Related papers: Direct Minimization for Ensemble Electronic Struct…
We propose a technique for reformulation of state and parameter estimation problems as that of matching explicitly computable definite integrals with known kernels to data. The technique applies for a class of systems of nonlinear ordinary…
In the recent work of S. Sharma \emph{et al.}, (arxiv.org: arxiv:0912.1118), a single-electron spectrum associated with the natural orbitals was defined as the derivative of the total energy with respect to the occupation numbers at half…
The direct parametrisation method for invariant manifold is a model-order reduction technique that can be applied to nonlinear systems described by PDEs and discretised e.g. with a finite element procedure in order to derive efficient…
Reduced-order simulation is an emerging method for accelerating physical simulations with high DOFs, and recently developed neural-network-based methods with nonlinear subspaces have been proven effective in diverse applications as more…
Ensemble learning has had many successes in supervised learning, but it has been rare in unsupervised learning and dimensionality reduction. This study explores dimensionality reduction ensembles, using principal component analysis and…
It has recently been shown that configuration state functions (CSF) with local orbitals can provide a compact reference state for low-spin open-shell electronic structures, such as antiferromagnetic states. However, optimizing a low-spin…
The long-term distributions of trajectories of a flow are described by invariant densities, i.e. fixed points of an associated transfer operator. In addition, global slowly mixing structures, such as almost-invariant sets, which partition…
We present an efficient scheme for accurate electronic structure interpolations based on the systematically improvable optimized atomic orbitals. The atomic orbitals are generated by minimizing the spillage value between the atomic basis…
We discuss our new implementation of the Real-space Electronic Structure method for studying the atomic and electronic structure of infinite periodic as well as finite systems, based on density functional theory. This improved version which…
We present a density difference based analysis for a range of orbital--dependent Kohn--Sham functionals. Results for atoms, some members of the neon isoelectronic series and small molecules are reported and compared with ab initio…
In this experience report, we apply deep active learning to the field of design optimization to reduce the number of computationally expensive numerical simulations. We are interested in optimizing the design of structural components, where…
The NEPv approach has been increasingly used lately for optimization on the Stiefel manifold arising from machine learning. General speaking, the approach first turns the first order optimality condition, also known as the KKT condition,…
Approximate solution of the ensemble representability problem for density operators of arbitrary order is obtained. This solution is closely related to the ``Q condition'' of A.J.Coleman. The representability conditions are formulated in…
We consider the problem of minimizing a composite convex function with two different access methods: an oracle, for which we can evaluate the value and gradient, and a structured function, which we access only by solving a convex…
Density functional theory has been an essential analysis tool for both theoretical and experimental chemists since accurate hybrid functionals were developed. Here we propose a local hybrid method derived from the optimized effective…
Discretizing an analytic function on a uniform real-space grid is often done via a straightforward collocation method. This is ubiquitous in all areas of computational physics and quantum chemistry. An example in Density Functional Theory…
Many physical questions in fluid dynamics can be recast in terms of norm constrained optimisation problems; which in-turn, can be further recast as unconstrained problems on spherical manifolds. Due to the nonlinearities of the governing…
Using the optimized effective potential method in conjunction with the semi-analytical approximation due to Krieger, Li and Iafrate, we have performed fully self-consistent exact exchange-only density-functional calculations for diatomic…
We propose a direct mesh-free method for performing topology optimization by integrating a density field approximation neural network with a displacement field approximation neural network. We show that this direct integration approach can…
This paper addresses the critical problem of co-optimizing the optimal locations for orbital depots and the sequence of in-space servicing for a satellite constellation. While most traditional studies used network optimization for this…