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DOE OSTI2025

Data-Efficient Strategies for Probabilistic Voltage Envelopes under Network Contingencies

This work presents an efficient data-driven method to construct probabilistic voltage envelopes (PVE) using power flow learning in grids with network contingencies. First, a network-aware Gaussian process (GP) termed Vertex-Degree Kernel (VDK-GP), developed in prior work, is used to estimate voltage–power functions for a few network configurations. The paper introduces a novel multi-task vertex degree kernel (MT-VDK) that amalgamates the learned VDK-GPs to determine power flows for unseen networks, with a significant reduction in the computational complexity and hyperparameter requirements compared to alternate approaches. Simulations on the IEEE 30-Bus network demonstrate the retention and transfer of power flow knowledge in both N-1 and N-2 contingency scenarios. The MT-VDK-GP approach achieves over 50 % reduction in mean prediction error for novel N-1 contingency network configurations in low training data regimes (50–250 samples) over VDK-GP. Additionally, MT-VDK-GP outperforms a hyper-parameter based transfer learning approach in over 75 % of N-2 contingency network structures, even without historical N-2 outage data. Furthermore, the proposed method demonstrates the ability to achieve PVEs using sixteen times fewer power flow solutions compared to Monte-Carlo sampling-based methods.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2019

Bandgap prediction by deep learning in configurationally hybridized graphene and boron nitride

Abstract It is well-known that the atomic-scale and nano-scale configuration of dopants can play a crucial role in determining the electronic properties of materials. However, predicting such effects is challenging due to the large range of atomic configurations that are possible. Here, we present a case study of how deep learning algorithms can enable bandgap prediction in hybridized boron–nitrogen graphene with arbitrary supercell configurations. A material descriptor that enables correlation of structure and bandgap was developed for convolutional neural networks. Bandgaps calculated by ab initio calculations, and corresponding structures, were used as training datasets. The trained networks were then used to predict bandgaps of systems with various configurations. For 4 × 4 and 5 × 5 supercells they accurately predict bandgaps, with a R 2 of >90% and root-mean-square error of ~0.1 eV. The transfer learning was performed by leveraging data generated from small supercells to improve the prediction accuracy for 6 × 6 supercells. This work will pave a route to future investigation of configurationally hybridized graphene and other 2D materials. Moreover, given the ubiquitous existence of configurations in materials, this work may stimulate interest in applying deep learning algorithms for the configurational design of materials across different length scales.

Dong, Yuan↗

DOE OSTI2021

Deep potential generation scheme and simulation protocol for the Li 10 GeP 2 S 12 -type superionic conductors

We report solid-state electrolyte materials with superior lithium ionic conductivities are vital to the next-generation Li-ion batteries. Molecular dynamics could provide atomic scale information to understand the diffusion process of Li-ion in these superionic conductor materials. Here, we implement the deep potential generator to set up an efficient protocol to automatically generate interatomic potentials for Li 10 GeP 2 S 12 -type solid-state electrolyte materials (Li 10 GeP 2 S 12 , Li 10 SiP 2 S 12 , and Li 10 SnP 2 S 12 ). The reliability and accuracy of the fast interatomic potentials are validated. With the potentials, we extend the simulation of the diffusion process to a wide temperature range (300 K–1000 K) and systems with large size (~1000 atoms). Important technical aspects such as the statistical error and size effect are carefully investigated, and benchmark tests including the effect of density functional, thermal expansion, and configurational disorder are performed. The computed data that consider these factors agree well with the experimental results, and we find that the three structures show different behaviors with respect to configurational disorder. Our work paves the way for further research on computation screening of solid-state electrolyte materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Equilibrium Core Model for Micro Pebble Bed Reactors Using OpenMC

Estimating the equilibrium state for pebble bed reactors (PBRs) presents complex challenges as it requires simultaneous consideration of changes in the pebbles’ movement as well as their fuel compositions. Whereas traditional approaches use multigroup diffusion codes for neutronics calculations of PBRs’ equilibrium state, the double-heterogeneity of PBRs complicates neutron cross-section generation. Continuous-energy Monte Carlo (MC) methods are better suited for detailed PBR analysis because of their natural handling of double-heterogeneity, but they demand substantially more computational resources. Here, this study introduces a novel method for efficiently estimating the equilibrium state in small and micro PBRs with reduced computational cost. The method is anticipated to accelerate the processes of core design and performing parametric studies for utilizing advanced fuel and structural materials. The HTR-10 reactor design was used for validating the method’s predictions and evaluating its computational efficiency. When compared to reference calculation values from the literature, criticality (k-effective) was predicted to be approximately within the margin of error of the MC transport calculation, average core power density (in megawatts per cubic meter) was predicted within 2.5% relative error, and maximum thermal flux (10 13 n/cm 2 .s −1 ) was predicted within 1.8% relative error. The calculated inventory of fission products and fuel composition in the equilibrium core were within 15% and 16.6%, respectively, when compared to reported values from the literature. The difference is attributed to variance in the considered values of the core temperature, which was found to significantly affect the depletion analyses.

Equilibrium core↗

DOE OSTI2019

Evaluation of Wind Speed Retrieval from Continuous-Wave Lidar Measurements of a Wind Turbine Wake Using Virtual Lidar Techniques

Wind lidar technology is being extensively used in utility-scale wind turbine wake measurements because of its capabilities to capture the dominant structures of interest in the near-wake region. However, wind lidar devices provide only line-of-sight (LOS) measurements, and retrieval of horizontal wind speed from the LOS measurements of a single lidar in the wind turbine wake could introduce errors due to the assumptions used in the retrieval process. With that in mind, the goals of this paper are to estimate the errors associated with the retrieval processes and provide guidelines for best practices. To achieve these goals, virtual lidar samples are obtained with large-eddy simulations (LES) by sampling the flow field with a model of the Technical University of Denmark (DTU) SpinnerLidar. LES is chosen to simulate the neutral and unstable atmospheric boundary layer (ABL), a benchmark case of the International Energy Agency Wind Technology Collaboration Programme (IEA Wind TCP) Task 31. The precursor ABL simulation is validated with the reference data provided by the IEA Wind Task 31 benchmark case. The data from the precursor simulation is used to drive a simulation of a wind turbine submerged in the ABL. A weighting function is applied to the LES data to mimic the real DTU SpinnerLidar measurements. In the end, the virtual lidar data are processed and compared with the original LES data to estimate the errors. Results show that lidar captures mean ABL profile without any noticeable error, whereas turbulence intensity is underpredicted ~15% at hub height for the neutral case. Volume averaging by the lidar technology has a significant effect in the shear layer of a wind turbine wake.

17 WIND ENERGY↗

DOE OSTI2025

Spatio-temporal Fourier Transformer for Long-term Dynamics Prediction (StFT) v1.0

We propose a novel machine learning model spatio-temporal Fourier transformer (StFT) to emulate long-term dynamics of multi-scale and multi-physics systems. Our method StFT overcomes the limitations of rapid error accumulation, particularly in long-term forecasting of systems characterized by complex and coupled dynamics. StFT achieves outstanding accuracy and computational efficiency by effectively capturing multi-scale interactions, and quantify the uncertainties inherent in the predictions. Our model leverages a structured hierarchy of StFT blocks, and explicitly captures dynamics across both macro- and micro- spatial scales. Evaluations conducted on three benchmark datasets (plasma, fluid, and atmospheric dynamics) demonstrate the advantages of our approach over state-of-the-art ML methods.

Bai, Zhe [Lawrence Berkeley National Laboratory (L↗

DOE OSTI2023

Codimension-2 defects and higher symmetries in (3+1)D topological phases

(3+1)D topological phases of matter can host a broad class of non-trivial topological defects of codimension-1, 2, and 3, of which the well-known point charges and flux loops are special cases. The complete algebraic structure of these defects defines a higher category, and can be viewed as an emergent higher symmetry. This plays a crucial role both in the classification of phases of matter and the possible fault-tolerant logical operations in topological quantum error-correcting codes. In this paper, we study several examples of such higher codimension defects from distinct perspectives. We mainly study a class of invertible codimension-2 topological defects, which we refer to as twist strings. We provide a number of general constructions for twist strings, in terms of gauging lower dimensional invertible phases, layer constructions, and condensation defects. We study some special examples in the context of \mathbb{Z}_2 ℤ 2 gauge theory with fermionic charges, in \mathbb{Z}_2 \times \mathbb{Z}_2 ℤ 2 × ℤ 2 gauge theory with bosonic charges, and also in non-Abelian discrete gauge theories based on dihedral ( D_n D n ) and alternating ( A_6 A 6 ) groups. The intersection between twist strings and Abelian flux loops sources Abelian point charges, which defines an H^4 H 4 cohomology class that characterizes part of an underlying 3-group symmetry of the topological order. The equations involving background gauge fields for the 3-group symmetry have been explicitly written down for various cases. We also study examples of twist strings interacting with non-Abelian flux loops (defining part of a non-invertible higher symmetry), examples of non-invertible codimension-2 defects, and examples of the interplay of codimension-2 defects with codimension-1 defects. We also find an example of geometric, not fully topological, twist strings in (3+1)D A_6 A 6 gauge theory.

Barkeshli, Maissam↗

DOE OSTI2022

DMC-ICE13 : Ambient and high pressure polymorphs of ice from diffusion Monte Carlo and density functional theory

Ice is one of the most important and interesting molecular crystals, exhibiting a rich and evolving phase diagram. Recent discoveries mean that there are now 20 distinct polymorphs; a structural diversity that arises from a delicate interplay of hydrogen bonding and van der Waals dispersion forces. This wealth of structures provides a stern test of electronic structure theories, with Density Functional Theory (DFT) often not able to accurately characterize the relative energies of the various ice polymorphs. Thanks to recent advances that enable the accurate and efficient treatment of molecular crystals with Diffusion Monte Carlo (DMC), we present here the DMC-ICE13 dataset; a dataset of lattice energies of 13 ice polymorphs. This dataset encompasses the full structural complexity found in the ambient and high-pressure molecular ice polymorphs, and when experimental reference energies are available, our DMC results deliver sub-chemical accuracy. Using this dataset, we then perform an extensive benchmark of a broad range of DFT functionals. Of the functionals considered, revPBE-D3 and RSCAN reproduce reference absolute lattice energies with the smallest error, while optB86b-vdW and SCAN+rVV10 have the best performance on the relative lattice energies. Our results suggest that a single functional achieving reliable performance for all phases is still missing, and that care is needed in the selection of the most appropriate functional for the desired application. The insights obtained here may also be relevant to liquid water and other hydrogen-bonded and dispersion-bonded molecular crystals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Review of analytical studies on seismic fluid-structure interaction of base-supported cylindrical tanks

Analytical solutions for seismic fluid-structure interaction (FSI) of tanks are used by analysts and engineers for a number of purposes, including preliminary sizing, risk assessment, and verification of numerical models. Analytical solutions for seismic FSI of tanks were first developed in the 1930s and have been extended and/or modified in the following nine decades to accommodate different seismic inputs and boundary conditions. This report reviews published analytical solutions for rigid and flexible, base-supported, cylindrical tanks subjected to unidirectional horizontal motion of a small amplitude. The studies parsed the fluid-structure (FSI) response into an impulsive and a convective component, and addressed frequencies of lateral motions of the tank (i.e., impulsive frequencies), hydrodynamic pressures, frequencies of waves (i.e., convective frequencies), wave heights, and reactions at the base. The solutions were categorized into exact and approximate solutions based on the methodologies used. Herein, FSI responses are calculated and compared for a range of tank dimensions using the analytical solutions from the different studies. The responses presented here are normalized to be unitless, and can be used for tanks with different dimensions and mechanical properties, and subjected to different input motions. A sample steel water tank is analyzed using the normalized solutions for two earthquake ground motions with different frequency contents. Ignoring tank flexibility may significantly underestimate seismic responses of the tank and its contained fluid. The approximate solutions, which have been widely used for decades, may not be sufficiently accurate in the modern era. Calculation errors in the reviewed studies are identified and corrected, and differences are quantified for the sample tank.

42 ENGINEERING↗

DOE OSTI2024

Training models using forces computed by stochastic electronic structure methods

Abstract Quantum Monte Carlo (QMC) can play a very important role in generating accurate data needed for constructing potential energy surfaces. We argue that QMC has advantages in terms of a smaller systematic bias and an ability to cover phase space more completely. The stochastic noise can ease the training of the machine learning model. We discuss how stochastic errors affect the generation of effective models by analyzing the errors within a linear least squares procedure, finding that there is an advantage to having many relatively imprecise data points for constructing models. We then analyze the effect of noise on a model of many-body silicon finding that noise in some situations improves the resulting model. We then study the effect of QMC noise on two machine learning models of dense hydrogen used in a recent study of its phase diagram. The noise enables us to estimate the errors in the model. We conclude with a discussion of future research problems.

Ceperley, David M. (ORCID:0000000150826271)↗

DOE OSTI2023

Domain-aware Control-oriented Neural Models for Autonomous Underwater Vehicles

Conventional physics-based modeling is a time-consuming bottleneck in control design for complex nonlinear systems like autonomous underwater vehicles (AUVs). In contrast, purely data-driven models, require a large number of observations and lack operational guarantees for safety-critical systems. Data-driven models leveraging available partially characterized dynamics have potential to provide reliable systems models in a typical data-limited scenario for high value complex systems, thereby avoiding months of expensive expert modeling time. In this work we explore this middle-ground between expert-modeled and pure data-driven modeling. We present control-oriented parametric models with varying levels of domain-awareness that exploit known system structure and prior physics knowledge to create constrained deep neural dynamical system models. We employ universal differential equations to construct data-driven blackbox and graybox representations of the AUV dynamics. In addition, we explore a hybrid formulation that explicitly models the residual error related to imperfect graybox models. We compare the prediction performance of the learned models for different distributions of initial conditions and control inputs to assess their suitability for control.

Shaw Cortez, Wenceslao E.↗

DOE OSTI2023

Single-Point Extrapolation to the Complete Basis Set Limit through Deep Learning

Machine learning (ML) offers an attractive method for making predictions about molecular systems while circumventing the need to run expensive electronic structure calculations. Once trained on ab initio data, the promise of ML is to deliver accurate predictions of molecular properties that were previously computationally infeasible. In this work, we develop and train a graph neural network model to correct the basis set incompleteness error (BSIE) between a small and large basis set at the RHF and B3LYP levels of theory. Our results show that, when compared to fitting to the total potential, an ML model fitted to correct the BSIE is better at generalizing to systems not seen during training. We test this ability by training on single molecules while evaluating on molecular complexes. We also show that ensemble models yield better behaved potentials in situations where the training data is insufficient. However, even when only fitting to the BSIE, acceptable performance is only achieved when the training data sufficiently resemble the systems one wants to make predictions on. As a result, the test error of the final model trained to predict the difference between the cc-pVDZ and cc-pV5Z potential is 0.184 kcal/mol for the B3LYP density functional, and the ensemble model accurately reproduces the large basis set interaction energy curves on the S66x8 dataset.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2017

How Well Can the M06 Suite of Functionals Describe the Electron Densities of Ne, Ne 6+ , and Ne 8+ ?

The development of better approximations to the exact exchange-correlation functional is essential to the accuracy of density functionals. A recent study indicated that functionals with few parameters offer more accurate electron densities than recently developed many-parameter functionals for light closed-shell atomic systems. In this study, we calculated electron densities, their gradients, and Laplacians of Ne, Ne 6+ , and Ne 8+ using 19 electronic structure methods, and we compared them to the CCSD reference results. Two basis sets, namely, aug-cc-pωCV5Z and aug-cc-pV5Z, are utilized in the calculations. We found that the choice of basis set has a significant impact on the errors and rankings of some of the selected methods. The errors of electron densities, their gradients, and Laplacians calculated with the aug-cc-pV5Z basis set are substantially reduced, especially for Minnesota density functionals, as compared to the results using the aug-cc-pωCV5Z basis set (a larger basis set utilized in earlier work (Medvedev et al. Science2017, 355, 49–52)). The rankings of the M06 suite of functionals among the 19 methods are greatly improved with the aug-cc-pV5Z basis set. Furthermore, the performances of the HSE06, BMK, MN12-L, and MN12-SX functionals are also improved with the aug-cc-pV5Z basis set. The M06 suite of functionals is capable of providing accurate electron densities, gradients, and Laplacians using the aug-cc-pV5Z basis set, and thus it is suitable for a wide range of applications in chemistry and physics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

In crystallo observation of three metal ion promoted DNA polymerase misincorporation

Error-free replication of DNA is essential for life. Despite the proofreading capability of several polymerases, intrinsic polymerase fidelity is in general much higher than what base-pairing energies can provide. Although researchers have investigated this long-standing question with kinetics, structural determination, and computational simulations, the structural factors that dictate polymerase fidelity are not fully resolved. Time-resolved crystallography has elucidated correct nucleotide incorporation and established a three-metal-ion-dependent catalytic mechanism for polymerases. Using X-ray time-resolved crystallography, we visualize the complete DNA misincorporation process catalyzed by DNA polymerase η. The resulting molecular snapshots suggest primer 3´-OH alignment mediated by A-site metal ion binding is the key step in substrate discrimination. Moreover, we observe that C-site metal ion binding preceded the nucleotidyl transfer reaction and demonstrate that the C-site metal ion is strictly required for misincorporation. Our results highlight the essential but separate roles of the three metal ions in DNA synthesis.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2017

Communication: Recovering the flat-plane condition in electronic structure theory at semi-local DFT cost

The flat-plane condition is the union of two exact constraints in electronic structure theory: (i) energetic piecewise linearity with fractional electron removal or addition and (ii) invariant energetics with change in electron spin in a half filled orbital. Semi-local density functional theory (DFT) fails to recover the flat plane, exhibiting convex fractional charge errors (FCE) and concave fractional spin errors (FSE) that are related to delocalization and static correlation errors. We previously showed that DFT+U eliminates FCE but now demonstrate that, like other widely employed corrections (i.e., Hartree-Fock exchange), it worsens FSE. To find an alternative strategy, we examine the shape of semi-local DFT deviations from the exact flat plane and we find this shape to be remarkably consistent across ions and molecules. We introduce the judiciously modified DFT (jmDFT) approach, wherein corrections are constructed from few-parameter, low-order functional forms that fit the shape of semi-local DFT errors. Here we select one such physically intuitive form and incorporate it self-consistently to correct semi-local DFT. We demonstrate on model systems that jmDFT represents the first easy-to-implement, no-overhead approach to recovering the flat plane from semi-local DFT.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2021

Cohesion and excitations of diamond-structure silicon by quantum Monte Carlo: Benchmarks and control of systematic biases

We have carried out quantum Monte Carlo (QMC) calculations of silicon crystal focusing on the accuracy and systematic biases that affect the electronic structure characteristics. The results show that 64 and 216 atom supercells provide an excellent consistency for extrapolated energies per atom in the thermodynamic limit for ground, excited, and ionized states. We have calculated the ground state cohesion energy with both systematic and statistical errors below ≈ 0.05 eV. The ground state exhibits a fixed-node error of only 1.3(2)% of the correlation energy, suggesting an unusually high accuracy of the corresponding single-reference trial wave function. We obtain a very good agreement between optical and quasiparticle gaps that affirms the marginal impact of excitonic effects. Our most accurate results for band gaps differ from the experiments by about 0.2 eV. This difference is assigned to a combination of residual finite-size and fixed-node errors. In conclusion, we have estimated the crystal Fermi level referenced to vacuum that enabled us to calculate the edges of valence and conduction bands in agreement with experiments.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2017

First-principles equation of state and shock compression predictions of warm dense hydrocarbons

We use path integral Monte Carlo and density functional molecular dynamics to construct a coherent set of equations of state (EOS) for a series of hydrocarbon materials with various C:H ratios (2:1, 1:1, 2:3, 1:2, and 1:4) over the range of 0.07–22.4gcm –3 and 6.7 × 10 3 – 1.29 × 10 8 K. The shock Hugoniot curve derived for each material displays a single compression maximum corresponding to K-shell ionization. For C:H = 1:1, the compression maximum occurs at 4.7-fold of the initial density and we show radiation effects significantly increase the shock compression ratio above 2 Gbar, surpassing relativistic effects. The single-peaked structure of the Hugoniot curves contrasts with previous work on higher-Z plasmas, which exhibit a two-peak structure corresponding to both K- and L-shell ionization. Analysis of the electronic density of states reveals that the change in Hugoniot structure is due to merging of the L-shell eigenstates in carbon, while they remain distinct for higher-Z elements. Lastly, we show that the isobaric-isothermal linear mixing rule for carbon and hydrogen EOS is a reasonable approximation with errors better than 1% for stellar-core conditions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Onset of Scrambling as a Dynamical Transition in Tunable-Range Quantum Circuits

In a fast-scrambling many-body quantum system, information is spread and entanglement is built up on a time scale that grows logarithmically with the system size. This is of fundamental interest in understanding the dynamics of many-body systems, as well as in efficiently producing entangled resource states and error-correcting codes. In this work, we identify a dynamical transition marking the onset of scrambling in quantum circuits with different levels of long-range connectivity. In particular, we show that as a function of the interaction range for circuits of different structures, the tripartite mutual information exhibits a scaling collapse around a critical point between two clearly defined regimes of different dynamical behavior. We study this transition analytically in a related long-range Brownian-circuit model and show how the transition can be mapped onto the statistical mechanics of a long-range Ising model in a particular region of parameter space. This mapping predicts mean-field critical exponents v=–1/(1 + s c ), which are consistent with the critical exponents extracted from Clifford-circuit numerics. In addition to systems with conventional power-law interactions, we identify the same phenomenon in deterministic sparse circuits that can be realized in experiments with neutral-atom arrays.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗