arXiv subjects

Karim K. Alaa El-Din

Publications and source records attributed to Karim K. Alaa El-Din.

5 recordsLinked to original sources

arXiv2026

Expander attention as exchange-correlation

Kohn-Sham density functional theory (DFT) is the workhorse of quantum chemistry, offering an attractive balance between accuracy and computational cost. Although exact in principle, DFT in practice relies on an approximation to the unknown exchange-correlation (XC) functional, which encodes the many-body quantum effects beyond the mean-field treatment. Many such approximations exist, and machine-learned XC functionals have proliferated in recent years. A persistent challenge in this area is the trade-off between accuracy and computational cost: while high-accuracy ML functionals have shown success on strongly correlated systems that are notoriously difficult for conventional approximations, their unfavorable scaling has limited broader adoption. Here, we propose a linearly scaling non-local XC approximation based on an expander graph transformer ansatz, improving the scaling of $O(N^2)$ or worse for previous ML functionals capable of reliably capturing strongly correlated systems. We show that it recovers the correct $\mathrm{H_2}$ dissociation curve in the strongly correlated regime, with promising results on planar $\mathrm{H_4}$, a system where even high-level coupled cluster methods break down. Our approach thus charts a path toward ML functionals that are both accurate on strongly correlated systems and cheap enough to deploy at scale.

quant-ph↗

arXiv2026

Overfitting by design: neural network density functionals for water

In density functional theory, simpler exchange-correlation (XC) approximations such as the local density approximation (LDA) are favored for computational speed but rely on limited information, leading to a trade-off between accuracy and generality. Machine-learned XC approximations have seen a lot of interest to address this problem. Here, we train a neural network LDA using a differentiable Kohn-Sham solver, imparting system-specific expertise for water and sacrificing generality for accuracy. Our model achieves 1 kcal / mol errors on gold standard coupled cluster ionization and atomization energies, and improves predictions of spectral lines, electron density distribution, and equilibrium geometry from as few as eight configurations used for training. We proceed to perform transfer learning and obtain results comparable to higher-rung PBE and B3LYP functionals on the WATER27 subset of the GMTKN55 database, even when only a single two-molecule binding energy is used in the transfer process. This result opens the door for specialist functionals to be trained on different systems from little data, enhancing predictions while maintaining low training costs. Our approach of training a modified XC density functional approximation (DFA) furthermore allows for a highly interpretable result, as the neural network directly corresponds to a correction of the XC energy per electron.

physics.chem-ph↗

arXiv2025

Structural evolution of iron oxides melts at Earth's outer-core pressures

Oxygen and other light elements comprise up to 5 wt% of the Earth's outer-core, and may significantly influence its physical properties and the operation of the geodynamo. Here we report in situ x-ray diffraction measurements of Fe, Fe + 4.5 FeO (atomic proportion), and Fe2O3 melts at 177-438 GPa, achieved using laser-driven shock compression at an x-ray free-electron laser. The melts exhibit Fe-O coordination numbers between 4.0(0.4) and 4.5(0.4), indicating predominantly four-fold coordination environments. These coordination states are significantly smaller than those of Fe-bearing lower-mantle phases such as bridgmanite and ferropericlase. Shorter Fe-Fe interatomic distances in compressed iron oxide melts drive the denser packing relative to ambient melts, while the structural differences between Fe + 4.5 FeO and Fe2O3 melts under shock indicate that the oxidation state modulates oxygen solubility in liquid Fe. At around 177 GPa (380 km below the core-mantle boundary), Fe2O3 melts exhibit higher Fe-O coordination, suggesting that local variations in oxygen content could contribute to the stratification in the uppermost outer-core inferred from seismological and geomagnetic observations.

cond-mat.mtrl-sci↗

arXiv2024

Efficient prediction of attosecond two-colour pulses from an X-ray free-electron laser with machine learning

X-ray free-electron lasers are sources of coherent, high-intensity X-rays with numerous applications in ultra-fast measurements and dynamic structural imaging. Due to the stochastic nature of the self-amplified spontaneous emission process and the difficulty in controlling injection of electrons, output pulses exhibit significant noise and limited temporal coherence. Standard measurement techniques used for characterizing two-coloured X-ray pulses are challenging, as they are either invasive or diagnostically expensive. In this work, we employ machine learning methods such as neural networks and decision trees to predict the central photon energies of pairs of attosecond fundamental and second harmonic pulses using parameters that are easily recorded at the high-repetition rate of a single shot. Using real experimental data, we apply a detailed feature analysis on the input parameters while optimizing the training time of the machine learning methods. Our predictive models are able to make predictions of central photon energy for one of the pulses without measuring the other pulse, thereby leveraging the use of the spectrometer without having to extend its detection window. We anticipate applications in X-ray spectroscopy using XFELs, such as in time-resolved X-ray absorption and photoemission spectroscopy, where improved measurement of input spectra will lead to better experimental outcomes.

physics.acc-ph↗

arXiv2024

Resonant inelastic x-ray scattering in warm-dense Fe compounds beyond the SASE FEL resolution limit

Resonant inelastic x-ray scattering (RIXS) is a widely used spectroscopic technique, providing access to the electronic structure and dynamics of atoms, molecules, and solids. However, RIXS requires a narrow bandwidth x-ray probe to achieve high spectral resolution. The challenges in delivering an energetic monochromated beam from an x-ray free electron laser (XFEL) thus limit its use in few-shot experiments, including for the study of high energy density systems. Here we demonstrate that by correlating the measurements of the self-amplified spontaneous emission (SASE) spectrum of an XFEL with the RIXS signal, using a dynamic kernel deconvolution with a neural surrogate, we can achieve electronic structure resolutions substantially higher than those normally afforded by the bandwidth of the incoming x-ray beam. We further show how this technique allows us to discriminate between the valence structures of Fe and Fe$_2$O$_3$, and provides access to temperature measurements as well as M-shell binding energies estimates in warm-dense Fe compounds.

cond-mat.mtrl-sci↗