Error In Total Energy Research Articles

Modeling Many-Body Interactions in Water with Gaussian Process Regression.

We report a first-principles water dimer potential that captures many-body interactions through Gaussian process regression (GPR). Modeling is upgraded from previous work by using a custom kernel function implemented through the KeOps library, allowing for much larger GPR models to be constructed and interfaced with the next-generation machine learning force field FFLUX. A new synthetic water dimer data set, called WD24, is used for model training. The resulting models can predict 90% of dimer geometries within chemical accuracy for a test set and in a simulation. The curvature of the potential energy surface is captured by the models, and a successful geometry optimization is completed with a total energy error of just 2.6 kJ mol-1, from a starting structure where water molecules are separated by nearly 4.3 Å. Dimeric modeling of a flexible, noncrystalline system with FFLUX is shown for the first time.

Distributed battery dispatch for uncertainty mitigation in renewable microgrids

In this work, we propose and analyze battery-level approaches to mitigate system welfare losses due to total energy forecast errors in energy-constrained microgrids. We present a receding horizon approach, develop a data-based method and heuristic approaches that leverage the receding horizon environment, and then analyze performance on a system based on real data. We find that the data-based method offers modest mitigation of the effects of total energy error, and a heuristic approach based on l2 regularization offers similar mitigation. We also find that the choice of load utility model affects mitigation strategies’ profitability. Finally, we show how these methods can be used in a distributed framework.

Predicting electrical power consumption of end milling using a virtual machining energy toolkit (V_MET)

Understanding electrical energy consumption of machines and processes is of increasing importance to (i) minimise costs and environmental impact of production activities and (ii) provide an additional information stream to inform condition monitoring systems (i.e. digital twins) about a machine’s status and health. The research outlined in this paper develops a Virtual Machining Energy Toolkit (V_MET) to predict the electrical power consumption of a Computer Numeric Control (CNC) milling machine cutting a particular part program from preparatory codes (i.e. G code). In this way the evaluation of the energy impact of manufacturing part programs prior to implementation and real-time monitoring of the process can become a routine activity at part of a total manufacturing system optimisation. The novelty of this work lies in the inclusion of a virtual CNC process model to determine cutting geometry (i.e. width and depth of cut) to enable the prediction of relatively complex part program geometry.V_MET consists of three components: (i) the NC interpreter to extract key parameters (e.g. spindle speed, feed rate, tool path) from G-code instructions, (ii) a virtual CNC process model to determine instantaneous cutting geometry (i.e. width and depth of cut) and the material removal from the resulting machining by simulating the motion of the tool path to predict the interaction between the tool tip and workpiece and (iii) an energy model to predict the electrical power consumption for a given set of conditions, developed using regression analysis of data collected under real manufacturing conditions.Validation of V_MET has been conducted by physical machining of different product features to evaluate the validity over a range of different cutting parameters, NC operations (i.e. linear, clockwise interpolations) and repasses over previously cut regions. Overall good accuracy has been observed for the predicted energy requirements as a function of the cutting regimes, with 4.3% error in total energy and Mean Average Percentage Error (MAPE) of 5.6% when compared with measurements taken during physical cutting trials.

Study on development of EV charging services coupled with power system conditions using IoT technology

Deployment of electric vehicles (EVs) has been accelerated in many countries. However, for further deployment of EVs and their contribution to electrical power systems, various new services need to be implemented related to EVs and their charging, called “Place of Use” (PoU) services. The combined menu of the charging services has been proposed which bundles EV charging fees with home electricity bills. Settlement will be needed for such combined menu. This paper proposes the combined menu of EV charging with settlement of electricity. Technical feasibility of the settlement has been tested by EV charging testbed with the IoT-HUB technology. IoT-HUB is the virtual infrastructure which interconnects various connected devices and application by using “drivers” for each device. This paper also proposes a forecast method of EV charging demand for the settlement after the charging starts. The proposed method has reduced the forecast error of total charged energy compared to the simple method, but some of the forecast error has remained because of the variability of the charging time at the final step of state of charge.

Accurate non-covalent interaction energies on noisy intermediate-scale quantum computers via second-order symmetry-adapted perturbation theory.

The calculation of non-covalent interaction energies on noisy intermediate-scale quantum (NISQ) computers appears to be challenging with straightforward application of existing quantum algorithms. For example, the use of the standard supermolecular method with the variational quantum eigensolver (VQE) would require extremely precise resolution of the total energies of the fragments to provide for accurate subtraction to the interaction energy. Here we present a symmetry-adapted perturbation theory (SAPT) method that may provide interaction energies with high quantum resource efficiency. Of particular note, we present a quantum extended random-phase approximation (ERPA) treatment of the SAPT second-order induction and dispersion terms, including exchange counterparts. Together with previous work on first-order terms (Chem. Sci., 2022, 13, 3094), this provides a recipe for complete SAPT(VQE) interaction energies up to second order, which is a well established truncation. The SAPT interaction energy terms are computed as first-level observables with no subtraction of monomer energies invoked, and the only quantum observations needed are the VQE one- and two-particle density matrices. We find empirically that SAPT(VQE) can provide accurate interaction energies even with coarsely optimized, low circuit depth wavefunctions from a quantum computer, simulated through ideal statevectors. The errors of the total interaction energy are orders of magnitude lower than the corresponding VQE total energy errors of the monomer wavefunctions. In addition, we present heme-nitrosyl model complexes as a system class for near term quantum computing simulations. They are strongly correlated, biologically relevant and difficult to simulate with classical quantum chemical methods. This is illustrated with density functional theory (DFT) as the predicted interaction energies exhibit a strong sensitivity with respect to the choice of functional. Thus, this work paves the way to obtain accurate interaction energies on a NISQ-era quantum computer with few quantum resources. It is the first step in alleviating one of the major challenges in quantum chemistry, where in-depth knowledge of both the method and system is required a priori to reliably generate accurate interaction energies.

Reconciling and Improving Formulations for Thermodynamics and Conservation Principles in Earth System Models (ESMs)

AbstractThis paper provides a comprehensive derivation of the total energy equations for the atmospheric components of Earth System Models (ESMs). The assumptions and approximations made in this derivation are motivated and discussed. In particular, it is emphasized that closing the energy budget is conceptually challenging and hard to achieve in practice without resorting to ad hoc fixers. As a concrete example, the energy budget terms are diagnosed in a realistic climate simulation using a global atmosphere model. The largest total energy errors in this example are spurious dynamical core energy dissipation, thermodynamic inconsistencies (e.g., coupling parameterizations with the host model) and missing processes/terms associated with falling precipitation and evaporation (e.g., enthalpy flux between components). The latter two errors are not, in general, reduced by increasing horizontal resolution. They are due to incomplete thermodynamic and dynamic formulations. Future research directions are proposed to reconcile and improve thermodynamics formulations and conservation principles.

Improving Results by Improving Densities: Density-Corrected Density Functional Theory.

Density functional theory (DFT) calculations have become widespread in both chemistry and materials, because they usually provide useful accuracy at much lower computational cost than wavefunction-based methods. All practical DFT calculations require an approximation to the unknown exchange-correlation energy, which is then used self-consistently in the Kohn-Sham scheme to produce an approximate energy from an approximate density. Density-corrected DFT is simply the study of the relative contributions to the total energy error. In the vast majority of DFT calculations, the error due to the approximate density is negligible. But with certain classes of functionals applied to certain classes of problems, the density error is sufficiently large as to contribute to the energy noticeably, and its removal leads to much better results. These problems include reaction barriers, torsional barriers involving π-conjugation, halogen bonds, radicals and anions, most stretched bonds, etc. In all such cases, use of a more accurate density significantly improves performance, and often the simple expedient of using the Hartree-Fock density is enough. This Perspective explains what DC-DFT is, where it is likely to improve results, and how DC-DFT can produce more accurate functionals. We also outline challenges and prospects for the field.

Performance-Based Compositive Passive Control Analysis of Multi-Tower Building with Chassis: Optimization of Kelvin-Voigt Dampers

The compositive passive control (CPC) method of “interlayer seismic isolation “plus “shock absorption between adjacent towers” was applied to a multi-tower building (MTB) with a large podium. The interaction between adjacent towers was used to reduce the structural response under seismic action. Based on the Clough–Penzien spectral seismic model, the extended state equation of random response of MTB was derived with the minimum total energy of structural vibration as the optimization control objective. By comparing the seismic scheme and interlayer seismic isolation scheme, the relationship between the control parameters of the connecting control device and the random response of the structure was discussed and analyzed, and the control effect of the composite passive control system under different control schemes was also studied from the perspective of seismic response time history and vibration cumulative energy time history. Through numerical analysis, it was proved that the damping coefficient of the Kelvin-Voigt model has a great influence on the mean square error of total vibration energy while the stiffness coefficient has a poor sensitivity to it. Under the optimization control objective, the connection control device was better arranged at the top of the structure. The control effect can reach 84.64% under the condition of random ground motion as input. The CPC method maintains the advantages of the interlayer seismic isolation scheme and reduces the defect of the response amplification caused by the interlayer isolation, which provides a reference for the follow-up study of the CPC method of MTB.

A novel method for state of energy estimation of lithium-ion batteries using particle filter and extended Kalman filter

State-of-energy (SOE) estimation of lithium-ion batteries (LIBs) is one of the core functions of battery management systems in electric vehicles. In this study, to improve the accuracy and robustness of SOE estimation, a novel SOE method using a particle filter (PF) and extended Kalman filter (EKF) insensitive to uncertain total available energy loss and ambient temperatures is proposed. First, a battery model is established, and then the model parameters at different temperatures in the whole SOE range are identified. Second, the PF algorithm is chosen to estimate the SOE, whereas the EKF algorithm is used to update the total available energy online. Finally, the effectiveness of the proposed SOE method is verified by experiments under dynamic conditions. The experimental results indicate that the maximum error of the SOE estimation with the proposed PF–EKF algorithm is less than 3% under the dynamic stress test at 0, 25, and 40 ℃. Moreover, even if there are large initial SOE and total available energy errors, the SOE estimation by the proposed algorithm would be able to quickly converge to it is reference trajectory with high accuracy and robustness.

Conformational Analysis of [60]PCBM from DFT Simulations of Electronic Energies, Bond Strain and the 13C NMR Spectrum: Input Geometry Determination and Ester Bond Rotation Dynamics

With the aim of determining the best input geometry for DFT calculations of [60]PCBM, the geometry of 24 chemically possible [60]PCBM conformers were optimised and their electronic energies and average bond strains were determined. A DFT analysis of the relevant dihedral angles provided insights into the dynamical behaviour of the ester group through sterically restricted bond rotations. In addition, the 13C NMR spectra of the six better performing conformers were simulated and compared with an experiment. There is a close correlation between average bond strain, total electronic energy and mean absolute error of the simulated 13C NMR spectra of the ester carbons. The best overall candidate conformer for the input geometry had the C61-C4, C4-C3 and C3-C2 single bonds of the alkyl chain in syn, anti and anti arrangements, respectively, and had the C2-C1 and C1-O single bonds of the ester in syn and anti arrangements, respectively. This contrasts strikingly with most representations of PCBM in the literature, which depict all relevant bonds in anti arrangements.

An End-to-End Machine Learning based Unified Architecture for Non-Intrusive Load Monitoring

Non-Intrusive Load Monitoring (NILM) or load disaggregation aims to analyze power consumption by decomposing the energy measured at the aggregate level into constituent appliances level. The conventional load disaggregation framework consists of signal processing and machine learning-based pipelined architectures, respectively for explicit feature extraction and decision making. Manual feature selection in such load disaggregation frameworks leads to biased decisions that eventually reduce system performance. This paper presents an efficient End-to-End (E2E) approach-based unified architecture using Gated Recurrent Units (GRU) for NILM. The proposed approach eliminates explicit feature engineering and has a unified classification and prediction model for appliance power. This eventually reduces the computational cost and enhances response time. The performance of the proposed system is compared with conventional algorithms' with the use of recall, precision, accuracy, F1 score, the relative error in total energy and Mean Absolute Error (MAE). These evaluation metrics are calculated on the power consumption of top priority appliances of Reference Energy Disaggregation Dataset (REDD). The proposed architecture with an overall accuracy of 91.2 and MAE of 25.23 outperforms conventional methods for all electrical appliances. It has been showcased through a series of experiments that feature extraction and event-based approaches for NILM can readily be replaced with E2E deep learning techniques allowing simpler and cost-efficient implementation pathways.

Improved One-Shot Total Energies from the Linearized GW Density Matrix.

The linearized GW density matrix (γGW) is an efficient method to improve the static portion of the self-energy compared to that of ordinary perturbative GW while keeping the single-shot simplicity of the calculation. Previous work has shown that γGW gives an improved Fock operator and total energy components that approach the self-consistent GW quality. Here, we test γGW for dimer dissociation for the first time by studying N2, LiH, and Be2. We also calculate a set of self-consistent GW results in identical basis sets for a direct and consistent comparison. γGW approaches self-consistent GW total energies for a starting point based on a high amount of exact exchange. We also compare the accuracy of different total energy functionals, which differ when evaluated with a non-self-consistent density or density matrix. While the errors in total energies among different functionals and starting points are small, the individual energy components show noticeable errors when compared to reference data. The energy component errors of γGW are smaller than functionals of the density and we suggest that the linearized GW density matrix is a route to improving total energy evaluations in the adiabatic connection framework.

Low-Complexity Scaling Methodsfor DCT-II Approximations

This paper introduces a collection of scaling methods for generating $2N$-point DCT-II approximations based on $N$-point low-complexity transformations. Such scaling is based on the Hou recursive matrix factorization of the exact $2N$-point DCT-II matrix. Encompassing the widely employed Jridi-Alfalou-Meher scaling method, the proposed techniques are shown to produce DCT-II approximations that outperform the transforms resulting from the JAM scaling method according to total error energy and mean squared error. Orthogonality conditions are derived and an extensive error analysis based on statistical simulation demonstrates the good performance of the introduced scaling methods. A hardware implementation is also provided demonstrating the competitiveness of the proposed methods when compared to the JAM scaling method.

Noise-Boosted Backpropagation Learning of Feedforward Threshold Neural Networks for Function Approximation

Aiming to ensure the feasibility of the backpropagation training of feedforward threshold neural networks, each hidden unit layer is designed to be composed of a sufficiently large number of hard-limiting activation functions that are excited by mutually independent external noise components and the weighted inputs simultaneously. The application of noise to nondifferentiable activation functions enables a proper definition of the gradients, and the injected noise is treated as a network parameter that can be adaptively updated by a stochastic gradient descent learning rule. This noise-boosted backpropagation learning process is found to converge to a nonzero optimized level of noise, indicating that the injected noise is beneficial both for the learning and for the ensuing retrieval phase. For minimizing the total error energy of the function approximation in the designed threshold neural network, the proposed noise-boosted backpropagation learning method is proven to be better than directly injecting noise into network inputs or weight coefficients. The Lipschitz continuous property of the noise-smoothed activation function in the hidden unit layer is demonstrated to guarantee the local convergence of the learning process. Beyond the Gaussian injected noise, the optimal noise type is also numerically solved for training the designed threshold neural network. Test experiments for approximating nonlinear functions and real-world datasets verify the feasibility of this noise-boosted backpropagation algorithm in the threshold neural network. These results not only extend the analysis of the beneficial effects of noise similar to stochastic resonance and exploited here to the universal approximation capabilities of threshold neural networks, but also allow backpropagation training of neural networks with a much wider family of nondifferentiable activation functions.

Coupling Constants, High Spin, and Broken Symmetry States of Organic Radicals: an Assessment of the Molecules-in-Molecules Fragmentation-Based Method.

We extend the application of our multilayer molecules-in-molecules (MIM) fragmentation-based method to the study of open-shell systems, particularly organic radicals. A test set of organic mono-, di- and polyradicals with a wide range in size, containing up to 360 atoms, was investigated. Total energies computed with MIM using density functional theory (DFT) were compared with full, unfragmented energies to assess the performance of MIM and to develop a systematic protocol for the treatment of large radical systems. More specifically, a two-layer (MIM2) model with a fragmentation scheme along the backbone involving covalently bonded dimers, trimers, or tetramers was considered, with DFT at a smaller basis set serving as the low level of theory. The MIM method was evaluated on the high-spin state and several possible broken-symmetry (BS) states for di- and polyradicals. When relevant spin-spin interactions were considered, the errors in total energies were less than 1 kcal mol-1. In addition, the applicability of MIM2 was extended to predict the intersite magnetic exchange coupling constants (J), which were compared with reference values. Further, since the energy levels derived from Hamiltonian diagonalization are physically more meaningful, the calculated J values estimated from the BS-DFT methodology were used to obtain the lower spin state energies of the polyradicals. The difference in calculated total energies of the lower spin state between full and MIM2 lie within 1 kcal mol-1 in the majority of these cases. Our rigorous, quantum chemical study demonstrates that MIM can be successfully applied to the study of large organic radicals reliably and accurately within the framework of BS-DFT.

A Total Energy Error Analysis of Dynamical Cores and Physics‐Dynamics Coupling in the Community Atmosphere Model (CAM)

AbstractA closed total energy (TE) budget is of utmost importance in coupled climate system modeling; in particular, the dynamical core or physics‐dynamics coupling should ideally not lead to spurious TE sources/sinks. To assess this in a global climate model, a detailed analysis of the spurious sources/sinks of TE in National Center for Atmospheric Research's Community Atmosphere Model (CAM) is given. This includes spurious sources/sinks associated with the parameterization suite, the dynamical core, TE definition discrepancies, and physics‐dynamics coupling. The latter leads to a detailed discussion of the pros and cons of various physics‐dynamics coupling methods commonly used in climate/weather modeling.

Enhanced approximate discrete cosine transforms for image compression and multimedia applications

Energy compaction property of the Discrete Cosine Transform (DCT) leads its usage in image and video compression applications. Nowadays power consumption is the major problem in modern multimedia applications. Hence circuit complexity and area reduction are the optimal ways for the power consumption reduction. In this paper the proposed DCTs represented as approximate DCT-Case I, II and III are constructed with basis elements Ci = {0, ±1, ±2}. Proposed Approximate DCT Case I and II have been derived from 16 × 16 point DCT rounding off operation and odd row sign replacement. Approximate DCT Case III has been derived based on (Potluri et al. in Meas Sci Technol 23(11):1–15, 2012). Peak signal to noise ratio (PSNR), total error energy and computational complexity wise approximate DCT Case III improved when compared to (Potluri et al. in Meas Sci Technol 23(11):1–15, 2012). Proposed approximate DCT Case I, II and III 8 × 8 matrixes satisfy the orthogonal property through a quantization process.

Automatic Generation of Auxiliary Basis Sets.

A procedure was developed to automatically generate auxiliary basis sets (ABSs) for use with the resolution of the identity (RI) approximation, starting from a given orbital basis set (OBS). The goal is to provide an accurate and universal solution for cases where no optimized ABSs are available. In this context, "universal" is understood as the ability of the ABS to be used for Coulomb, exchange, and correlation energy fitting. The generation scheme (denoted AutoAux) works by spanning the product space of the OBS using an even-tempered expansion for each atom in the system. The performance of AutoAux in conjunction with different OBSs [def2-SVP, def2-TZVP, def2-QZVPP, and cc-pwCVnZ (n = D, T, Q, 5)] has been evaluated for elements from H to Rn and compared to existing predefined ABSs. Due to the requirements of simplicity and universality, the generated ABSs are larger than the optimized ones but lead to similar errors in MP2 total energies (on the order of 10-5 to 10-4 Eh/atom).

Influence of the choice of projection manifolds in the CASPT2 implementation

ABSTRACTThe Complete Active Space Second-Order Perturbation Theory (CASPT2) is well-established as a high-accuracy electronic structure method. It was originally implemented in the early 1990s to an efficient computer code in the molcas program suite, and this implementation has been extensively used as a standard tool. Here, we report a comparison of it against two independent computer-aided implementations of the CASPT2 method, revealing that the CASPT2 energies provided by the original code of molcas (version 8 or earlier) are inconsistent with the predictions of the lately developed computer-aided implementations. It is shown that this error is associated with the projections of the first-order equation onto the fully internally contracted multireference bases which are partially inconsistent between the left- and right-hand sides. The degree of the errors is assessed by performing illustrative CASPT2 calculations. The errors in total CASPT2 energies are demonstrated to be negligible relative to chemical accuracy in many cases, while there is a difficult case where they may substantially alter chemical description. The incorporation of the consistent projections into molcas has been carried out, which is available in the version 8 sp1.

The application of cholesky decomposition in valence bond calculation.

The Cholesky decomposition (CD) technique, used to approximate the two-electron repulsion integrals (ERIs), is applied to the valence bond self-consistent field (VBSCF) method. Test calculations on ethylene, C2 n H2 n +2 , and C2 n H4 n -2 molecules (n = 1-7) show that the performance of the VBSCF method is much improved using the CD technique, and thus, the integral transformation from basis functions to VB orbitals is no longer the bottleneck in VBSCF calculations. The errors of the CD-based ERIs and of the total energy are controlled by the CD threshold, for which a value of 10(-6) ensures to control the total energy error within 10(-6) Hartree. © 2016 Wiley Periodicals, Inc.