Relative Energy Error Research Articles

Near Real-Time Low Frequency Load Disaggregation

Device-level power consumption information can lead to considerable energy savings. Smart meters are being adopted in several countries, but they are only capable of measuring the total power consumption. NonIntrusive Load Monitoring (NILM) aims to infer the power consumption of individual electrical loads by analyzing the aggregate power signal taken from a single-point measurement. Most existing NILM solutions are offline methods that do not allow the end-user to get real-time feedback on his energy consumption. In this paper, we present a near real-time NILM solution based on multi-label classification and multi-output regression. We use the multi-label classifier to predict the state of each load and use the multi-output regressor to estimate the disaggregated active power consumptions. We test our method using a publically available dataset of real power measurements. Performance results show that the proposed near real-time method can accurately estimate the energy consumption of the targeted loads with an average relative energy error of 1.55 %.

Improvement of the Force Field for β-d-Glucose with Machine Learning.

While the construction of a dependable force field for performing classical molecular dynamics (MD) simulation is crucial for elucidating the structure and function of biomolecular systems, the attempts to do this for glycans are relatively sparse compared to those for proteins and nucleic acids. Currently, the use of GLYCAM06 force field is the most popular, but there have been a number of concerns about its accuracy in the systematic description of structural changes. In the present work, we focus on the improvement of the GLYCAM06 force field for -d-glucose, a simple and the most abundant monosaccharide molecule, with the aid of machine learning techniques implemented with the TensorFlow library. Following the pre-sampling over a wide range of configuration space generated by MD simulation, the atomic charge and dihedral angle parameters in the GLYCAM06 force field were re-optimized to accurately reproduce the relative energies of -d-glucose obtained by the density functional theory (DFT) calculations according to the structural changes. The validation for the newly proposed force-field parameters was then carried out by verifying that the relative energy errors compared to the DFT value were significantly reduced and that some inconsistencies with experimental (e.g., NMR) results observed in the GLYCAM06 force field were resolved relevantly.

Wind Speed and Power Density Analyses Based on Mixture Weibull and Maximum Entropy Distributions

Wind resource is important part of the utilization of renewable energy. To effectively estimate the wind energy potential for a given area, a variety of probability density functions (pdf) have been available in literature. In this paper, the bimodal mixture Weibull function (WW) and the probability function derived with maximum entropy principle (MEP) will be used and com- pared with the conventional Weibull function. Wind speed data measured at three wind farms experiencing different climatic environments in Taiwan are selected as sample data to test their performance. Judgment criterions include four kinds of statistical errors, i.e. the max error in Kolmogorov-Smirnov test, Chi-square error, root mean square error and relative error of wind potential energy. The results show that the proposed WW and MEP pdfs describe wind charac- terizations better than the conventional Weibull pdf, irrespective of wind speed and wind power density data, particularly for a location where wind regime presents two humps on it. For wind speed distributions, the WW pdf describes best according to the Kolmogorov-Smirnov test; while for wind power density, the MEP pdf outperforms the others.

Scalable Electron Correlation Methods. 8. Explicitly Correlated Open-Shell Coupled-Cluster with Pair Natural Orbitals PNO-RCCSD(T)-F12 and PNO-UCCSD(T)-F12.

We present explicitly correlated open-shell pair natural orbital local coupled-cluster methods, PNO-RCCSD(T)-F12 and PNO-UCCSD(T)-F12. The methods are extensions of our previously reported PNO-R/UCCSD methods (J. Chem. Theory Comput., 2020, 16, 3135-3151, https://pubs.acs.org/doi/10.1021/acs.jctc.0c00192) with additions of explicit correlation and perturbative triples corrections. The explicit correlation treatment follows the spin-orbital CCSD-F12b theory using Ansatz 3*A, which is found to yield comparable or better basis set convergence than the more rigorous Ansatz 3C in computed ionization potentials and reaction energies using double- to quaduple-ζ basis sets. The perturbative triples correction is adapted from the spin-orbital (T) theory to use triples natural orbitals (TNOs). To address the coupling due to off-diagonal Fock matrix elements, the local triples amplitudes are iteratively solved using small domains of TNOs, and a semicanonical (T0) domain correction with larger domains is applied to reduce the domain errors. The performance of the methods is demonstrated through benchmark calculations on ionization potentials, radical stabilization energies, reaction energies of fragmentations and rearrangements in radical cations, and spin-state energy differences of iron complexes. For a few test sets where canonical calculations are feasible, PNO-RCCSD(T)-F12 results agree with the canonical ones to within 0.4 kcal mol-1, and this maximum error is reduced to below 0.2 kcal mol-1 when large local domains are used. For larger systems, results using different thresholds for the local approximations are compared to demonstrate that 1 kcal mol-1 level of accuracy can be achieved using our default settings. For a couple of difficult cases, it is demonstrated that the errors from individual approximations are only a fraction of 1 kcal mol-1, and the overall accuracy of the method does not rely on error compensations. In contrast to canonical calculations, the use of spin-orbitals does not lead to a significant increase of computational time and memory usage in the most expensive steps of PNO-R/UCCSD(T)-F12 calculations. The only exception is the iterative solution of the (T) amplitudes, which can be avoided without significant errors by using a perturbative treatment of the off-diagonal coupling, known as (T1) approximation. For most systems, even the semicanonical approximation (T0) leads only to small errors in relative energies. Our program is well parallelized and capable of computing accurate correlation energies for molecules with 100-200 atoms using augmented triple-ζ basis sets in less than a day of elapsed time on a small computer cluster.

Modeling the dynamic behavior of laminated steels using a Fourier-based approach

A new magneto-dynamic model is proposed to approximate the dynamic hysteresis effect in laminated steels considering the static hysteresis, eddy-current field, and excess field. An accurate congruency-based hysteresis model is used to predict the static hysteresis field. The eddy-current is determined from the 1D diffusion equation and the well-known Bertotti empirical equation is utilized to model the excess-field effect. The dynamic lamination model obtained from coupling three field components is solved using a Fourier-based approach. In this approach, the flux density across the lamination thickness is approximated by a cosine-based Fourier series. The coefficients of the Fourier series are determined by solving a system of nonlinear equations through an iterative procedure. Owing to the employed congruency-based static hysteresis model, the proposed magneto-dynamic model offers high accuracy for arbitrary magnetization regimes. To validate the model accuracy, the model results are compared with sinusoidal and multi-harmonic measurements. The comparison shows that the proposed model predicts the dynamic hysteresis phenomenon in laminated steels with a relative energy error of less than 7%.

Efficient evaluation of exact exchange for periodic systems via concentric atomic density fitting.

The evaluation of the exact [Hartree-Fock (HF)] exchange operator is a crucial ingredient for the accurate description of the electronic structure in periodic systems through ab initio and hybrid density functional approaches. An efficient formulation of periodic HF exchange in a linear combination of atomic orbitals representation presented here is based on the concentric atomic density fitting approximation, a domain-free local density fitting approach in which the product of two atomic orbitals is approximated using a linear combination of fitting basis functions centered at the same nuclei as the AOs in that product. A significant reduction in the computational cost of exact exchange is demonstrated relative to the conventional approach due to avoiding the need to evaluate four-center two-electron integrals, with sub-millihartree/atom errors in absolute HF energies and good cancellation of fitting errors in relative energies. The novel aspects of the evaluation of the Coulomb contribution to the Fock operator, such as the use of real two-center multipole expansions and spheropole-compensated unit cell densities, are also described.

Trotter errors in digital adiabatic quantum simulation of quantum ℤ2 lattice gauge theory

Trotter decomposition is the basis of the digital quantum simulation. Asymmetric and symmetric decompositions are used in our GPU demonstration of the digital adiabatic quantum simulations of (2[Formula: see text]+[Formula: see text]1)-dimensional quantum [Formula: see text] lattice gauge theory. The actual errors in Trotter decompositions are investigated as functions of the coupling parameter and the number of Trotter substeps in each step of the variation of coupling parameter. The relative error of energy is shown to be equal to the Trotter error usually defined in terms of the evolution operators. They are much smaller than the order-of-magnitude estimation. The error in the symmetric decomposition is much smaller than that in the asymmetric decomposition. The features of the Trotter errors obtained here are useful in the experimental implementation of digital quantum simulation and its numerical demonstration.

Elastic SH- and Love-wave Full-Waveform Inversion for shallow shear wave velocity with a preconditioned technique

In contrast to the Rayleigh waves, the system of SH- and Love-wave Full-Waveform Inversion (FWI) is simpler (Only S-wave velocity and density is inverted). However, the gradient is not scaled with the increasing depth in gradient-based FWI. The main reasons for the phenomenon are the limited frequency band of the wavelet, non-uniform coverage of the excitation-receiving points and the double scattering. The illumination can be enhanced by adding a preconditioned operator to the inversion. To compensate the illumination, we presented a preconditioned technique abiding by the theory of inverse scattering in SH- and Love-wave FWI. The synthetic tests demonstrate that the preconditioned technique can expedite the convergence rate and enhance the illumination intensity to the deeper medium compared with the conventional gradient-based FWI. The results also indicate that the preconditioned conjugate gradient (PCG) method has the best parameter reconstruction performance among the local optimization algorithms. Subsequently, we adopt the PCG method to inverse the field data acquired in the village of Čachtice, northwestern Slovakia. In addition, a multiscale strategy is employed and the Wiechert-Herglotz method is followed to estimate the initial S-wave velocity model in inversion. Eventually, this paper illustrates the credibility of the inverted result from the perspectives of waveform fitting, common-offset profile, signal similarity, relative error of channel energy and normalized misfit function values. This study primarily seeks to delineate the foundations of historical buildings under the survey line. According to the range of S-wave velocity, we assert that there are no foundation remains in the subsurface.

Comparison of Preisach and Congruency-Based Static Hysteresis Models Applied to Non-Oriented Steels

Two hysteresis models are investigated for modeling static hysteresis phenomenon in nonoriented magnetic steels. First, the static Preisach model is studied, and two types of experimental data, i.e., first-order reversal curves (FORCs) and concentric hysteresis loops, are employed to identify the weight function. Due to negative values in the obtained experimental weight functions, the resulting Preisach models show nonphysical behavior. To eliminate this nonphysical behavior, an optimization procedure is applied to remove these negative values. The nonphysical behavior is resolved in the modified Preisach model; however, the model still has poor accuracy for asymmetric loops. Alternatively, a new congruency-based static hysteresis model is proposed. In this model, third- or higher-order reversal curves are approximated using measured FORCs and second-order reversal curves (SORCs) by means of a congruency regularity. According to this regularity, any third- or higher-order reversal curve is congruent to SORCs with the same reversal point. A 3-D piecewise interpolation function is employed to interpolate the measured major loop, FORCs, and SORCs. The proposed model results are compared with quasi-static measurements. The comparison reveals that the model is capable of approximating the magnetization curves for the measurements containing complex-shaped $B$ waveforms with a relative energy error of less than 4%.

Analysis of the performance of numerical integration methods for the tracking of ultra-high energy cosmic rays

We analyzed the performance of several numerical integration methods in the ultra-relativistic regime. The integration methods include the fourth order Runge-Kutta, Boris, Vay, and a new method (called New Euler). For a proton traveling in a circular trajectory through a uniform perpendicular magnetic field, we have calculated the relative percentage error of Larmor radius of the particle's trajectory, relative efficiency between the methods, and relative percentage error of the particle's energy as a function of CPU time. In these calculations, we have investigated the influence of the following parameters: particle's energy, magnetic field strength, and the integration step. On calculating the Larmor radius, the four methods examined have all presented great precision. Among all studied cases, the most efficient method was the Boris method, which completes within a given CPU time more than twice cycles (complete circles, or periods of revolution) given by the Runge-Kutta one. The least efficient was the New Euler method (0.08 cycles), followed by Vay one (0.21 cycles). On the calculation of the particle's energy, New Euler method has exhibited the best properties, with the maximum relative percentage error of the particle's energy of roughly 10−13% remaining constant during the entire simulation. Except in the cases with the biggest simulation step, when for the Runge-Kutta method the particle's energy diverges asymptotically from its initial value, and with the smallest simulation step and lowest energy, when the Boris method has presented less precision than the Runge-Kutta one. The Runge-Kutta and Boris methods have presented approximately the same precision, with the maximum relative percentage error of ∼10−11%. The Vay method has presented the worst precision, with the particle's energy diverging asymptotically for all studied cases, with the relative percentage error of the particle's energy reaching approximately 10−8%, in ten seconds of CPU time.

On determining the unknown band-parameter and truncated sinc series coefficients from a time sampled band-limited function

In this paper, we address the problem of either approximating or estimating the band-parameter B^ and a coefficient vector C^=[c^−(m−1)/2,c^−(m−1)/2+1,…,c^(m−1)/2]T of specified odd dimension m so that X(t)≈∑k=−(m−1)/2(m−1)/2c^ksinc(2B^t−k), in which the band-limited real-valued sampled function X(t)∈C2(−∞,∞) with true band-parameter B† ∈ [r1,r2]⊂R + , the positive reals.We formulate the problem as the minimization of the over-determined nonlinear least squares function: f:R×Rm→R+, f∈C2([r1,r2]×Rm), f(B,C)=(1/2)∥H(B)C−X∥22, H(B) an n × m matrix of sinc function values at an odd number, n, of equally spaced sampling points such that n > m + 1.We show that this nonlinear least squares problem in m + 1 variables reduces to minimizing a function of a single real variable, f*(B), f* ∈ C2([r1,r2]). In both noise-free and Gaussian error-perturbed data cases, an FFT is first applied to a vector X of equally spaced time samples. The FFT is followed by a simple threshold search on the transform spectrum. This search yields an accurate first guess of B^=argminB∈[r1,r2](f*(B)) that initiates a Gauss–Newton iterative algorithm.Monte Carlo performance statistics for one hundred sample problems in both the approximation and estimation cases are tabulated. These statistics are the mean, standard deviation, the median of the relative band error, the root mean square coefficient error, the relative energy error, an approximate Cramer–Rao error bound in B^ as an estimate of B†, and the mean and standard deviation of the approximate Cramer–Rao normalized error of the estimate in the estimation cases.

On contractivity preserving 4- to 7-step predictor-corrector HBO series for ODEs

The contractivity-preserving 2- and 3-step predictor-corrector series methods for ODEs (T. Nguyen-Ba, A. Alzahrani, T. Giordano and R. Vaillancourt, On contractivity-preserving 2- and 3-step predictor-corrector series for ODEs, J. Mod. Methods Numer. Math. 8:1-2 (2017), pp. 17--39. doi:10.20454/jmmnm.2017.1130) are expanded into new optimal, contractivity-preserving (CP), d-derivative, k-step, predictor-corrector, Hermite- Birkhoff--Obrechkoff series methods, denoted by HBO(d,k,p), k=4,5,6,7, with nonnegative coefficients for solving nonstiff first-order initial value problems \(y'=f(t,y)\), \(y(t_0)=y_0\). The main reason for considering this class of formulae is to obtain a set of methods which have larger regions of stability and generally higher upper bound \(p_u\) of order \(p\) of HBO(d,k,p) for a given d. Their stability regions have generally a good shape and grow generally with decreasing \(p-d\). A selected CP HBO method: 6-derivative 4-step HBO of order 14, denoted by HBO(6,4,14) which has maximum order 14 based on the CP conditions compares satisfactorily with Adams--Cowell of order 13 in PECE mode, denoted by AC(13), in solving standard N-body problems over an interval of 1000 periods on the basis of the relative error of energy as a function of the CPU time. HBO(6,4,14) also compares well with AC(13) in solving standard N-body problems on the basis of the growth of relative positional error, relative energy error and 10000 periods of integration. The coefficients of HBO(6,4,14) are listed in the appendix.

Numerical Solutions for the Orbital Motion of the Solar System over the Past 100 Myr: Limits and New Results*

Abstract I report results from accurate numerical integrations of solar system orbits over the past 100 Myr with the integrator package HNBody. The simulations used different integrator algorithms, step sizes, and initial conditions, and included effects from general relativity, different models of the Moon, the Sun’s quadrupole moment, and up to 16 asteroids. I also probed the potential effect of a hypothetical Planet 9, using one set of possible orbital elements. The most expensive integration (Bulirsch–Stoer) required 4 months of wall-clock time with a maximum relative energy error . The difference in Earth’s eccentricity ( ) was used to track the difference between two solutions, considered to diverge at time τ when max irreversibly crossed ∼10% of mean ( ). The results indicate that finding a unique orbital solution is limited by initial conditions from current ephemerides and asteroid perturbations to ∼54 Myr. Bizarrely, the 4-month Bulirsch–Stoer integration and a symplectic integration that required only 5 hr of wall-clock time (12-day time step, with the Moon as a simple quadrupole perturbation), agree to ∼63 Myr. Internally, such symplectic integrations are remarkably consistent even for large time steps, suggesting that the relationship between time step and τ is not a robust indicator of the absolute accuracy of symplectic integrations. The effect of a hypothetical Planet 9 on becomes discernible at ∼65 Myr. Using τ as a criterion, the current state-of-the-art solutions all differ from previously published results beyond ∼50 Myr. I also conducted an eigenmode analysis, which provides some insight into the chaotic nature of the inner solar system. The current study provides new orbital solutions for applications in geological studies.

On contractivity-preserving 2- and 3-step predictor-corrector series for ODEs

New optimal, contractivity-preserving (CP), \(d\)-derivative, 2- and 3-step, predictor-corrector, Hermite-Birkhoff-Obrechkoff series methods, denoted by \(HBO(d,k,p)\), \(k=2,3\), with nonnegative coefficients are constructed for solving nonstiff first-order initial value problems \(y'=f(t,y)\), \(y(t_0)=y_0\). The upper bounds \(p_u\) of order \(p\) of \(HBO(d,k,p)\), \(k=2,3\) methods are approximately 1.4 and 1.6 times the number of derivatives \(d\), respectively. Their stability regions have generally a good shape and grow with decreasing \(p-d\). Two selected CP HBO methods: 9-derivative 2-step HBO of order 13, denoted by HBO(9,2,13), which has maximum order 13 based on the CP conditions, and 8-derivative 3-step HBO of order 14, denoted by HBO(8,3,14), compare well with Adams-Cowell of order 13 in PECE mode, denoted by AC(13), in solving standard N-body problems over an interval of 1000 periods on the basis of the relative error of energy as a function of the CPU time. They also compare well with AC(13) in solving standard N-body problems on the basis of the growth of relative error of energy and 10000 periods of integration. The coefficients of selected HBO methods are listed in the appendix.

Communication: Multipole approximations of distant pair energies in local correlation methods with pair natural orbitals.

The accuracy of multipole approximations for distant pair energies in local second-order Møller-Plesset perturbation theory (LMP2) as introduced by Hetzer et al. [Chem. Phys. Lett. 290, 143 (1998)] is investigated for three chemical reactions involving molecules with up to 92 atoms. Various iterative and non-iterative approaches are compared, using different energy thresholds for distant pair selection. It is demonstrated that the simple non-iterative dipole-dipole approximation, which has been used in several recent pair natural orbitals (PNO)-LMP2 and PNO-LCCSD (local coupled-cluster with singles and doubles) methods, may underestimate the distant pair energies by up to 50% and can lead to significant errors in relative energies, unless very tight thresholds are used. The accuracy can be much improved by including higher multipole orders and by optimizing the distant pair amplitudes iteratively along with all other amplitudes. A new approach is presented in which very small special PNO domains for distant pairs are used in the iterative approach. This reduces the number of distant pair amplitudes by 3 orders of magnitude and keeps the additional computational effort for the iterative optimization of distant pair amplitudes minimal.

Influence of Mass Ratio on Forward and Reverse Ballistic Impact Equivalence: Experiments, Simulations, and Mechanism Analysis

Reverse ballistic impact tests are widely used for studying dynamic responses because they provide more comprehensive and quantitative projectile/rod response results than forward impact tests. To examine equivalent forward and reverse conditions, a series of 8-cm length oxygen-free copper rods with varying length–diameter ratios was used in forward and reverse ballistic Taylor impact experiments with velocities and strain ratios of 104–215 m/s and 1.25 × 103–2.5 × 103 s-1, respectively. Digital image correlation (DIC) and traditional optical measurements were used to determine instantaneous responses at the μs level. Based on DIC, transient structural deformation, and plastic wave propagation, the forward and reverse length difference at similar velocities ranges from 2 to 6.95 %. Rules governing deformation from the perspective of energy, along with rules for changes in energy and plastic wave propagation were determined. The relative deformation energy error was below 5 % for target projectile mass ratios above 20.

Investigating Trends in Streamflow and Precipitation in Huangfuchuan Basin with Wavelet Analysis and the Mann-Kendall Test

This study aims to investigate trends in streamflow and precipitation in the period 1954–2010 in a semiarid region of the Yellow River watershed, Huangfuchuan basin, China. The combination of the wavelet transform and different Mann-Kendall (MK) tests were employed to figure out the basic trends structure in streamflow and precipitation and what time scales are affecting the observed trends. The comparative analysis with five MK test methods showed that the modified MK tests with full serial correlation structure performed better when significant autocorrelations exhibited for more than one lag. Three criteria were used to determine the optimal smooth mother wavelet, the decomposition level and the extension mode used in the discrete wavelet transform (DWT) procedure. The first criteria referred to the relative error of the wavelet approximated component and the original series. The second one was the relative error of MK Z-values of approximation component and the original series. Additionally, a new criterion (Er), based on the relative error of energy between the approximate component and the original series, was proposed in this study, with better performance than the previous two criteria. Further, a new powerful index, the energy of the hydrological time series, was proposed to verify the dominant periodic components for the observed trends. The analysis indicated that all monthly, seasonal and annual streamflow showed significant decreasing trends, while no significant trends were found in precipitation. Results from the DWT and MK tests revealed that the main factors influencing the trends in the monthly and seasonal series in Huangfuchuan watershed are intra-annual cycles, while the leading factors affecting the trends in the annual series are decadal events. Different driving factors (e.g., seasonal cycles, solar activities, etc.) related to the periodicities identified in these data types resulted in this discrepancy.

Performance analysis of parallel gravitational N-body codes on large GPU clusters

We compare the performance of two very different parallel gravitational N-body codes for astrophysical simulations on large Graphics Processing Unit (GPU) clusters, both of which are pioneers in their own fields as well as on certain mutual scales - NBODY6++ and Bonsai. We carry out benchmarks of the two codes by analyzing their performance, accuracy and efficiency through the modeling of structure decomposition and timing measurements. We find that both codes are heavily optimized to leverage the computational potential of GPUs as their performance has approached half of the maximum single precision performance of the underlying GPU cards. With such performance we predict that a speed-up of 200 – 300 can be achieved when up to 1k processors and GPUs are employed simultaneously. We discuss the quantitative information about comparisons of the two codes, finding that in the same cases Bonsai adopts larger time steps as well as larger relative energy errors than NBODY6++, typically ranging from 10 – 50 times larger, depending on the chosen parameters of the codes. Although the two codes are built for different astrophysical applications, in specified conditions they may overlap in performance at certain physical scales, thus allowing the user to choose either one by fine-tuning parameters accordingly.

Contractivity-preserving explicit multistep Hermite–Obrechkoff series differential equation solvers

New optimal, contractivity-preserving (CP), explicit, d-derivative, k-step Hermite–Obrechkoff series methods of order p up to $$p=20$$ , denoted by CP HO(d, k, p), with nonnegative coefficients are constructed. These methods are used to solve nonstiff first-order initial value problems $$y'=f(t,y)$$ , $$y(t_0)=y_0$$ . The upper bound $$p_u$$ of order p of HO(d, k, p) can reach, approximately, as high as 2.4 times the number of derivatives d. The stability regions of HO(d, k, p) have generally a good shape and grow with decreasing $$p-d$$ . We, first, note that three selected CP HO methods: 4-derivative 7-step HO of order 13, denoted by HO(4, 7, 13), 5-derivative 6-step HO of order 13, denoted by HO(5, 6, 13), and 9-derivative 2-step HO of order 13, denoted by CMDAHO(13) compare favorably with Adams–Cowell of order 13, denoted by AC(13), in solving standard N-body problems over an interval of 1000 periods on the basis of the relative error of energy as a function of the CPU time. Next, the three HO methods compare positively with AC(13) in solving standard N-body problems on the basis of the growth of relative positional error and relative energy error over 10, 000 periods of integration. Finally, these three methods compare also well with P-stable methods of Cash and Franco et al. on some quasi periodic, second-order linear and nonlinear problems. The coefficients of selected HO methods are listed in the appendix.

Ff14SB: Improving the Accuracy of Protein Side Chain and Backbone Parameters from ff99SB.

Molecular mechanics is powerful for its speed in atomistic simulations, but an accurate force field is required. The Amber ff99SB force field improved protein secondary structure balance and dynamics from earlier force fields like ff99, but weaknesses in side chain rotamer and backbone secondary structure preferences have been identified. Here, we performed a complete refit of all amino acid side chain dihedral parameters, which had been carried over from ff94. The training set of conformations included multidimensional dihedral scans designed to improve transferability of the parameters. Improvement in all amino acids was obtained as compared to ff99SB. Parameters were also generated for alternate protonation states of ionizable side chains. Average errors in relative energies of pairs of conformations were under 1.0 kcal/mol as compared to QM, reduced 35% from ff99SB. We also took the opportunity to make empirical adjustments to the protein backbone dihedral parameters as compared to ff99SB. Multiple small adjustments of φ and ψ parameters were tested against NMR scalar coupling data and secondary structure content for short peptides. The best results were obtained from a physically motivated adjustment to the φ rotational profile that compensates for lack of ff99SB QM training data in the β-ppII transition region. Together, these backbone and side chain modifications (hereafter called ff14SB) not only better reproduced their benchmarks, but also improved secondary structure content in small peptides and reproduction of NMR χ1 scalar coupling measurements for proteins in solution. We also discuss the Amber ff12SB parameter set, a preliminary version of ff14SB that includes most of its improvements.