Kernel Ridge Regression Research Articles

Toward Robust Car-Following Dynamics Modeling via Blackbox Models: Methodology, Analysis, and Recommendations

The selection of the target variable is critical for the performance of classical car-following (CF) models. There is a vast body of literature on which target variable is optimal for classical CF models, but there is no study that evaluates the selection of optimal target variables for black-box models prevalent in machine learning, which are increasingly being used to model CF behavior. This paper evaluates different target variables, for example acceleration, velocity, and headway, for three models: Gaussian processes (GP), kernel ridge regression, and long short-term memory (LSTM). These models have different objective functions and work in different vector spaces, for example, GP work in function space, and LSTM in parameter space. Furthermore, this paper evaluates the efficacy of black box and classical CF models across datasets, including diverse traffic scenarios and human versus automated control. Finally, this paper evaluates the coupling of design choices across selection of model type, target variable during model calibration, and dataset characteristics. The experiments show that the optimal target variable recommendations for black-box models differ from classical CF models, depending on the objective function and the vector space. Statistical analysis indicates that selection of models couples greatly with target variables, while recommended target variables do not depend on the datasets used during model calibration. These results provide a path toward more robust CF models, potentially resulting in more accurate and generalizable capacity and/or traffic flow estimates for roadways, even as driving behaviors change with the introduction of new types of automation.

A short trajectory is all you need: A transformer-based model for long-time dissipative quantum dynamics.

In this Communication, we demonstrate that a deep artificial neural network based on a transformer architecture with self-attention layers can predict the long-time population dynamics of a quantum system coupled to a dissipative environment provided that the short-time population dynamics of the system is known. The transformer neural network model developed in this work predicts the long-time dynamics of spin-boson model efficiently and very accurately across different regimes, from weak system-bath coupling to strong coupling non-Markovian regimes. Our model is more accurate than classical forecasting models, such as recurrent neural networks, and is comparable to the state-of-the-art models for simulating the dynamics of quantum dissipative systems based on kernel ridge regression.

Machine learning approaches for modelling of molecular polarizability in gold nanoclusters

The polarizability of molecules describes their response to an external electric field. It quantifies the ability of a system to form an induced dipole moment when subjected to an electric field. In this work, we investigated isotropic polarizability and anisotropy in the polarizability of gold nanoclusters using various machine-learning algorithms. We utilized high-order invariant descriptors based on spherical harmonics, integrated with machine-learning models like artificial neural network, Gaussian process regression, and kernel ridge regression. Our results demonstrate the efficacy of machine-learning in accurately predicting the polarizability of gold nanoclusters. We find that ANN-based model performs better than the other models.

A Bond-Based Machine Learning Model for Molecular Polarizabilities and A Priori Raman Spectra.

The use of machine learning (ML) algorithms in molecular simulations has become commonplace in recent years. There now exists, for instance, a multitude of ML force field algorithms that have enabled simulations approaching ab initio level accuracy at time scales and system sizes that significantly exceed what is otherwise possible with traditional methods. Far fewer algorithms exist for predicting rotationally equivariant, tensorial properties such as the electric polarizability. Here, we introduce a kernel ridge regression algorithm for machine learning of the polarizability tensor. This algorithm is based on the bond polarizability model and allows prediction of the tensor components at the cost similar to that of scalar quantities. We subsequently show the utility of this algorithm by simulating gas phase Raman spectra of biphenyl and malonaldehyde using classical molecular dynamics simulations of these systems performed with the recently developed MACE-OFF23 potential. The calculated spectra are shown to agree very well with the experiments and thus confirm the expediency of our algorithm as well as the accuracy of the used force field. More generally, this work demonstrates the potential of physics-informed approaches to yield simple yet effective machine learning algorithms for molecular properties.

Chemical space-informed machine learning models for rapid predictions of x-ray photoelectron spectra of organic molecules

Abstract We present machine learning models based on kernel-ridge regression for predicting X-ray photoelectron spec- tra of organic molecules originating from the ionization energies of 1s electrons in carbon (C), nitrogen (N), oxygen (O), and fluorine (F) atoms. We constructed training dataset through high-throughput calculations of core-electron binding energies (CEBEs) for 12,880 small organic molecules in the bigQM7ω dataset, employing the ∆-SCF formalism coupled with meta-GGA-DFT and a variationally converged basis set. The models are cost-effective, as they require the atomic coordinates of a molecule generated using universal force fields while estimating the target-level CEBEs corresponding to DFT-level equilibrium geometry. We explore transfer learning by utilizing the atomic environment feature vectors learned using a graph neural network framework in kernel-ridge regression. Additionally, we enhance accuracy using the ∆-machine learning framework by leveraging inexpensive baseline spectra derived from Kohn–Sham eigenvalues. Upon application to 208 com- binatorially substituted uracil molecules, larger than those in the training set, our analyses reveal that while the models may not yield quantitatively accurate predictions of CEBEs on a molecule-by-molecule basis, they do exhibit a strong linear correlation, which proves valuable for virtual high-throughput screening purposes. We present the dataset and models as the Python module, cebeconf, to facilitate further explorations.

FEM-driven machine learning approach for characterizing stress magnitude, peak temperature and weld zone deformation in ultrasonic welding of metallic multilayers: application to battery cells

Abstract This study investigates the innovative application of machine learning (ML) models to predict critical parameters—stress magnitude (SM), peak temperature (PT), and plastic strain (PS)—in ultrasonic welding of metallic multilayers. Extensive numerical simulations were employed to develop and evaluate three ML models: Radial Basis Function (RBF), Random Forest (RF), and Kernel Ridge Regression (KRR). According to the results, the KRR model demonstrated superior performance, achieving the lowest RMSE and highest R 2 values of 0.068 (R 2 = 0.941) for SM, 0.075 (R 2 = 0.929) for PT, and 0.071 (R 2 = 0.946) for PS, with fewer data samples required. KRR also exhibited low squared bias and variance values, ranging from 1 × 10 − 4 − 3.2 × 10 − 4 for bias and 2.2 × 10 − 4 − 3.6 × 10 − 4 for variance, indicating its precision in predicting the output targets. Moreover, the systematic categorization of input features, including material properties, geometrical factors, and welding parameters, highlighted their significant influence on predictive accuracy, particularly the crucial role of welding parameters at higher output values. Finally, a case study on ultrasonic welding of copper multilayers underscores the model’s effectiveness in unraveling complex relationships, providing a robust tool for optimizing and advancing ultrasonic welding processes.

Integration of machine learning and CFD for modeling mass transfer in water treatment using membrane separation process

This study aims to assess the efficacy of machine learning models in predicting solute concentration (C) distribution in a membrane separation process, using the input parameters which are spatial coordinates. Computational fluid dynamics (CFD) was employed with machine learning for simulation of process. The models evaluated include Kernel Ridge Regression (KRR), Radius nearest neighbor regression (RNN), K-nearest neighbors (KNN), LASSO, and Multi-Layer Perceptron (MLP). Additionally, Harris Hawks Optimization (HHO) was utilized to fine-tune the hyperparameters of these models. Leading the way is the MLP model, which achieves a remarkable test R2 value of 0.98637 together with very low RMSE and MAE values. Strongness and generalization capacity are shown by its consistent performance on test and training datasets. To conclude, the effectiveness of using machine learning regression methods more especially, KRR, KNN, RNN, LASSO, and MLP in estimating concentration from spatial coordinates was demonstrated in this work. For separation science via membranes where predictive modeling of spatial data is essential, the results offer important new perspectives by developing hybrid model.

Thawed Gaussian Wavepacket Dynamics with Δ-Machine-Learned Potentials.

A method for performing variable-width (thawed) Gaussian wavepacket (GWP) variational dynamics on machine-learned potentials is presented. Instead of fitting the potential energy surface (PES), the anharmonic correction to the global harmonic approximation (GHA) is fitted using kernel ridge regression─this is a Δ-machine learning approach. The training set consists of energy differences between ab initio electronic energies and values given by the GHA. The learned potential is subsequently used to propagate a single thawed GWP by using the time-dependent variational principle to compute the autocorrelation function, which provides direct access to vibronic spectra via its Fourier transform. We applied the developed method to simulate the photoelectron spectrum of ammonia and found excellent agreement between theoretical and experimental spectra. We show that fitting the anharmonic corrections requires a smaller training set as compared to fitting total electronic energies. We also demonstrate that our approach allows to reduce the dimensionality of the nuclear space used to scan the PES when constructing the training set. Thus, only the degrees of freedom associated with large-amplitude motions need to be treated with Δ-machine learning, which paves a way for reliable simulations of vibronic spectra of large floppy molecules.

Community identification and carbon storage monitoring of Heritiera littoralis with UAV hyperspectral imaging

The Heritiera littoralis, an important rare semi-mangrove species found in coastal protective forests, plays a crucial role in carbon storage and cycling within mangrove wetland ecosystems. Despite its importance, previous studies have overlooked remote monitoring of its carbon storage. Taking the world’s oldest and largest natural community of H. littoralis in Shenzhen, China, as the study area, this research pioneers the use of UAV hyperspectral imaging to identify the H. littoralis community and estimate its above-ground, below-ground, and total carbon storage. The impacts of five geo-environmental factors (elevation, slope, aspect, vegetation communities, and inland distance from the coastline) on the spatial variability of carbon storage using SHapley Additive exPlanations (SHAP) and multiscale geographically weighted regression (MGWR) methods were also investigated. The results demonstrate that the first derivative bands within the red edge and near-infrared regions, the anthocyanin reflectance index 2 (ARI2) and newly-developed three-band VIs, were sensitive features for community identification and carbon storage estimation within the H. littoralis community. Among the four machine learning models (eXtreme Gradient Boosting (XGBoost), Random Forest (RF), Support Vector Machine (SVM), and Logistic Regression (LR)), the best identification accuracy for the H. littoralis community was achieved by XGBoost. Among the four machine learning models (XGBoost, RF, SVM and kernel ridge regression (KRR)), RF model achieved the best performance in estimating above-ground (R2 = 0.749, RMSE=1.723 kg/m2, EV (explained variance) = 0.704), below-ground (R2 = 0.636, RMSE=0.6 kg/m2, EV=0.606) and total carbon storage (R2 = 0.613, RMSE=2.592 kg/m2, EV=0.597). SHAP and MGWR analysis showed that elevation and inland distance from the coastline were key factors influencing the spatial variability of carbon storage. In conclusion, this study showcases significant advantages in community identification and carbon storage monitoring of rare mangrove communities, providing valuable insights for biodiversity conservation efforts and management within the H. littoralis ecosystem.

Adaptive Weighted Multi-kernel Learning for Blast-Induced Flyrock Distance Prediction

AbstractIn the field of civil and mining engineering, blasting operations are widely and frequently used for rock excavation, However, some undesirable environmental problems induced by blasting operations cannot be ignored. Blast-induced flyrock is one important issue induced by blasting operation, which needs to be well predicted to identify the blasting zone’s safety zone. This study introduces an adaptive weighted multi-kernel learning model (AW-MKL) to provide an accurate prediction of blast-induced flyrock distance in Sungun Copper Mine site. The proposed model uses a combination of multi-kernel learning (MKL) approach and adaptive weighting strategy based on weighted Euclidean distance and modified local outlier factor (MLOF) to maximally improve the predictive ability of kernel ridge regression (KRR). To demonstrate the superiority of the proposed approach, six machine learning models were developed as comparisons, i.e., KRR, RF, GBDT, SVM, M5 Tree, MARS and AdaBoost. The outcomes of the proposed method achieved the highest accuracy in testing phase, with RMSE of 2.05, MAE of 0.98 and VAF of 99.92, which confirmed the strong predictive capability of the proposed AW-MKL in predicting blast-induced flyrock distance.

A generic fusion framework integrating deep learning and Kalman filter for state of charge estimation of lithium-ion batteries: Analysis and comparison

Lithium-ion batteries (LIBs) are extensively utilized in power and energy storage systems. Accurately estimating state of charge (SOC) of LIBs using single methods is still challenging to fully address the problem associated with SOC. This paper proposes a novel generic fusion framework that integrates deep learning (DL) and Kalman filter (KF), characterized by an effective fusion of the results obtained by multiple-methods. Within the DL-based method, a spatial-temporal awareness model and an improved dung beetle optimizer are proposed to enhance the capture of spatial-temporal features and optimize hyperparameters. Additionally, three adaptive nonlinear KFs are employed for SOC estimation based on a simplified electrochemical model, with the adaptive cubature KF emerging as the most suitable following comparative analysis. Subsequently, the results from both approaches are integrated to derive the final result using various fusion methodologies. The effectiveness of the fusion framework is validated using experimental data, with kernel ridge regression emerging as the optimal fusion method. The best fusion results yield a mean absolute error of 0.2341% and a root mean square error of 0.3072%, demonstrating that proposed framework can effectively process and utilize multiple-source information, thereby enhancing accuracy and robustness compared to single methods and exhibiting adaptability to complex situations.

Heterogeneous Transfer Learning of Electrohydrodynamic Printing Under Zero-Gravity Toward In-Space Manufacturing

Abstract As we continue to commercialize space and mature in-space manufacturing (ISM) processes, there is a strong need to transfer the knowledge we learn from experiments on the ground to zero-gravity environments. Physics-motivated manufacturing processes, like additive manufacturing, experience a shift in fabrication parameters due to the absence of gravity and the change of environments. Thus, we found traditional machine learning methods are not capable of addressing this domain shift and present a transfer learning scheme as a solution in this paper. We tested a kernel ridge regression model built for heterogeneous transfer learning (KRR-HeITL) on data from the electrohydrodynamic inkjet printing (EHD printing) process. EHD printing is a process that uses electrical force to control material flows, thus achieving the fabrication of electronics without requiring gravity. Our team has successfully conducted three rounds of parabolic flights to validate this technology for ISM. We trained on multiple datasets built from on-ground experiments and tested using zero-gravity printing data obtained from parabolic flight tests. Measurements of the Taylor cone both on-ground and in zero-gravity were taken and exploited as a part of the training data. We found that our method obtains good interpolation accuracy (MAPE 3.85%) compared to traditional machine learning methods (MAPE 16.84%) for predicting the printed line width. We concluded that the KRR-HeITL method is well suited for zero-gravity domain shifts of EHD printing parameters. This study paves the way for future predictions of ISM parameters when there are only on-ground experiments or very limited zero-gravity datasets for a given process.

An enhanced chlorophyll estimation model with a canopy structural trait in maize crops: Use of multi-spectral UAV images and machine learning algorithm

Leaf chlorophyll concentration (LCC) is a key indicator of leaf nitrogen (N) and changes in canopy structure, particularly the leaf area index (LAI), play a significant role in estimating LCC. Spectral prediction models for chlorophyll are a useful tool for timely nutritional management, particularly in precision agriculture. However, the accuracy of LCC estimation is influenced by the LAI. Considering LAI data as input in the spectral prediction model is still inadequate for improving LCC estimation. This study tested the hypothesis that LCC estimate accuracy could be enhanced by using LAI as an input using high-resolution (5 cm) multi-spectral images from an unmanned aerial vehicle (UAV). For this, maize was grown as a test crop under different nutrient management in the hilly ecosystem of Meghalaya. LCC was measured using laboratory destruction methods from ground sampling that coincided with UAV flights. Machine learning algorithms such as random forest (RF), support vector machine (SVM), and kernel ridge regression (KKR) were employed to develop the LCC estimation model, utilizing band reflectance, vegetation indexes, and measured chlorophyll. The model was assessed for its sensitivity to LCC estimation using LAI data. KKR outperformed other two algorithms (RF and SVM) in accuracy of LCC estimation by >11.0 to 19.0 %. The KKR-derived LCC estimation model was significantly improved by the inclusion of LAI (R2 increased from 0.785 to 0.928 and RMSE decreased from 0.065 to 0.053 mg g−1). The model's reliability was proven on multiple UAV flights for maize crops that are healthy and nutrient-stressed. Thus, LCC models derived from multispectral UAV images using KKR algorithms could benefit the adoption of precision agriculture at field scale in mountain ecosystems.

Co-training machine learning enables interpretable discovery of near-infrared phosphors with high performance

Near-infrared (NIR) phosphors based on Cr3+ doped garnets present great potential in the next generation of NIR light sources. Nevertheless, the huge searching space for the garnet composition makes the rapid discovery of NIR phosphors with high performance remain a great challenge for the scientific community. Herein, a generalizable machine learning (ML) strategy is designed to accelerate the exploration of innovative NIR phosphors via establishing the relationship between key parameters and emission peak wavelength (EPW). We propose a semi-supervised co-training model based on kernel ridge regression (KRR) and support vector regression (SVR), which successfully establishes an expanded dataset with unlabeled dataset (previously unidentified garnets), addressing the overfitting issue resulted from a small dataset and greatly improving the model generalization capability. The model is then interpreted to extract valuable insights into the contribution originated from different features. And a new type NIR luminescent material of Lu3Y2Ga3O12: Cr3+ (EPW~750 nm) is efficiently screened, which demonstrates a high internal (external) quantum efficiency of 97.1% (38.8%) and good thermal stability, particularly exhibiting promising application in the NIR phosphor-converted LEDs (pc-LED). These results suggest the strategy proposed in this work could provide new viewpoint and direction for developing NIR luminescence materials.

Convergence analysis for complementary-label learning with kernel ridge regression

Convergence analysis for complementary-label learning with kernel ridge regression

Multiple Machine Learning Models in House Price Prediction: Performance Evaluation and Comparison

House pricing is one of the most critical concerns for people. Accurately predicting house prices is essential for participants and investors in the real estate market. This study delves into the realm of predictive modeling for house prices using a multimodal approach in machine learning. The research methodology spans various stages including data collection, preprocessing, feature engineering, and model selection. Based on a dataset sourced from Kaggle, housing data from Iowa comprising 79 pertinent features influencing property prices is utilized. Performance evaluation is conducted using the root mean square error (RMSE), comparing the efficacy of linear regression models such as Lasso regression, Kernel Ridge regression, and ElasticNet regression against tree-based models including XGBoost, Gradient Boosting, and LightGBM. Additionally, the study implements two stacked ensemble models to identify the most optimal predictive model for house prices. Experimental procedures involve training and evaluating these models on specific datasets to gauge their predictive accuracy. Findings and discussions underscore the comparative analysis of diverse machine learning models within the context of house price prediction. Moreover, the study employs the Gradient Boosting method in machine learning to pinpoint the ten most influential features impacting house prices. Recommendations for future research are provided to enhance the precision and robustness of house price prediction models. This research contributes to the advancement of predictive modeling in the real estate domain, offering insights into the efficacy of various machine learning techniques for forecasting property prices.

Data-driven prediction of electrospun nanofiber diameter using machine learning: A comprehensive study and web-based tool development

Electrospinning has emerged as a versatile technique for fabricating polymer nanofibers with diameters ranging from tens to hundreds of nanometers. Precisely controlling and predicting the nanofiber diameter is crucial for various applications. The complex interplay of multiple electrospinning parameters presents a significant challenge in this endeavor. This study introduces a novel data-driven approach using machine learning (ML) to predict and optimize the diameter of electrospun nanofibers. A comprehensive dataset of approximately 430 data points was compiled from literature sources, including polymer properties and electrospinning process parameters. Six ML algorithms were evaluated: Decision Tree (DT), Extra Trees Regression (ETR), Kernel Ridge Regression (KRR), Random Forest (RF), Support Vector Regression (SVR), and eXtreme Gradient Boosting (XGB). A 75/25 train-test split was selected for optimal model evaluation, with 10-fold cross-validation employed for hyperparameter tuning and estimating the variability of performance metrics. RF and ETR demonstrated the best predictive accuracy, with R2 values of 0.9468 and 0.9421, and RMSE values of 92.3 nm and 96.1 nm, respectively, on the test set. Feature importance analysis and SHapley Additive exPlanations (SHAP) values revealed that polymer concentration, applied voltage, and feed rate significantly influence the nanofiber diameter, which was further elucidated by partial dependence plots. To facilitate accessibility and collaboration, an interactive web server called ENDP was developed, allowing users to input polymer properties and process parameters to predict the nanofiber diameter. This study showcases the potential of ML in guiding the design and optimization of electrospun nanofibers, providing valuable insights for tailoring their properties into specific applications.

Machine learning-based acoustic emission technique for corrosion-induced damage monitoring in reinforced concrete structures

Early-stage detection of corrosion in reinforcement embedded inside concrete, generally considered as the major problem in structures under extreme marine environments, can help to schedule timely maintenance/repair and to avoid any catastrophic failure. However, quantitative evaluation of the degree of deterioration, especially at a very early stage, i.e., before its appearance on the surface, is extremely difficult due to the complex process in heterogeneous material. This study aims to characterize the critical damage stages in reinforced concrete specimens under accelerated conditions using the Acoustic emission (AE) damage quantification methods supported by machine learning (ML) techniques. The stages of corrosion-induced damage are predicted by a two-step predictive model that involve both regression and classification tasks. Three supervised regression models — support vector regression (SVR), relevance vector machine (RVM) and kernel ridge regression (KRR) —are first adopted to evaluate the amount of current. Then the output from regression model is given as an input to the classification problem to predict the discrete class label output. Characterized damage stages are validated based on mass loss and crack width measurements. The results show that the corrosion initiation (at day 3) and crack formation (at day 7) can be determined from the sudden change in acoustic parameters. Further, a double layer (supervised-unsupervised) model is proposed which is found be more effective in correctly detecting the progression of damage. The findings indicate that the proposed approach that combines corrosion detection by analysing AE signals with ML technique can accurately and robustly predict corrosion severity.

Predicting tremor improvement after MRgFUS thalamotomy in essential tremor from preoperative spontaneous brain activity: A machine learning approach

Magnetic resonance-guided focused ultrasound surgery (MRgFUS) thalamotomy is an emerging technique for medication-refractory essential tremor (ET), but with variable outcomes. This study used pattern regression analysis to identify brain signatures predictive of tremor improvements. Fifty-four ET patients (mean age = 63.06 years, standard deviation (SD) = 10.55 years, 38 males) underwent unilateral MRgFUS thalamotomy and were scanned for resting-state functional magnetic resonance imaging (rs-fMRI). Seventy-four healthy controls (mean age = 58.09 years, SD = 10.30 years, 38 males) were recruited for comparison. Tremor responses at 12 months posttreatment were evaluated by the Clinical Rating Scale for Tremor. The fractional amplitude of low-frequency fluctuations (fALFF) was calculated from rs-fMRI data. Two-sample t-test was used to generate a disease-specific mask, within which Multivariate Kernel Ridge Regression analyses were conducted. Predicted and actual clinical scores were compared using Pearson’s correlation coefficient (r) and normalized mean squared error (Norm. MSE). Permutation test and leave-one-out strategy were applied for results validation. KRR identified fALFF patterns that significantly predicted the hand tremor improvement (r = 0.23, P = 0.025; Norm. MSE = 0.05, P = 0.026) and the postural tremor improvement (r = 0.28, P = 0.025; Norm. MSE = 0.06, P = 0.023), but not action tremor improvement. Lobule VI of right cerebellum (Cerebelum_6_R), right superior occipital gyrus (Occipital_Sup_R) and lobule X of vermis (Vermis_10) contributed most for hand tremor prediction (normalized weights (NW): 2.77%, 2.40%, 2.34%) while Vermis_10, left supplementary motor area (Supp_Motor_Area_L) and right hippocampus (Hippocampus_R) for postural tremor prediction (NW: 2.69%, 2.12%, 2.05%). The low contributing NW of the individual brain regions suggested that the fALFF pattern as a whole is an overall predicting feature. Preoperative fALFF pattern predicts tremor benefits induced by MRgFUS thalamotomy. ClinicalTrials.gov number: NCT04570046.

Predicting Selectivity with a Bifurcating Surface: Inaccurate Model or Inaccurate Statistics of Dynamics?

Reactions on post-transition-state bifurcation (PTSB) energy surfaces are an important class of reaction in which classical rate theories, such as the transition state theory, fail to account for the selectivity. Quasiclassical trajectory molecular dynamic (QCT-MD) simulation is an important computational approach to understanding reactions mechanisms, especially for reactions that cannot be predicted from conventional rate theories. However, the applicability of direct dynamic simulations is hampered by huge computational costs for collecting a statistically meaningful set of trajectories, making it difficult to compare simulation results with theoretical or physical insights-based predictions (non-MD predictions). In this work, we examine the PTSB of Schmidt-Aubé reactions studied by Tantillo and co-workers. With machine-learning using kernel-ridge regression (KRR) to predict atomic forces, statistical reliability was enhanced by significantly increasing the number of trajectories. With KRR, the bottleneck of simulating dynamics (atomic forces in QCT-MD with density functional theory) was accelerated more than 100-fold. We found that this KRR-aided QCT-MD approach is successful in predicting branching ratios with a much larger number of trajectories. With our approach, statistical errors are greatly reduced, and hypothetical non-MD models for predicting selectivity are tested with much higher confidence. By comparison with non-MD models, dynamical properties that affect branching ratios become more clearly described.