arXiv subjects

Kenneth O. Berard

Publications and source records attributed to Kenneth O. Berard.

3 recordsLinked to original sources

arXiv2026

Denoising Diffusion Monte Carlo Electron Densities with Physically Informed Variance Stabilization: From Fourier Filters to 3D UNETs

Obtaining accurate electron densities is important for the fundamental description of molecular and condensed matter systems, as well as for the development of next-generation density functionals. Diffusion Monte Carlo (DMC), in particular, is known to produce benchmark-quality data; however, the predicted real-space electron densities contain substantial amounts of statistical noise. In this work, we study denoising approaches for DMC densities, judged on the basis of the information-theoretic Jensen-Shannon divergence. The denoising is facilitated by an approximate heteroscedastic to homoscedastic transformation leveraging the density functional theory density as a physical prior. We systematically compare a range of denoising techniques-including Fourier transform, regression, and 3D UNETs-on materials showing a wide range of density variations: carbon diamond, blue phosphorus, and rutile VO2. Our results indicate that simple flattened machine learning models and 2D image-based models introduce line artifacts and struggle to capture the full spatial correlation. In contrast, when using variance stabilization, regression methods outperform all others in both the high and low- noise limits across all materials considered. The best denoisers reduce the required cost of density-generating DMC simulations by 10-100x, providing a promising route forward for application in noise-sensitive tasks such as DFT functional inversion.

cond-mat.mtrl-sci↗

arXiv2024

Efficient and Scalable Wave Function Compression Using Corner Hierarchical Matrices

The exponential scaling of complete active space (CAS) and full configuration interaction (CI) calculations limits the ability of quantum chemists to simulate the electronic structures of strongly correlated systems. Herein, we present corner hierarchically approximated CI (CHACI), an approach to wave function compression based on corner hierarchical matrices (CH-matrices) -- a new variant of hierarchical matrices based on a block-wise low-rank decomposition. By application to dodecacene, a strongly correlated molecule, we demonstrate that CH matrix compression provides superior compression compared to a truncated global singular value decomposition. The compression ratio is shown to improve with increasing active space size. By comparison of several alternative schemes, we demonstrate that superior compression is achieved by a) using a blocking approach that emphasizes the upper-left corner of the CI vector, b) sorting the CI vector prior to compression, and c) optimizing the rank of each block to maximize information density.

physics.chem-ph↗

arXiv2024

Gaussian Processes for Finite Size Extrapolation of Many-Body Simulations

Key to being able to accurately model the properties of realistic materials is being able to predict their properties in the thermodynamic limit. Nevertheless, because most many-body electronic structure methods scale as a high-order polynomial, or even exponentially, with system size, directly simulating large systems in their thermodynamic limit rapidly becomes computationally intractable. As a result, researchers typically estimate the properties of large systems that approach the thermodynamic limit by extrapolating the properties of smaller, computationally-accessible systems based on relatively simple scaling expressions. In this work, we employ Gaussian processes to more accurately and efficiently extrapolate many-body simulations to their thermodynamic limit. We train our Gaussian processes on Smooth Overlap of Atomic Positions (SOAP) descriptors to extrapolate the energies of one-dimensional hydrogen chains obtained using two high-accuracy many-body methods: Coupled Cluster theory and Auxiliary Field Quantum Monte Carlo (AFQMC). In so doing, we show that Gaussian processes trained on relatively short, 10-30-atom chains can predict the energies of both homogeneous and inhomogeneous hydrogen chains in their thermodynamic limit with sub-milliHartree accuracy. Unlike standard scaling expressions, our GPR-based approach is highly generalizable given representative training data and is not dependent on systems' geometries or dimensionality. This work highlights the potential for machine learning to correct for the finite size effects that routinely complicate the interpretation of finite size many-body simulations.

physics.chem-ph↗