Related papers: Machine-learned, finite temperature Fermi-operator…
In this work, we propose an Operator Learning (OpL) method for solving boundary value inverse problems in partial differential equations (PDEs), focusing on recovering diffusion coefficients from boundary data. Inspired by the classical…
Optimization in machine learning, both theoretical and applied, is presently dominated by first-order gradient methods such as stochastic gradient descent. Second-order optimization methods, that involve second derivatives and/or second…
Over the past decade, Finite Element Method (FEM) has served as a foundational numerical framework for approximating the terms of Time Series Expansion (TSE) as solutions to transient Partial Differential Equation (PDE). However, the…
We derive finite temperature expansions for relativistic fermion systems in the presence of background magnetic fields, and with nonzero chemical potential. We use the imaginary-time formalism for the finite temperature effects, the…
A fundamental step in the development of machine learning models commonly involves the tuning of hyperparameters, often leading to multiple model training runs to work out the best-performing configuration. As machine learning tasks and…
Topology Optimization (TO), which maximizes structural robustness under material weight constraints, is becoming an essential step for the automatic design of mechanical parts. However, existing TO algorithms use the Finite Element Analysis…
We suggest a new technique of the asymptotic heat kernel expansion for minimal higher derivative operators of a generic $2M$-th order, $F(\nabla)=(-\Box)^M+\cdots$, in the background field formalism of gauge theories and quantum gravity.…
Smooth, highly accurate analytical representations of Fermi-Dirac (FD) integral combinations important in free-energy density functional calculations are presented. Specific forms include those that occur in the local density approximation…
The $hp$-adaptive finite element method (FEM) - where one independently chooses the mesh size ($h$) and polynomial degree ($p$) to be used on each cell - has long been known to have better theoretical convergence properties than either $h$-…
Topology optimization (TO) is a popular and powerful computational approach for designing novel structures, materials, and devices. Two computational challenges have limited the applicability of TO to a variety of industrial applications.…
The high-temperature series expansion for quantum spin models is a well-established tool to compute thermodynamic quantities and equal-time spin correlations, in particular for frustrated interactions. We extend the scope of this expansion…
An extended atomistic spin model allowing for studies of the finite temperature magnetic properties of alloys is proposed. The model is obtained by extending the Heisenberg Hamiltonian via a parameterization from a first principles basis,…
Exploring low-cost applications is paramount to creating value in early fault-tolerant quantum computers. Here we optimize both gate and qubit counts of recent algorithms for simulating the Fermi-Hubbard model. We further devise and compile…
Brain-inspired spiking neural networks (SNNs) replace the multiply-accumulate operations of traditional neural networks by integrate-and-fire neurons, with the goal of achieving greater energy efficiency. Specialized hardware…
Computing finite temperature properties of a quantum many-body system is key to describing a broad range of correlated quantum many-body physics from quantum chemistry and condensed matter to thermal quantum field theories. Quantum…
A computer aided high temperature expansion of the magnetic susceptibility and the magnetic specific heat is presented and demonstrated for frustrated and unfrustrated spin chains. The results are analytic in nature since the calculations…
We present an \textit{ab initio} auxiliary field quantum Monte Carlo method for studying the electronic structure of molecules, solids, and model Hamiltonians at finite temperature. The algorithm marries the \textit{ab initio} phaseless…
Recently, several studies proposed methods to utilize some classes of optimization problems in designing deep neural networks to encode constraints that conventional layers cannot capture. However, these methods are still in their infancy…
The computational efficiency of many neural operators, widely used for learning solutions of PDEs, relies on the fast Fourier transform (FFT) for performing spectral computations. As the FFT is limited to equispaced (rectangular) grids,…
Ga2O3 is being actively explored for high-power and high-temperature electronics, deep-ultraviolet optoelectronics, and other applications. Efficient n-type doping of Ga2O3 has been achieved, but p-type doping faces fundamental obstacles…