliced inverse regression, then constructs a Hermite polynomial expansion of the reduced model. This method allows us to approximate the statistics accurately with even less available data. Both methods are non-intrusive and require no a priori information of the sparsity of the system. We demonstrate the effectiveness of these two methods (Algorithms 4 and 5) using problems with up to 500 random dimensions.

Yang, Xiu↗

DOE OSTI2025

Greenhouse gas emissions reduction strategies that maximize portfolio-wide life cycle cost reduction, resilience, and environmental justice benefits

While strategies to achieve net-zero emissions at an individual site are well understood, new analysis methods are required for organizations seeking to achieve net-zero across multiple facilities, each with concurrent priority goals. At a portfolio level, distinct locations present varied challenges that cannot be addressed through singular solutions, and competing goals can take precedence with the assumption that net-zero emissions strategies deter from energy resilience and cost savings, therefore negatively impacting nearby communities. This study tests these assumptions by analyzing 16 diverse sites (varying in size, climate, and energy use) to identify strategies that reduce emissions and assess the impact these strategies have on life cycle costs, resilience, and communities with environmental justice concerns. Methods were developed to approximate missing information essential to net-zero evaluation. Established methods were augmented to evaluate life cycle costs, resilience, and environmental justice impacts across a set of strategies and accommodate the multi-criteria analyses. Potential benefits from identified strategies were quantified using site characteristics and a set of corresponding metrics. The net-zero analysis found that 11 sites could use on-site strategies to eliminate all but 2% of emissions generated. The remaining emissions can be offset, for instance through sequestration, executed at the portfolio scale. On-site carbon-free energy was found to reduce 51% of emissions across all sites; efficiency reduced 19% of emissions; sequestration 16%; procured carbon-free energy 15%; fuel switching 1.6%; and fleet electrification 1.3%. Building electrification, however, increased emissions by 4.4%. Different strategies also provide cost, resilience, and/or environmental justice benefits—the degree to which varies with individual site conditions. The findings indicate an advantage to considering the strategies as a comprehensive set, which leads to co-benefits, both in the ability to achieve net-zero goals and in advancing other goals. The results present the case for comprehensive advanced planning at the portfolio level to prioritize investments that will balance the minimization of emissions and life cycle cost with the maximization of resilience and environmental justice benefits. The novel methods for evaluation and integration, valuation of benefits, and consideration at the portfolio scale allow organizations to select investments that simultaneously address multiple key priorities.

Net-Zero Emissions↗

DOE OSTI2022

Computational Workflow for Accelerated Molecular Design Using Quantum Chemical Simulations and Deep Learning Models

Efficient methods for searching the chemical space of molecular compounds are needed to automate and accelerate the design of new functional molecules such as pharmaceuticals. Given the high cost in both resources and time for experimental efforts, computational approaches play a key role in guiding the selection of promising molecules for further investigation. Here, we construct a workflow to accelerate design by combining approximate quantum chemical methods [i.e. density-functional tight-binding (DFTB)], a graph convolutional neural network (GCNN) surrogate model for chemical property prediction, and a masked language model (MLM) for molecule generation. Property data from the DFTB calculations are used to train the surrogate model; the surrogate model is used to score candidates generated by the MLM. The surrogate reduces computation time by orders of magnitude compared to the DFTB calculations, enabling an increased search of chemical space. Furthermore, the MLM generates a diverse set of chemical modifications based on pre-training from a large compound library. We utilize the workflow to search for near-infrared photoactive molecules by minimizing the predicted HOMO-LUMO gap as the target property. Our results show that the workflow can generate optimized molecules outside of the original training set, which suggests that iterations of the workflow could be useful for searching vast chemical spaces in a wide range of design problems.

Blanchard, Andrew↗

DOE OSTI2025

Bias-Variance Trade-Off in Physics-Informed Neural Networks with Randomized Smoothing for High-Dimensional PDEs

Physics-Informed Neural Networks (PINNs) have triggered a paradigm shift in scientific computing, leveraging mesh-free properties and robust approximation capabilities. While proving effective for low-dimensional partial differential equations (PDEs), the computational cost of PINNs remains a hurdle in high-dimensional scenarios. This is particularly pronounced when computing high-order and high-dimensional derivatives in the physics-informed loss. Randomized Smoothing PINN (RS-PINN) introduces Gaussian noise for stochastic smoothing of the original neural net model, enabling the use of Monte Carlo methods for derivative approximation, which eliminates the need for costly automatic differentiation. Despite its computational efficiency, especially in the approximation of high-dimensional derivatives, RS-PINN introduces biases in both loss and gradients, negatively impacting convergence, especially when coupled with stochastic gradient descent (SGD) algorithms. We present a comprehensive analysis of biases in RS-PINN, attributing them to the nonlinearity of the Mean Squared Error (MSE) loss as well as the intrinsic nonlinearity of the PDE itself. We propose tailored bias correction techniques, delineating their application based on the order of PDE nonlinearity. The derivation of an unbiased RS-PINN allows for a detailed examination of its advantages and disadvantages compared to the biased version. Specifically, the biased version has a lower variance and runs faster than the unbiased version, but it is less accurate due to the bias. To optimize the bias-variance trade-off, we combine the two approaches in a hybrid method that balances the rapid convergence of the biased version with the high accuracy of the unbiased version. In addition to methodological contributions, we present an enhanced implementation of RS-PINN. Extensive experiments on diverse high-dimensional PDEs, including Fokker-Planck, Hamilton-Jacobi-Bellman (HJB), viscous Burgers’, Allen-Cahn, and Sine-Gordon equations, illustrate the bias-variance trade-off and highlight the effectiveness of the hybrid RS-PINN. Empirical guidelines are provided for selecting biased, unbiased, or hybrid versions, depending on the dimensionality and nonlinearity of the specific PDE problem.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

Parameterizing the Variability and Uncertainty of Wind and Solar in CEMs

We present current and improved methods for estimating the capacity value and curtailment impacts from variable generation (VG) in capacity expansion models (CEMs). The ideal calculation of these variability metrics is through an explicit co-optimized investment-dispatch model using multiple years of VG and load data. Because of data and computational limitations, existing CEMs typically approximate these metrics using a subset of all hours from a single year and/or using statistical methods, which often do not capture the tail-event impacts or the broader set of interactions between VG, storage, and conventional generators. In our proposed new methods, we use hourly generation and load values across all hours of the year to characterize the (1) contribution of VG to system capacity during high load hours, (2) the curtailment level of VG, and (3) the reduction in VG curtailment due to storage and shutdown of select thermal generators. Using CEM model outputs from a preceding model solve period, we apply these methods to exogenously calculate capacity value and curtailment metrics for the subsequent model solve period. Preliminary results suggest that these hourly methods offer improved capacity value and curtailment representations of VG in the CEM from existing approximation methods without additional computational burdens.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2016

Inference of reaction rate parameters based on summary statistics from experiments

Here, we present the results of an application of Bayesian inference and maximum entropy methods for the estimation of the joint probability density for the Arrhenius rate para meters of the rate coefficient of the H 2 /O 2 -mechanism chain branching reaction H + O 2 → OH + O. Available published data is in the form of summary statistics in terms of nominal values and error bars of the rate coefficient of this reaction at a number of temperature values obtained from shock-tube experiments. Our approach relies on generating data, in this case OH concentration profiles, consistent with the given summary statistics, using Approximate Bayesian Computation methods and a Markov Chain Monte Carlo procedure. The approach permits the forward propagation of parametric uncertainty through the computational model in a manner that is consistent with the published statistics. A consensus joint posterior on the parameters is obtained by pooling the posterior parameter densities given each consistent data set. To expedite this process, we construct efficient surrogates for the OH concentration using a combination of Pad'e and polynomial approximants. These surrogate models adequately represent forward model observables and their dependence on input parameters and are computationally efficient to allow their use in the Bayesian inference procedure. We also utilize Gauss-Hermite quadrature with Gaussian proposal probability density functions for moment computation resulting in orders of magnitude speedup in data likelihood evaluation. Despite the strong non-linearity in the model, the consistent data sets all res ult in nearly Gaussian conditional parameter probability density functions. The technique also accounts for nuisance parameters in the form of Arrhenius parameters of other rate coefficients with prescribed uncertainty. The resulting pooled parameter probability density function is propagated through stoichiometric hydrogen-air auto-ignition computations to illustrate the need to account for correlation among the Arrhenius rate parameters of one reaction and across rate parameters of different reactions.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

Should thermostatted ring polymer molecular dynamics be used to calculate thermal reaction rates?

We apply Thermostatted Ring Polymer Molecular Dynamics (TRPMD), a recently proposed approximate quantum dynamics method, to the computation of thermal reaction rates. Its short-time transition-state theory limit is identical to rigorous quantum transition-state theory, and we find that its long-time limit is independent of the location of the dividing surface. TRPMD rate theory is then applied to one-dimensional model systems, the atom-diatom bimolecular reactions H + H{sub 2}, D + MuH, and F + H{sub 2}, and the prototypical polyatomic reaction H + CH{sub 4}. Above the crossover temperature, the TRPMD rate is virtually invariant to the strength of the friction applied to the internal ring-polymer normal modes, and beneath the crossover temperature the TRPMD rate generally decreases with increasing friction, in agreement with the predictions of Kramers theory. We therefore find that TRPMD is approximately equal to, or less accurate than, ring polymer molecular dynamics for symmetric reactions, and for certain asymmetric systems and friction parameters closer to the quantum result, providing a basis for further assessment of the accuracy of this method.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Uniform Subspace Correction Preconditioners for Discontinuous Galerkin Methods with hp-Refinement

In this paper, we develop subspace correction preconditioners for discontinuous Galerkin (DG) discretizations of elliptic problems with hp-refinement. These preconditioners are based on the decomposition of the DG finite element space into a conforming subspace, and a set of small nonconforming edge spaces. The conforming subspace is preconditioned using a matrix-free low-order refined technique, which in this work, we extend to the hp-refinement context using a variational restriction approach. The condition number of the resulting linear system is independent of the granularity of the mesh h, and the degree of the polynomial approximation p. The method is amenable to use with meshes of any degree of irregularity and arbitrary distribution of polynomial degrees. Furthermore, numerical examples are shown on several test cases involving adaptively and randomly refined meshes, using both the symmetric interior penalty method and the second method of Bassi and Rebay (BR2).

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Performance of high-order Godunov-type methods in simulations of astrophysical low Mach number flows

High-order Godunov methods for gas dynamics have become a standard tool for simulating different classes of astrophysical flows. Their accuracy is mostly determined by the spatial interpolant used to reconstruct the pair of Riemann states at cell interfaces and by the Riemann solver that computes the interface fluxes. In most Godunov-type methods, these two steps can be treated independently, so that many different schemes can in principle be built from the same numerical framework. Because astrophysical simulations often test out the limits of what is feasible with the computational resources available, it is essential to find the scheme that produces the numerical solution with the desired accuracy at the lowest computational cost. However, establishing the best combination of numerical options in a Godunov-type method to be used for simulating a complex hydrodynamic problem is a nontrivial task. In fact, formally more accurate schemes do not always outperform simpler and more diffusive methods, especially if sharp gradients are present in the flow. For this work, we used our fully compressible Seven-League Hydro (SLH) code to test the accuracy of six reconstruction methods and three approximate Riemann solvers on two- and three-dimensional (2D and 3D) problems involving subsonic flows only. We considered Mach numbers in the range from 10 −3 to 10 −1 , which are characteristic of many stellar and geophysical flows. In particular, we considered a well-posed, 2D, Kelvin–Helmholtz instability problem and a 3D turbulent convection zone that excites internal gravity waves in an overlying stable layer. Although the different combinations of numerical methods converge to the same solution with increasing grid resolution for most of the quantities analyzed here, we find that (i) there is a spread of almost four orders of magnitude in computational cost per fixed accuracy between the methods tested in this study, with the most performant method being a combination of a low-dissipation Riemann solver and a sextic reconstruction scheme; (ii) the low-dissipation solver always outperforms conventional Riemann solvers on a fixed grid when the reconstruction scheme is kept the same; (iii) in simulations of turbulent flows, increasing the order of spatial reconstruction reduces the characteristic dissipation length scale achieved on a given grid even if the overall scheme is only second order accurate; (iv) reconstruction methods based on slope-limiting techniques tend to generate artificial, high-frequency acoustic waves during the evolution of the flow; and (v) unlimited reconstruction methods introduce oscillations in the thermal stratification near the convective boundary, where the entropy gradient is steep.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2018

Hanford Direct Feed Low Activity Waste Real Time Monitoring Program - 18336

Effective operation of the Low-Activity Waste (LAW) Facility at Hanford will rely on information provided from monitoring and control of chemical process streams to maintain safety and environmental compliance, product quality, and operational efficiency. The LAW Facility has been designed as a contact-maintained facility and it was recognized that establishing a real time, in-line monitoring program could have substantial benefits to the U.S. Department of Energy, Office of River Protection in the long-term, which include significant time savings, increased processing efficiency and effectiveness, reducing worker exposure to radiation and chemical hazards, reducing secondary wastes, and a better understanding of the flowsheet to support direct-feed LAW (DFLAW). The Assistant Manager/Federal Project Director for the Waste Treatment and Immobilization Plant (WTP) Project chartered a multidisciplinary integrated technical team comprised of federal, contractor, and national laboratory staff to develop a phased program to support this initiative. A three-phase approach was adopted: - Phase 1: Requirements and Opportunities Analysis for Sampling Reduction; - Phase 2: Applications and Benefits Determination; - Phase 3: Qualification and Demonstration. The focus of Phase 1 is to identify the drivers behind any requirements for sampling and any opportunities to benefit from a real-time monitoring program. The effort identified 18 sample points and approximately 2,600 potential samples to be collected annually with analytical methods to be performed approximately 18,000 times annually. Based on Savannah River National Laboratory experience and discussions with WTP Analytical Laboratory personnel, these sample analyses will generate approximately 5,000 L of liquid secondary waste and approximately 1,300 m{sup 3} of solid secondary waste each year. Additional solid and liquid secondary wastes will be generated from sample collection. A preliminary evaluation indicates that employing real-time, in-line monitoring, mass balances, and periodic sampling could significantly reduce the number of samples collected, analytical methods performed, and secondary waste generated. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2015

Approximate spin projected spin-unrestricted density functional theory method: Application to diradical character dependences of second hyperpolarizabilities

We develop a novel method for the calculation and the analysis of the one-electron reduced densities in open-shell molecular systems using the natural orbitals and approximate spin projected occupation numbers obtained from broken symmetry (BS), i.e., spin-unrestricted (U), density functional theory (DFT) calculations. The performance of this approximate spin projection (ASP) scheme is examined for the diradical character dependence of the second hyperpolarizability (γ) using several exchange-correlation functionals, i.e., hybrid and long-range corrected UDFT schemes. It is found that the ASP-LC-UBLYP method with a range separating parameter μ = 0.47 reproduces semi-quantitatively the strongly-correlated [UCCSD(T)] result for p-quinodimethane, i.e., the γ variation as a function of the diradical character.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Optimal control of coupled quantum systems based on the first-order Magnus expansion: Application to multiple dipole-dipole-coupled molecular rotors

This paper presents a method for performing approximate optimal control simulations for quantum systems with multiple coupled degrees of freedom. In this work, the time evolution is simulated using the first-order Magnus expansion in the interaction picture, where the couplings between different degrees of freedom are treated as the perturbation. A numerical implementation procedure is presented that leverages upon pairwise couplings and the separability of the zeroth-order time evolution operator to achieve a reduced computational cost, which is analyzed with respect to the number of degrees of freedom. The formulation is compatible with gradient-free methods to optimize the control field, and a stochastic hill climbing algorithm is adopted for this purpose. As illustrations, optimal control simulations are performed for systems of two and three dipole-dipole-coupled molecular rotors under the influence of a control field. For the two-rotor system, the field is optimized to achieve either orientation or entanglement objectives. For the three-rotor system, the field is optimized either to orient all three rotors in the same direction or to orient one rotor in a particular direction while the other two rotors point in the opposite direction.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Superfluidity of heated Fermi systems in the static fluctuation approximation

Superfluidity properties of heated finite Fermi systems are studied in the static fluctuation approximation, which is an original method. This method relies on a single and controlled approximation, which permits taking correctly into account quasiparticle correlations and thereby going beyond the independent-quasiparticle model. A closed self-consistent set of equations for calculating correlation functions at finite temperature is obtained for a finite Fermi system described by the Bardeen–Cooper–Schrieffer Hamiltonian. An equation for the energy gap is found with allowance for fluctuation effects. It is shown that the phase transition to the supefluid state is smeared upon the inclusion of fluctuations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2018

Compact video content representation for video coding using low multi-linear tensor rank approximation with dynamic core tensor order

Tensor is a multi-way representation of an entity that is widely used in many applications of mathematics and physics. The wide range of tensor algebra operations attract the researchers of graphical and vision field to identify unique methods for various applications such as segmentation, compression, indexing and so on. In this paper, low multi-linear rank approximation of a tensor is used for decomposition so as to perform compression on a video that is represented as a 4D tensor. Thus, the encoder has blocks for (1) multilinear rank approximation method so as to aid decomposition, (2) sparsity removal of residual data to reduce the required memory storage to a small level, (3) quantization on the sparse less residual data and (4) LZ77 dictionary coding for the video. The decoder uses a tensor reconstruction block along with residual error correction block that reduces loss/error in the reconstructed video. The size of core tensor is an important factor in rank approximation. It is identified at run time depending on the video contents. This size is determined adaptively using Tikhonov’s regularization method. The best value of core tensor size is identified with the corner of L-curve which preserves the video contents from heavy loss/error. Experimental results of the proposed work on comparison with H.264/AVC compression method indicate that the proposed method achieves up to 10% improvement in compression ratio with the least amount of loss and a maximum signal to noise ratio of 0.14. The proposed system gives better compression ratio than H.265 for videos with more number of frames without compromising quality.

97 MATHEMATICS AND COMPUTING↗