arXiv subjects

William A. Wheeler

Publications and source records attributed to William A. Wheeler.

7 recordsLinked to original sources

arXiv2025

Identifying the Smallest Adversarial Load Perturbation that Renders DC-OPF Infeasible

What is the globally smallest load perturbation that renders DC-OPF infeasible? Reliably identifying such "adversarial attack" perturbations has useful applications in a variety of emerging grid-related contexts, including machine learning performance verification, cybersecurity, and operational robustness of power systems dominated by stochastic renewable energy resources. In this paper, we formulate the inherently nonconvex adversarial attack problem by applying a parameterized version of Farkas' lemma to a perturbed set of DC-OPF equations. Since the resulting formulation is very hard to globally optimize, we also propose a parameterized generation control policy which, when applied to the primal DC-OPF problem, provides solvability guarantees. Together, these nonconvex problems provide guaranteed upper and lower bounds on adversarial attack size; by combining them into a single optimization problem, we can efficiently "squeeze" these bounds towards a common global solution. We apply these methods on a range of small- to medium-sized test cases from PGLib, benchmarking our results against the best adversarial attack lower bounds provided by Gurobi 12.0's spatial Branch and Bound solver.

eess.SY↗

arXiv2025

Expressivity of determinantal ansatzes for neural network wave functions

Neural network wave functions have shown promise as a way to achieve high accuracy on the many-body quantum problem. These wave functions most commonly use a determinant or sum of determinants to antisymmetrize many-body orbitals which are described by a neural network. In many cases, the wave function is projected onto a fixed-spin state. Such a treatment is allowed for spin-independent operators; however, it cannot be applied to spin-dependent problems, such as Hamiltonians containing spin-orbit interactions. We show that for spin-independent Hamiltonians, a strict upper bound property is obeyed between a traditional Hartree-Fock like determinant, full spinor wave function, the full determinant wave function, and a generalized spinor wave function. The relationship between a spinor wave function and the full determinant arises because the full determinant wave function is the spinor wave function projected onto a fixed-spin, after which antisymmetry is implicitly restored in the spin-independent case. For spin-dependent Hamiltonians, the full determinant wave function is not applicable, because it is not antisymmetric. Numerical experiments on the H$_3$ molecule and two-dimensional homogeneous electron gas confirm the bounds.

cond-mat.str-el↗

arXiv2025

Reproducibility of fixed-node diffusion Monte Carlo across diverse community codes: The case of water-methane dimer

Fixed-node diffusion quantum Monte Carlo (FN-DMC) is a widely-trusted many-body method for solving the Schrödinger equation, known for its reliable predictions of material and molecular properties. Furthermore, its excellent scalability with system complexity and near-perfect utilization of computational power makes FN-DMC ideally positioned to leverage new advances in computing to address increasingly complex scientific problems. Even though the method is widely used as a computational gold standard, reproducibility across the numerous FN-DMC code implementations has yet to be demonstrated. This difficulty stems from the diverse array of DMC algorithms and trial wave functions, compounded by the method's inherent stochastic nature. This study represents a community-wide effort to assess the reproducibility of the method, affirming that: Yes, FN-DMC is reproducible (when handled with care). Using the water-methane dimer as the canonical test case, we compare results from eleven different FN-DMC codes and show that the approximations to treat the non-locality of pseudopotentials are the primary source of the discrepancies between them. In particular, we demonstrate that, for the same choice of determinantal component in the trial wave function, reliable and reproducible predictions can be achieved by employing the T-move (TM), the determinant locality approximation (DLA), or the determinant T-move (DTM) schemes, while the older locality approximation (LA) leads to considerable variability in results. These findings demonstrate that, with appropriate choices of algorithmic details, fixed-node DMC is reproducible across diverse community codes-highlighting the maturity and robustness of the method as a tool for open and reliable computational science.

physics.comp-ph↗

arXiv2024

Capturing spin fluctuations in CaCuO$_2$: $\textit{Ab initio}$ QMC calculations with multi-determinant wave functions

We present an advanced $\textit{ab initio}$ quantum Monte Carlo (QMC) calculation of the ground state of undoped CaCuO$_2$. We extend the traditional single-determinant Slater-Jastrow approach to include multi-determinant wave functions, inhomogeneous Jastrow factors, and orbital optimization. Our results demonstrate not only an improvement in the variational bound of the ground state energy -- 2.3 eV per formula unit lower than previous state of the art techniques -- but also confirm the presence of spin fluctuations in multi-determinant wave functions in a strongly correlated cuprate system, which is integral to understanding high-$T_c$ superconductivity. This is the first demonstration of capturing spin fluctuations in QMC wave functions on a cuprate, establishing the groundwork for new studies on doped cuprates in the superconducting state, where spin fluctuations require more accurate characterization.

cond-mat.str-el↗

arXiv2023

Ensemble variational Monte Carlo for optimization of correlated excited state wave functions

Variational Monte Carlo methods have recently been applied to the calculation of excited states; however, it is still an open question what objective function is most effective. A promising approach is to optimize excited states using a penalty to minimize overlap with lower eigenstates, which has the drawback that states must be computed one at a time. We derive a general framework for constructing objective functions with minima at the the lowest $N$ eigenstates of a many-body Hamiltonian. The objective function uses a weighted average of the energies and an overlap penalty, which must satisfy several conditions. We show this objective function has a minimum at the exact eigenstates for a finite penalty, and provide a few strategies to minimize the objective function. The method is demonstrated using ab initio variational Monte Carlo to calculate the degenerate first excited state of a CO molecule.

physics.comp-ph↗

arXiv2022

PyQMC: an all-Python real-space quantum Monte Carlo module in PySCF

We describe a new open-source Python-based package for high accuracy correlated electron calculations using quantum Monte Carlo (QMC) in real space: PyQMC. PyQMC implements modern versions of QMC algorithms in an accessible format, enabling algorithmic development and easy implementation of complex workflows. Tight integration with the PySCF environment allows for simple comparison between QMC calculations and other many-body wave function techniques, as well as access to high accuracy trial wave functions.

cond-mat.mtrl-sci↗

arXiv2019

Many-Body Electric Multipole Operators in Extended Systems

The quantum mechanical position operators, and their products, are not well-defined in systems obeying periodic boundary conditions. Here we extend the work of Resta who developed a formalism to calculate the electronic polarization as an expectation value of a many-body operator, to include higher multipole moments, e.g., quadrupole and octupole. We define $n$-th order multipole operators whose expectation values can be used to calculate the $n$-th multipole moment when all of the lower moments are vanishing (modulo a quantum). We show that changes in our operators are tied to flows of $n-1$-st multipole currents, and encode the adiabatic evolution of the system in the presence of an $n-1$-st gradient of the electric field. Finally, we test our operators on a set of tightbinding models to show that they correctly determine the phase diagrams of topological quadrupole and octupole models, capture an adiabatic quadrupole pump, and distinguish a bulk quadrupole moment from other mechanisms that generate corner charges.

cond-mat.str-el↗