Kernel methods

Pinheiro, Max; Dral, Pavlo O.

doi:10.1016/b978-0-323-90049-2.00009-3

Cited by 7 publications

(8 citation statements)

References 51 publications

(87 reference statements)

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“…The user can choose from one of the implemented kernel functions, including the linear, ,, Gaussian, ,, exponential, ,, Laplacian, ,, and Matérn ,− as well as periodic ,, and decaying periodic ,, functions, which are summarized in Table . These kernel functions k ( x , x j ; h ) are key components required to solve the KRR problem of finding the regression coefficients α of the approximating function f̂ ( x ; h ) of the input vector x : , f̂ ( x ; h ) = ∑ j = 1 N tr α j k ( x , boldx j ; h ) …”

Section: Models and Methodsmentioning

confidence: 99%

“…MLatom also provides the flexibility of training custom models based on kernel ridge regression (KRR) for a given set of input vectors x or XYZ coordinates and any labels y . , If XYZ coordinates are provided, they can be transformed in one of the several supported descriptors (e.g., inverse internuclear distances and their version normalized relative to the equilibrium structure (RE) and the Coulomb matrix). The user can choose from one of the implemented kernel functions, including the linear, ,, Gaussian, ,, exponential, ,, Laplacian, ,, and Matérn ,− as well as periodic ,, and decaying periodic ,, functions, which are summarized in Table . These kernel functions k ( x , x j ; h ) are key components required to solve the KRR problem of finding the regression coefficients α of the approximating function f̂ ( x ; h ) of the input vector x : , f̂ ( x ; h ) = ∑ j = 1 N tr α j k ( x , boldx j ; h ) …”

Section: Models and Methodsmentioning

confidence: 99%

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MLatom 3: A Platform for Machine Learning-Enhanced Computational Chemistry Simulations and Workflows

Dral,

Ge,

Hou

et al. 2024

J. Chem. Theory Comput.

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Machine learning (ML) is increasingly becoming a common tool in computational chemistry. At the same time, the rapid development of ML methods requires a flexible software framework for designing custom workflows. MLatom 3 is a program package designed to leverage the power of ML to enhance typical computational chemistry simulations and to create complex workflows. This open-source package provides plenty of choice to the users who can run simulations with the command-line options, input files, or with scripts using MLatom as a Python package, both on their computers and on the online XACS cloud computing service at XACScloud.com. Computational chemists can calculate energies and thermochemical properties, optimize geometries, run molecular and quantum dynamics, and simulate (ro)vibrational, one-photon UV/vis absorption, and two-photon absorption spectra with ML, quantum mechanical, and combined models. The users can choose from an extensive library of methods containing pretrained ML models and quantum mechanical approximations such as AIQM1 approaching coupled-cluster accuracy. The developers can build their own models using various ML algorithms. The great flexibility of MLatom is largely due to the extensive use of the interfaces to many state-of-the-art software packages and libraries.

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Section: Models and Methodsmentioning

confidence: 99%

Section: Models and Methodsmentioning

confidence: 99%

MLatom 3: A Platform for Machine Learning-Enhanced Computational Chemistry Simulations and Workflows

Dral,

Ge,

Hou

et al. 2024

J. Chem. Theory Comput.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Kernel ridge regression (KRR) belongs to the kernel methods and is directly related to the Gaussian process regression (GPR). The fitting functions of KRR and GPR are identical, but GPR is derived from the perspective of the Bayesian approach, which provides variance (can be useful for determining uncertainty) and the hyperparameter optimization is often done differently in GPR (where, often, log marginal likelihood is optimized). , For each input vector x i , the prediction of KRR is given as , .25ex2ex f false( boldx i false) = y prior + ∑ j = 1 N tr α j k ( x i , x j ) where N tr is the number of training points, α j is the regression coefficient and k ( x i , x j ) is the kernel function that will be discussed below, and y prior is, following related Gaussian process regression terminology, a prior function. In the MLatom implementation, y prior is simply a constant that is by default set to zero or can be set to the mean of the reference values or any other user-defined value.…”

Section: Methodsmentioning

confidence: 99%

Explicit Learning of Derivatives with the KREG and pKREG Models on the Example of Accurate Representation of Molecular Potential Energy Surfaces

Hou

Dral

2023

J. Chem. Theory Comput.

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The KREG and pKREG models were proven to enable accurate learning of multidimensional single-molecule surfaces of quantum chemical properties such as ground-state potential energies, excitation energies, and oscillator strengths. These models are based on kernel ridge regression (KRR) with the Gaussian kernel function and employ a relative-to-equilibrium (RE) global molecular descriptor, while pKREG is designed to enforce invariance under atom permutations with a permutationally invariant kernel. Here we extend these two models to also explicitly include the derivative information from the training data into the models, which greatly improves their accuracy. We demonstrate on the example of learning potential energies and energy gradients that KREG and pKREG models are better or on par with state-of-the-art machine learning models. We also found that in challenging cases both energy and energy gradient labels should be learned to properly model potential energy surfaces and learning only energies or gradients is insufficient. The models’ open-source implementation is freely available in the MLatom package for general-purpose atomistic machine learning simulations, which can be also performed on the MLatom@XACS cloud computing service.

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“…The GEK − approacha GPR variantis an ML method that has been applied with significant success to, for example, molecular structure optimizations. ,− In this report, such a GEK implementation especially modified for the case of SCF orbital optimizations is presented. The size of the parameter space, N SCF , however, is a significant problem for an efficient implementation, as reported by Ritterhoff, who demonstrated that the GEK procedure applied to SCF orbital optimization can have competitive iteration counts, while the timings are very unfavorable due to the N 3 scaling of the procedure.…”

Section: Theorymentioning

confidence: 99%

A Story of Three Levels of Sophistication in SCF/KS-DFT Orbital Optimization Procedures

Sethio,

Azzopardi,

Fdez. Galván

et al. 2024

J. Phys. Chem. A

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In this work, three versions of self-consistent field/ Kohn−Sham density functional theory (SCF/KS-DFT) orbital optimization are described and benchmarked. The methods are a modified version of the geometry version of the direct inversion in the iterative subspace approach (which we call r-GDIIS), the modified restricted step rational function optimization method (RS-RFO), and the novel subspace gradient-enhanced Kriging method combined with restricted variance optimization (S-GEK/ RVO). The modifications introduced are aimed at improving the robustness and computational scaling of the procedures. In particular, the subspace approach in S-GEK/RVO allows the application to SCF/KS-DFT optimization of a machine learning technique that has proven to be successful in geometry optimizations. The performance of the three methods is benchmarked for a large number of small-to medium-sized organic molecules, at equilibrium structures and close to a transition state, and a second set of molecules containing closed-and open-shell transition metals. The results indicate the importance of the resetting technique in boosting the performance of the r-GDIIS procedure. Moreover, it is demonstrated that already at the inception of the subspace version of GEK to optimize SCF wave functions, it displays superior and robust convergence properties as compared to those of the standard state-of-the-art SCF/KS-DFT optimization methods.

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Kernel methods

Cited by 7 publications

References 51 publications

MLatom 3: A Platform for Machine Learning-Enhanced Computational Chemistry Simulations and Workflows

MLatom 3: A Platform for Machine Learning-Enhanced Computational Chemistry Simulations and Workflows

Explicit Learning of Derivatives with the KREG and pKREG Models on the Example of Accurate Representation of Molecular Potential Energy Surfaces

A Story of Three Levels of Sophistication in SCF/KS-DFT Orbital Optimization Procedures

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