Gradient type optimization methods for electronic structure calculations

The density functional theory (DFT) in electronic structure calculations can be formulated as either a nonlinear eigenvalue or direct minimization problem. The most widely used approach for solving the former is the so-called self-consistent field (SCF) iteration. A common observation is that the convergence of SCF is not clear theoretically while approaches with convergence guarantee for solving the latter are often not competitive to SCF numerically. In this paper, we study gradient type methods for solving the direct minimization problem by constructing new iterations along the gradient on the Stiefel manifold. Global convergence (i.e., convergence to a stationary point from any initial solution) as well as local convergence rate follows from the standard theory for optimization on manifold directly. A major computational advantage is that the computation of linear eigenvalue problems is no longer needed. The main costs of our approaches arise from the assembling of the total energy functional and its gradient and the projection onto the manifold. These tasks are cheaper than eigenvalue computation and they are often more suitable for parallelization as long as the evaluation of the total energy functional and its gradient is efficient. Numerical results show that they can outperform SCF consistently on many practically large systems.Comment: 24 pages, 11 figures, 59 references, and 1 acknowledgement

Identification of Biological Regulatory Networks from Process Hitting models

International audienceQualitative formalisms offer a well-established alternative to the more tradi-tionally used differential equation models of Biological Regulatory Networks (BRNs). These formalisms led to numerous theoretical works and practical tools to understand emerging behaviors. The analysis of the dynamics of very large models is however a rather hard problem, which led us to previously in-troduce the Process Hitting framework (PH), which is a particular class of non-deterministic asynchronous automata network (or safe Petri nets). Its major advantage lies in the efficiency of several static analyses recently designed to assess dynamical properties, making it possible to tackle very large models. In this paper, we address the formal identification of qualitative models of BRNs from PH models. First, the inference of the Interaction Graph from a PH model summarizes the signed influences between the components that are effective for the dynamics. Second, we provide the inference of all René-Thomas models of BRNs that are compatible with a given PH. As the PH allows the specification of nondeterministic interactions between components, our inference emphasizes the ability of PH to deal with large BRNs with incomplete knowledge on interactions, where Thomas's approach fails because of the combinatorics of parameters. The inference of corresponding Thomas models is implemented using An-swer Set Programming, which allows in particular an efficient enumeration of (possibly numerous) compatible parametrizations

A Parallel-Oriented Language for Modeling Constraint-Based Solvers

International audienceThis paper presents the Parallel-Oriented Solver Language (POSL, pronounced " puzzle "): a new framework to build interconnected meta-heuristic based solvers working in parallel. The goal of this work is to obtain a framework to easily build solvers and reduce the developing effort, by providing a mechanism for reusing code from other solvers. The novelty of this approach lies in looking at solver as a set of components with specific goals, written in a parallel-oriented language based on operators. An interesting advantage of POSL is the possibility to share not only information, but also behaviors, allowing solvers modifications. POSL allows solver's components to be transferred and executed by other solvers. It provides an additional layer to dynamically define the connectivity between the solvers. The implementation of POSL remains a work in progress, therefore this paper will focus on POSL concepts only

Analyzing Large Network Dynamics with Process Hitting

In this chapter, we introduce the Process Hitting framework, which provides the methodology of constructing the most permissive dynamics and then using successive refinements to fine tune the model. We present static analysis methods designed to identify fixed points or answer successive reachability questions, and introduce the stochastic semantics of Process Hitting too