Related papers: Optimized Effective Potentials in Finite Basis Set…

The well-posedness of a class of optimal control problems is analysed, where the state equation couples a nonlinear degenerate Fokker-Planck equation with a system of Ordinary Differential Equations (ODEs). Such problems naturally arise as…

Recently, a new testing approach for response-adaptive clinical trials was proposed based on the allocation probabilities (AP) rather than the outcome data. While original work on the AP test focused on binary and normal endpoints and…

We suggest to include the density of electron charge explicitly in the electron potential of density functional theory, rather than implicitly via exchange-correlation functionals. The advantages of the approach are conceptual and…

We present an implementation of the optimised effective potential (OEP) scheme for the exact-exchange (EXX) and random phase approximation (RPA) energy functionals and apply these methods to a range of bulk materials. We calculate the…

Entropy is a central concept in physics, but can be challenging to calculate even for systems that are easily simulated. This is exacerbated out of equilibrium, where generally little is known about the distribution characterizing simulated…

In the context of functional data analysis, probability density functions as non-negative functions are characterized by specific properties of scale invariance and relative scale which enable to represent them with the unit integral…

Inverse Kohn-Sham (iKS) problems are needed to fully understand the one-to-one mapping between densities and potentials on which Density Functional Theory is based. They are also important to advance computational schemes that rely on…

Finite temperature density functional theory requires representations for the internal energy, entropy, and free energy as functionals of the local density field. A central formal difficulty for an orbital-free representation is…

Non-adiabatic effects play an important role in many chemical processes. In order to study the underlying non-adiabatic potential-energy surfaces (PESs), we present a locally-constrained density-functional theory approach, which enables us…

We derive an analytic connection between the screened self-consistent effective potential from density functional theory (DFT) and atomic effective pseudopotentials (AEPs). The motivation to derive AEPs is to address structures with…

Maximum entropy principle (MEP) offers an effective and unbiased approach to inferring unknown probability distributions when faced with incomplete information, while neural networks provide the flexibility to learn complex distributions…

This paper presents a meta-theory of the usage of the free energy principle (FEP) and examines its scope in the modelling of physical systems. We consider the so-called `map-territory fallacy' and the fallacious reification of model…

The Performance Estimation Problem (PEP) approach consists in computing worst-case performance bounds on optimization algorithms by solving an optimization problem: one maximizes an error criterion over all initial conditions allowed and…

Accurate estimation of parameters is paramount in developing high-fidelity models for complex dynamical systems. Model-based optimal experiment design (OED) approaches enable systematic design of dynamic experiments to generate input-output…

This article proposes an improved trajectory optimization approach for stochastic optimal control of dynamical systems affected by measurement noise by combining optimal control with maximum likelihood techniques to improve the reduction of…

The derivation of the state of the art tensorial versions of Fundamental Measure Theory (a form of classical Density Functional Theory for hard spheres) are re-examined in the light of the recently introduced concept of global stability of…

We consider the optimal control of a differential equation that involves the suprema of the state over some part of the history. In many applications, this non-smooth functional dependence is crucial for the successful modeling of…

A model is developed, based on the density functional perturbation theory and the inverse Kohn-Sham method, that can be used to improve relativistic nuclear energy density functionals towards an exact but unknown Kohn-Sham…

In the density functional (DF) theory of Kohn and Sham, the kinetic energy of the ground state of a system of noninteracting electrons in a general external field is calculated using a set of orbitals. Orbital free methods attempt to…

Several semilocal exchange potentials usually employed in the framework of density-functional theory (DFT) are tested and compared with their exact counterpart, the exchange Optimized Effective Potential (OEP), as applied to the…