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Source author record

Ove Christiansen

Ove Christiansen appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

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physics.chem-phcond-mat.str-elMachine Learningphysics.comp-ph

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Published work

5 published item(s)

preprint2026arXiv

Don't Get Your Kroneckers in a Twist: Gaussian Processes on High-Dimensional Incomplete Grids

We introduce CUTS-GPR, a new method for performing numerically exact Gaussian process regression (GPR) in high-dimensional settings. The key component of CUTS-GPR is an extremely fast kernel matrix-vector product, which exhibits near-linear or even linear scaling with the amount of training data, $N$, and low-order polynomial scaling with dimensionality, $D$. This is obtained by combining an additive kernel with an incomplete grid and exploiting the resulting structure of the kernel matrix. We demonstrate the scalability of the matrix-vector product by running benchmarks with billions of data points and thousands of dimensions. Full GPR calculations, including hyperparameter optimization, are completed in a matter of hours for $N = 447 265$ and $D = 24$. We demonstrate that our CUTS-GPR enables Bayesian modeling of high-dimensional potential energy surfaces - a longstanding challenge in computational chemistry.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Adaptive Density-Guided Approach to Double Incremental Potential Energy Surface Construction

We present a combination of the recently developed double incremental expansion of potential energy surfaces with the well-established adaptive density-guided approach to grid construction. This unique methodology is based on the use of an incremental expansion for potential energy surfaces, known as n-mode expansion, an incremental many-body representation of the electronic energy, and an efficient vibrational density-guided approach to automated determination of grid dimensions and granularity. The reliability of the method is validated calculating potential energy surfaces and obtaining fundamental excitation energies for three moderate-size chain-like molecular systems. The results are compared to other approaches, which utilize static grid construction for supersystem and fragmentation calculation setups. The use of our methodology leads to considerable computational savings for potential energy surface construction and a major reduction in the number of required single point calculations can be achieved, while maintaining a high level of accuracy in the resulting potential energy surfaces. Additional investigations indicate that our method can be applied to covalently bound and strongly interacting molecular systems, even though these cases are known as being very unfavorable for fragmentation schemes. We therefore conclude that the presented methodology is a robust and flexible approach to potential energy surface construction, which introduces considerable computational savings without compromising the accuracy of vibrational spectra calculations.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Bypassing the computational bottleneck of quantum-embedding theories for strong electron correlations with machine learning

A cardinal obstacle to performing quantum-mechanical simulations of strongly-correlated matter is that, with the theoretical tools presently available, sufficiently-accurate computations are often too expensive to be ever feasible. Here we design a computational framework combining quantum-embedding (QE) methods with machine learning. This allows us to bypass altogether the most computationally-expensive components of QE algorithms, making their overall cost comparable to bare Density Functional Theory (DFT). We perform benchmark calculations of a series of actinide systems, where our method describes accurately the correlation effects, reducing by orders of magnitude the computational cost. We argue that, by producing a larger-scale set of training data, it will be possible to apply our method to systems with arbitrary stoichiometries and crystal structures, paving the way to virtually infinite applications in condensed matter physics, chemistry and materials science.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Vibrationally Resolved Coupled Cluster X-Ray Absorption Spectra from Vibrational Configuration Interaction Anharmonic Calculations

Vibrationally resolved near-edge x-ray absorption spectra at the K-edge for a number of small molecules have been computed from anharmonic vibrational configuration interaction calculations of the Franck-Condon factors. The potential energy surfaces for ground and core-excited states were obtained at the core-valence separated CC2, CCSD, CCSDR(3), and CC3 levels of theory, employing the Adaptive Density-Guided Approach (ADGA) scheme to select the single points at which to perform the energy calculations. We put forward an initial attempt to include pair-mode coupling terms to describe the potential of polyatomic molecules

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preprint2016arXiv

Linear-scaling generation of potential energy surfaces using a double incremental expansion

We present a combination of the incremental expansion of potential energy surfaces (PESs), known as n-mode expansion, with the incremental evaluation of the electronic energy in a many-body approach. The application of semi-local coordinates in this context allows the generation of PESs in a very cost-efficient way. For this, we employ the recently introduced flexible adaptation of local coordinates of nuclei (FALCON) coordinates. By introducing an additional transformation step, concerning only a fraction of the vibrational degrees of freedom, we can achieve linear scaling of the accumulated cost of the single point calculations required in the PES generation. Numerical examples of these double incremental approaches for oligo-phenyl examples show fast convergence with respect to the maximum number of simultaneously treated fragments and only a modest error introduced by the additional transformation step. The approach, presented here, represents a major step towards the applicability of vibrational wave function methods to sizable, covalently bound systems.

0 citations0 reviewsNo code linkedOpen access