A network pruning algorithm for combined function and derivative approximation

Pukrittayakamee, A.; Hagan, Martin T.; Raff, Lionel M.; Bukkapatnam, Satish T. S.; Komanduri, R.

doi:10.1109/ijcnn.2009.5178765

Cited by 3 publications

(11 citation statements)

References 18 publications

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“…In a previously reported study, 37 we employed the CFDA to fit five other systems that include four analytical potentials and a database for Si 5 obtained from electronic structure calculations. In each case, every test that we have run shows that CFDA training ͑without a validation set͒ has produced smaller, out-of-sample testing error than early stopping ͑with a validation set͒ or Bayesian regularization ͑without a validation set͒.…”

Section: B Sampling Procedures and Fitting Resultsmentioning

confidence: 99%

“…37 By using Eq. ͑2͒, we are able to approximate both a potential surface and its gradient with a NN that has a single neuron in the last layer, representing only the potential.…”

Section: Nn Training Methodsmentioning

confidence: 99%

“…The details of the gradient calculation are provided by Pukrittayakamee et al 37 We will provide a summary of the calculations here. We begin by introducing the notation that we will use for the NN.…”

Section: Nn Training Methodsmentioning

confidence: 99%

“…The details of this selection are given by Pukrittayakamee et al 37 We will provide a summary of the calculations here. The first step was to write as…”

Section: ͑16͒mentioning

confidence: 99%

“…The same value of the parameter can then be used over a variety of problems. This was tested by Pukrittayakamee et al 37 and it was found that =10 4 produced accurate results over a wide variety of fitting problems. That is the value that we will use in the remainder of this paper.…”

Section: ͑16͒mentioning

confidence: 99%

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Simultaneous fitting of a potential-energy surface and its corresponding force fields using feedforward neural networks

Pukrittayakamee

Malshe

Hagan

et al. 2009

The Journal of Chemical Physics

117

111

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An improved neural network (NN) approach is presented for the simultaneous development of accurate potential-energy hypersurfaces and corresponding force fields that can be utilized to conduct ab initio molecular dynamics and Monte Carlo studies on gas-phase chemical reactions. The method is termed as combined function derivative approximation (CFDA). The novelty of the CFDA method lies in the fact that although the NN has only a single output neuron that represents potential energy, the network is trained in such a way that the derivatives of the NN output match the gradient of the potential-energy hypersurface. Accurate force fields can therefore be computed simply by differentiating the network. Both the computed energies and the gradients are then accurately interpolated using the NN. This approach is superior to having the gradients appear in the output layer of the NN because it greatly simplifies the required architecture of the network. The CFDA permits weighting of function fitting relative to gradient fitting. In every test that we have run on six different systems, CFDA training (without a validation set) has produced smaller out-of-sample testing error than early stopping (with a validation set) or Bayesian regularization (without a validation set). This indicates that CFDA training does a better job of preventing overfitting than the standard methods currently in use. The training data can be obtained using an empirical potential surface or any ab initio method. The accuracy and interpolation power of the method have been tested for the reaction dynamics of H+HBr using an analytical potential. The results show that the present NN training technique produces more accurate fits to both the potential-energy surface as well as the corresponding force fields than the previous methods. The fitting and interpolation accuracy is so high (rms error=1.2 cm(-1)) that trajectories computed on the NN potential exhibit point-by-point agreement with corresponding trajectories on the analytic surface.

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Section: B Sampling Procedures and Fitting Resultsmentioning

confidence: 99%

“…37 By using Eq. ͑2͒, we are able to approximate both a potential surface and its gradient with a NN that has a single neuron in the last layer, representing only the potential.…”

Section: Nn Training Methodsmentioning

confidence: 99%

Section: Nn Training Methodsmentioning

confidence: 99%

“…The details of this selection are given by Pukrittayakamee et al 37 We will provide a summary of the calculations here. The first step was to write as…”

Section: ͑16͒mentioning

confidence: 99%

Section: ͑16͒mentioning

confidence: 99%

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Simultaneous fitting of a potential-energy surface and its corresponding force fields using feedforward neural networks

Pukrittayakamee

Malshe

Hagan

et al. 2009

The Journal of Chemical Physics

117

111

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Molecular Dynamics Investigation of the Bimolecular Reaction BeH + H₂ → BeH₂ + H on an ab Initio Potential-Energy Surface Obtained Using Neural Network Methods with Both Potential and Gradient Accuracy Determination

Raff

2009

J. Phys. Chem. A

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The classical reaction dynamics of a four-body, bimolecular reaction on a neural network (NN) potential-energy surface (PES) fitted to a database obtained solely from ab initio MP2/6-311G(d,p) calculations are reported. The present work represents the first reported application of ab initio NN methods to a four-body, bimolecular, gas-phase reaction where bond extensions reach 8.1 A for the BeH + H(2) --> BeH(2) + H reaction. A modified, iterative novelty sampling method is used to select data points based on classical trajectories computed on temporary NN surfaces. After seven iterations, the sampling process is found to converge after selecting 9604 configurations. Incorporation of symmetry increases this to 19 208 BeH(3) configurations. The analytic PES for the system is obtained from the ensemble average of a five-member (6-60-1) NN committee. The mean absolute error (MAE) for the committee is 0.0046 eV (0.44 kJ mol(-1)). The total energy range of the BeH(3) database is 147.0 kJ mol(-1). Therefore, this MAE represents a percent energy error of 0.30%. Since it is the gradient of the PES that constitutes the most important quantity in molecular dynamics simulations, the paper also reports mean absolute error for the gradient. This result is 0.026 eV A(-1) (2.51 kJ mol(-1) A(-1)). Since the gradient magnitudes span a range of 15.32 eV A(-1) over the configuration space tested, this mean absolute gradient error represents a percent error of 0.17%. The mean percent absolute relative gradient error is 4.67%. The classically computed reaction cross sections generally increase with total energy. They vary from 0.007 to 0.030 A(2) when H(2) is at ground state, and from 0.05 to 0.10 A(2) when H(2) is in the first excited state. Trajectory integration is very fast using the five-member NN PES. The average trajectory integration time is 1.07 s on a CPU with a clock speed of 2.4 GHz. Zero angular momentum collisions are also investigated and compared with previously reported quantum dynamics on the same system. The quantum reaction probabilities exhibit pronounced resonance effects that are absent in the classical calculations. The magnitudes of quantum and classical results are in fair accord with the classical results being about 30-40% higher due to the lack of quantum restrictions on the zero-point vibrational energy.

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Applications of machine learning techniques to broaden operating envelope of biodiesel-fueled HCCI engines

Bukkarapu,

Krishnasamy

2024

International Journal of Engine Research

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A significant shortcoming of Homogeneous charge compression ignition (HCCI) engines is their narrow operating envelope, particularly with high-reactivity fuels like biodiesel. Additionally, the compositional variability of biodiesels, reflected in cetane number variations based on different source feedstocks, poses another challenge. While various strategies have successfully extended the maximum load limit in diesel-HCCI engines, they have not been adequately explored in biodiesel-fueled HCCI engines. This study is the first to comprehensively investigate the interplay of biodiesel composition, cetane number, engine compression ratio, and charge dilution strategy for extending the operating envelope of a light-duty HCCI engine. Given the impracticality of controlling multiple variables experimentally, this work focuses on the potential of machine learning (ML) algorithms to predict the operational limits of an HCCI engine using neat biodiesels derived from diverse sources. Among the ML models explored, artificial neural networks were the most accurate in predicting the minimum stable load, with prediction errors of 3.5% (calibration) and 3.9% (validation). Support vector machine models predicted the maximum load (with and without dilution) with errors below 5%. Notably, biodiesel produced from a blend of linseed, karanja, coconut, and mustard oils in specific proportions (42%, 3%, 25%, and 30% mass, respectively) yielded a wide HCCI operating range from 0.4 to 3.25 bar (without dilution) and up to 3.67 bar BMEP with charge dilution. This study highlights the novelty and practicality of using ML to predict and extend the operating envelope for biodiesel-fueled HCCI engines, demonstrating their suitability for future applications.

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A network pruning algorithm for combined function and derivative approximation

Cited by 3 publications

References 18 publications

Simultaneous fitting of a potential-energy surface and its corresponding force fields using feedforward neural networks

Simultaneous fitting of a potential-energy surface and its corresponding force fields using feedforward neural networks

Molecular Dynamics Investigation of the Bimolecular Reaction BeH + H₂ → BeH₂ + H on an ab Initio Potential-Energy Surface Obtained Using Neural Network Methods with Both Potential and Gradient Accuracy Determination

Applications of machine learning techniques to broaden operating envelope of biodiesel-fueled HCCI engines

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A network pruning algorithm for combined function and derivative approximation

Cited by 3 publications

References 18 publications

Simultaneous fitting of a potential-energy surface and its corresponding force fields using feedforward neural networks

Simultaneous fitting of a potential-energy surface and its corresponding force fields using feedforward neural networks

Molecular Dynamics Investigation of the Bimolecular Reaction BeH + H2 → BeH2 + H on an ab Initio Potential-Energy Surface Obtained Using Neural Network Methods with Both Potential and Gradient Accuracy Determination

Applications of machine learning techniques to broaden operating envelope of biodiesel-fueled HCCI engines

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Product

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Molecular Dynamics Investigation of the Bimolecular Reaction BeH + H₂ → BeH₂ + H on an ab Initio Potential-Energy Surface Obtained Using Neural Network Methods with Both Potential and Gradient Accuracy Determination