Reconstruction of Fine Scale Auroral Dynamics

We present a feasibility study for a high frame rate, short baseline auroral tomographic imaging system useful for estimating parametric variations in the precipitating electron number flux spectrum of dynamic auroral events. Of particular interest are auroral substorms, characterized by spatial variations of order 100 m and temporal variations of order 10 ms. These scales are thought to be produced by dispersive Alfvén waves in the near-Earth magnetosphere. The auroral tomography system characterized in this paper reconstructs the auroral volume emission rate to estimate the characteristic energy and location in the direction perpendicular to the geomagnetic field of peak electron precipitation flux using a distributed network of precisely synchronized ground-based cameras. As the observing baseline decreases, the tomographic inverse problem becomes highly ill-conditioned; as the sampling rate increases, the signal-to-noise ratio degrades and synchronization requirements become increasingly critical. Our approach to these challenges uses a physics-based auroral model to regularize the poorly-observed vertical dimension. Specifically, the vertical dimension is expanded in a low-dimensional basis consisting of eigenprofiles computed over the range of expected energies in the precipitating electron flux, while the horizontal dimension retains a standard orthogonal pixel basis. Simulation results show typical characteristic energy estimation error less than 30% for a 3 km baseline achievable within the confines of the Poker Flat Research Range, using GPS-synchronized Electron Multiplying CCD cameras with broad-band BG3 optical filters that pass prompt auroral emissions.National Science Foundation Atmosphere and Geospace Directorate, Grants 1216530, 123737

Refinement of molecular dynamics ensembles using experimental data and flexible forward models

A novel method combining maximum entropy principle, the Bayesian-inference of ensembles approach, and the optimization of empirical forward models is presented. Here we focus on the Karplus parameters for RNA systems, which relate the dihedral angles of $\gamma$, $\beta$, and the dihedrals in the sugar ring to the corresponding $^3J$-coupling signal between coupling protons. Extensive molecular simulations are performed on a set of RNA tetramers and hexamers and combined with available nucleic-magnetic-resonance data. Within the new framework, the sampled structural dynamics can be reweighted to match experimental data while the error arising from inaccuracies in the forward models can be corrected simultaneously and consequently does not leak into the reweighted ensemble. Carefully crafted cross-validation procedure and regularization terms enable obtaining transferable Karplus parameters. Our approach identifies the optimal regularization strength and new sets of Karplus parameters balancing good agreement between simulations and experiments with minimal changes to the original ensemble.Comment: Submitted to journal; added zenodo link; replaced fig. 3 with correct on

Variational quantum eigensolver with reduced circuit complexity

The variational quantum eigensolver (VQE) is one of the most promising algorithms to find eigenstates of a given Hamiltonian on noisy intermediate-scale quantum devices (NISQ). The practical realization is limited by the complexity of quantum circuits. Here we present an approach to reduce quantum circuit complexity in VQE for electronic structure calculations. Our ClusterVQE algorithm splits the initial qubit space into clusters which are further distributed on individual (shallower) quantum circuits. The clusters are obtained based on mutual information reflecting maximal entanglement between qubits, whereas inter-cluster correlation is taken into account via a new “dressed” Hamiltonian. ClusterVQE therefore allows exact simulation of the problem by using fewer qubits and shallower circuit depth at the cost of additional classical resources, making it a potential leader for quantum chemistry simulations on NISQ devices. Proof-of-principle demonstrations are presented for several molecular systems based on quantum simulators as well as IBM quantum devices

Equilibrium path and stability analysis of rigid origami using energy minimization of frame model

This paper presents a method of equilibrium path analysis and stability analysis of an equilibrium state for a rigid origami, which consists of rigid flat faces connected by straight crease lines (folding lines) and can be folded and unfolded without deformation of its faces. This property is well suited to the application to deployable structures and morphing building envelopes consisting of stiff panels. In this study, a frame model which consists of hinges and rigid frame members is used to model the kinematics of a rigid origami. Faces and crease lines of a rigid origami are represented by frame members and hinges, respectively. External loads are applied to the nodes of a frame model, and the displacements of some nodes are fixed. Small rotational stiffness proportional to the length of a crease line is assumed in each hinge to uniquely determine the equilibrium state, which is obtained by solving the optimization problem for minimizing the total potential energy under the conditions so that the displacements of the nodes and the members are compatible. The optimization problem is solved by the augmented Lagrangian method, and the positive definiteness of the Hessian of the augmented Lagrangian is investigated to determine the stability of the equilibrium state. Equilibrium path analyses are carried out and bifurcations of the equilibrium paths are investigated for examples with waterbomb patterns

Low-dimensional space modeling-based differential evolution for large scale global optimization problems

Large-Scale Global Optimization (LSGO) has been an active research field. Part of this interest is supported by its application to cutting-edge research such as Deep Learning, Big Data, and complex real-world problems such as image encryption, real-time traffic management, and more. However, the high dimensionality makes solving LSGO a significant challenge. Some recent research deal with the high dimensionality by mapping the optimization process to a reduced alternative space. Nonetheless, these works suffer from the changes in the search space topology and the loss of information caused by the dimensionality reduction. This paper proposes a hybrid metaheuristic, so-called LSMDE (Low-dimensional Space Modeling-based Differential Evolution), that uses the Singular Value Decomposition to build a low-dimensional search space from the features of candidate solutions generated by a new SHADE-based algorithm (GM-SHADE). GM-SHADE combines a Gaussian Mixture Model (GMM) and two specialized local algorithms: MTS-LS1 and L-BFGS-B, to promote a better exploration of the reduced search space. GMM mitigates the loss of information in mapping high-dimensional individuals to low-dimensional individuals. Furthermore, the proposal does not require prior knowledge of the search space topology, which makes it more flexible and adaptable to different LSGO problems. The results indicate that LSMDE is the most efficient method to deal with partially separable functions compared to other state-of-the-art algorithms and has the best overall performance in two of the three proposed experiments. Experimental results also show that the new approach achieves competitive results for non-separable and overlapping functions on the most recent test suite for LSGO problems

Gradient-based quantum optimal control on superconducting qubit systems

Quantum technologies are expected to help solve many of today's global challenges, revolutionizing several fields such as computing, sensing and secure communications. In this regard, the need for precise manipulation of the dynamics of a quantum system and its optimization has given rise to the field of quantum control theory. In the search for optimal controls, accurate derivatives are a possible method to traverse and ultimately converge in quantum optimization landscapes. In this work we study an efficient algorithm for computing analytically-exact derivatives by formulating the control problem in the basis that diagonalizes the control Hamiltonian and applying a specific Trotterized time propagation scheme. The method is numerically verified for a system of superconducting transmon qubits in the few- and many body regime using matrix product states. The comparison between the results obtained using an exact dynamics via Krylov subspace methods shows how the approximate dynamics ultimately sets a trade-off between computational complexity and quality of the final solutions.Quantum technologies are expected to help solve many of today's global challenges, revolutionizing several fields such as computing, sensing and secure communications. In this regard, the need for precise manipulation of the dynamics of a quantum system and its optimization has given rise to the field of quantum control theory. In the search for optimal controls, accurate derivatives are a possible method to traverse and ultimately converge in quantum optimization landscapes. In this work we study an efficient algorithm for computing analytically-exact derivatives by formulating the control problem in the basis that diagonalizes the control Hamiltonian and applying a specific Trotterized time propagation scheme. The method is numerically verified for a system of superconducting transmon qubits in the few- and many body regime using matrix product states. The comparison between the results obtained using an exact dynamics via Krylov subspace methods shows how the approximate dynamics ultimately sets a trade-off between computational complexity and quality of the final solutions

An introduction to continuous optimization for imaging

International audienceA large number of imaging problems reduce to the optimization of a cost function , with typical structural properties. The aim of this paper is to describe the state of the art in continuous optimization methods for such problems, and present the most successful approaches and their interconnections. We place particular emphasis on optimal first-order schemes that can deal with typical non-smooth and large-scale objective functions used in imaging problems. We illustrate and compare the different algorithms using classical non-smooth problems in imaging, such as denoising and deblurring. Moreover, we present applications of the algorithms to more advanced problems, such as magnetic resonance imaging, multilabel image segmentation, optical flow estimation, stereo matching, and classification

Modelos multiobjetivo para la planificación forestal en Galicia: un enfoque continuo

En esta tesis se presentan varios modelos multiobjetivo para la planificación de cortas en montes constituidos por rodales regulares monoespecíficos (los más habituales en Galicia), utilizando una formulación temporal continua que busca maximizar la rentabilidad económica y la renta constante en volumen en el primer turno y/o en el monte regulado. Para ello, se han diseñado nuevas métricas para medir esa constancia de rentas que permiten trabajar con variables de decisión continuas. Para la resolución de los problemas, se propone una estrategia que combina una técnica de escalarización (método de pesos) con un algoritmo de tipo gradiente (L-BFGS-B) que permite obtener el frente Pareto. Esto posibilita que el tomador de decisiones especifique sus preferencias con posterioridad al proceso de optimización, ya que dispone de toda la información sobre los costes de oportunidad que asume cuando elige una solución satisfactoria entre el conjunto de soluciones no dominadas del frente. Con el fin de analizar el rendimiento de la estrategia planteada, se comparan los resultados que proporciona con los obtenidos mediante el algoritmo evolutivo para optimización multiobjetivo NSGA-II. Para evaluar los modelos propuestos se usan varios montes de Eucalyptus globulus Labill. La formulación continua ha demostrado ser robusta en montes con distinto número de rodales y diferente estructura de edades, y ha proporcionado resultados mejores que los obtenidos con el enfoque combinatorio tradicional. Con respecto a la resolución de los problemas, la estrategia propuesta ha resultado claramente más eficiente que el algoritmo evolutivo, y tanto más eficaz cuanto mayor ha sido la dimensión del problema

Time-Varying Optimization and Its Application to Power System Operation

The main topic of this thesis is time-varying optimization, which studies algorithms that can track optimal trajectories of optimization problems that evolve with time. A typical time-varying optimization algorithm is implemented in a running fashion in the sense that the underlying optimization problem is updated during the iterations of the algorithm, and is especially suitable for optimizing large-scale fast varying systems. Motivated by applications in power system operation, we propose and analyze first-order and second-order running algorithms for time-varying nonconvex optimization problems. The first-order algorithm we propose is the regularized proximal primal-dual gradient algorithm, and we develop a comprehensive theory on its tracking performance. Specifically, we provide analytical results in terms of tracking a KKT point, and derive bounds for the tracking error defined as the distance between the algorithmic iterates and a KKT trajectory. We then provide sufficient conditions under which there exists a set of algorithmic parameters that guarantee that the tracking error bound holds. Qualitatively, the sufficient conditions for the existence of feasible parameters suggest that the problem should be "sufficiently convex" around a KKT trajectory to overcome the nonlinearity of the nonconvex constraints. The study of feasible algorithmic parameters motivates us to analyze the continuous-time limit of the discrete-time algorithm, which we formulate as a system of differential inclusions; results on its tracking performance as well as feasible and optimal algorithmic parameters are also derived. Finally, we derive conditions under which the KKT points for a given time instant will always be isolated so that bifurcations or merging of KKT trajectories do not happen. The second-order algorithms we develop are approximate Newton methods that incorporate second-order information. We first propose the approximate Newton method for a special case where there are no explicit inequality or equality constraints. It is shown that good estimation of second-order information is important for achieving satisfactory tracking performance. We also propose a specific version of the approximate Newton method based on L-BFGS-B that handles box constraints. Then, we propose two variants of the approximate Newton method that handle explicit inequality and equality constraints. The first variant employs penalty functions to obtain a modified version of the original problem, so that the approximate Newton method for the special case can be applied. The second variant can be viewed as an extension of the sequential quadratic program in the time-varying setting. Finally, we discuss application of the proposed algorithms to power system operation. We formulate the time-varying optimal power flow problem, and introduce partition of the decision variables that enables us to model the power system by an implicit power flow map. The implicit power flow map allows us to incorporate real-time feedback measurements naturally in the algorithm. The use of real-time feedback measurement is a central idea in real-time optimal power flow algorithms, as it helps reduce the computation burden and potentially improve robustness against model mismatch. We then present in detail two real-time optimal power flow algorithms, one based on the regularized proximal primal-dual gradient algorithm, and the other based on the approximate Newton method with the penalty approach