An overview of neighbourhood search metaheuristics

This paper gives details of the steps needed to undertake neighbourhood search for a combinatorial optimization problem. The main variations are briefly described and pointers for future research briefly discussed. Throughout there is extensive referencing to some of the most important publications in the are

Adiabatic approaches to non-equilibrium systems: Topology, Optimization, and Learning

Non-equilibrium phenomena in quantum physics are ubiquitous in current research because of their extremely rich phenomenology. Among them, adiabatic processes are particularly interesting because they connect two of the cornerstone of modern condensed matter theory: topological phases of matter and quantum information. Indeed with adiabatic periodic driving, it is possible to engineer exotic non-equilibrium phases with tunable topological properties, which are of great interest for both fundamental research and future quantum technologies. Adiabatic processes can also be used to implement optimization processes on quantum hardware and lie at the basis of hybrid quantum-classical algorithms that are extremely promising for near-term quantum devices. In this thesis, I focus on these two aspects of adiabatic dynamics in quantum systems. In the first part, I investigate the robustness of topological phases, arising in periodically driven systems, with respect to the driving protocol and disorder. In particular, I show that quantized transport and Anderson localization coexist in one-dimensional systems displaying Thouless pumping, because of a delocalization-localization transition in the Floquet spectrum. This transition is linked to the topological nature of the adiabatic driving and disappears if the phase is trivial in the clean limit. In the second part, I study one of the most popular hybrid optimization method, the quantum approximate optimization algorithm (QAOA). I show that QAOA can tackle the first-order phase transition arising in the infinite range p-spin model with polynomial resources, in stark contrast with adiabatic quantum computation, which requires exponentially long evolution time to reach similar performances. Finally, I present an approach to QAOA based on reinforcement learning (RL). Interestingly, the RL agent automatically adopts strategies that converge towards optimal adiabatic schedules and that can be easily transferred between systems with different sizes, even in the presence of disorder

The simulated tempering method in the infinite switch limit with adaptive weight learning

We investigate the theoretical foundations of the simulated tempering method and use our findings to design efficient algorithms. Employing a large deviation argument first used for replica exchange molecular dynamics [Plattner et al., J. Chem. Phys. 135:134111 (2011)], we demonstrate that the most efficient approach to simulated tempering is to vary the temperature infinitely rapidly. In this limit, we can replace the equations of motion for the temperature and physical variables by averaged equations for the latter alone, with the forces rescaled according to a position-dependent function defined in terms of temperature weights. The averaged equations are similar to those used in Gao's integrated-over-temperature method, except that we show that it is better to use a continuous rather than a discrete set of temperatures. We give a theoretical argument for the choice of the temperature weights as the reciprocal partition function, thereby relating simulated tempering to Wang-Landau sampling. Finally, we describe a self-consistent algorithm for simultaneously sampling the canonical ensemble and learning the weights during simulation. This algorithm is tested on a system of harmonic oscillators as well as a continuous variant of the Curie-Weiss model, where it is shown to perform well and to accurately capture the second-order phase transition observed in this model

Accelerated sampling schemes for high dimensional systems

In this thesis we discuss accelerated sampling schemes for high dimensional systems, for example molecular dynamics (MD). The development of these methods is fundamental to the effective study of a large class of problems, for which traditional methods converge slowly to the system’s underlying invariant probability distribution. Due to the complexity of the landscape defined by an energy function (or, in statistical models, the log likelihood of the target probability density), the exploration of the probability distribution is severely restricted. This can have detrimental effects on the conclusions drawn from numerical experiments when potentially important states and solutions are absent in the examination of the results as a consequence of poor sampling. The aim of accelerated sampling schemes is to enhance the exploration of the invariant measure by improving the rate of convergence to it. In this work, we first focus our attention on numerical methods based on canonical sampling by studying Langevin dynamics, for which the convergence is accelerated by extending the phase-space. We introduce a scheme based on simulated tempering which makes temperature into a dynamical variable and allows switching the temperature up or down during the exploration in such a way that the target probability distribution can be easily obtained from the extended distribution. We show that this scheme is optimal when operated in the infinite switch limit. We discuss the limitations of this method and demonstrate the excellent exploratory properties of it for a moderately complicated biomolecule, alanine-12. Next, we derive a novel approach to constant pressure simulation that forms the basis for a family of pure Langevin barostats. We demonstrate the excellent numerical performance of Lie-Trotter splitting schemes for these systems and the superior accuracy and precision of the simultaneous temperature and pressure control in comparison to currently available schemes. The scientific importance of this method lies in the ability to control the simulation and to make better predictions for applications in both materials modelling and drug design. We demonstrate this method in simulations of state transitions in crystalline materials using the “Mercedes Benz” potential. In a final contribution, we extend the infinite switch schemes to incorporate a general class of collective variables. In particular this allows for tempering in both temperature and pressure when combined with our new barostat. We conclude this thesis by presenting a numerical study of the computational prospects of these methods

Deriving Protein Structures Efficiently by Integrating Experimental Data into Biomolecular Simulations

Proteine sind molekulare Nanomaschinen in biologischen Zellen. Sie sind wesentliche Bausteine aller bekannten Lebensformen, von Einzellern bis hin zu Menschen, und erfüllen vielfältige Funktionen, wie beispielsweise den Sauerstofftransport im Blut oder als Bestandteil von Haaren. Störungen ihrer physiologischen Funktion können jedoch schwere degenerative Krankheiten wie Alzheimer und Parkinson verursachen. Die Entwicklung wirksamer Therapien für solche Proteinfehlfaltungserkrankungen erfordert ein tiefgreifendes Verständnis der molekularen Struktur und Dynamik von Proteinen. Da Proteine aufgrund ihrer lichtmikroskopisch nicht mehr auflösbaren Größe nur indirekt beobachtet werden können, sind experimentelle Strukturdaten meist uneindeutig. Dieses Problem lässt sich in silico mittels physikalischer Modellierung biomolekularer Dynamik lösen. In diesem Feld haben sich datengestützte Molekulardynamiksimulationen als neues Paradigma für das Zusammenfügen der einzelnen Datenbausteine zu einem schlüssigen Gesamtbild der enkodierten Proteinstruktur etabliert. Die Strukturdaten werden dabei als integraler Bestandteil in ein physikbasiertes Modell eingebunden. In dieser Arbeit untersuche ich, wie sogenannte strukturbasierte Modelle verwendet werden können, um mehrdeutige Strukturdaten zu komplementieren und die enthaltenen Informationen zu extrahieren. Diese Modelle liefern eine effiziente Beschreibung der aus der evolutionär optimierten nativen Struktur eines Proteins resultierenden Dynamik. Mithilfe meiner systematischen Simulationsmethode XSBM können biologische Kleinwinkelröntgenstreudaten mit möglichst geringem Rechenaufwand als physikalische Proteinstrukturen interpretiert werden. Die Funktionalität solcher datengestützten Methoden hängt stark von den verwendeten Simulationsparametern ab. Eine große Herausforderung besteht darin, experimentelle Informationen und theoretisches Wissen in geeigneter Weise relativ zueinander zu gewichten. In dieser Arbeit zeige ich, wie die entsprechenden Simulationsparameterräume mit Computational-Intelligence-Verfahren effizient erkundet und funktionale Parameter ausgewählt werden können, um die Leistungsfähigkeit komplexer physikbasierter Simulationstechniken zu optimieren. Ich präsentiere FLAPS, eine datengetriebene metaheuristische Optimierungsmethode zur vollautomatischen, reproduzierbaren Parametersuche für biomolekulare Simulationen. FLAPS ist ein adaptiver partikelschwarmbasierter Algorithmus inspiriert vom Verhalten natürlicher Vogel- und Fischschwärme, der das Problem der relativen Gewichtung verschiedener Kriterien in der multivariaten Optimierung generell lösen kann. Neben massiven Fortschritten in der Verwendung von künstlichen Intelligenzen zur Proteinstrukturvorhersage ermöglichen leistungsoptimierte datengestützte Simulationen detaillierte Einblicke in die komplexe Beziehung von biomolekularer Struktur, Dynamik und Funktion. Solche computergestützten Methoden können Zusammenhänge zwischen den einzelnen Puzzleteilen experimenteller Strukturinformationen herstellen und so unser Verständnis von Proteinen als den Grundbausteinen des Lebens vertiefen

Predicting Structure-Property Relationships in Polymers through the Development of Thermodynamically Consistent Coarse-Grained Molecular Models

abstract: Improved knowledge connecting the chemistry, structure, and properties of polymers is necessary to develop advanced materials in a materials-by-design approach. Molecular dynamics (MD) simulations can provide tremendous insight into how the fine details of chemistry, molecular architecture, and microstructure affect many physical properties; however, they face well-known restrictions in their applicable temporal and spatial scales. These limitations have motivated the development of computationally-efficient, coarse-grained methods to investigate how microstructural details affect thermophysical properties. In this dissertation, I summarize my research work in structure-based coarse-graining methods to establish the link between molecular-scale structure and macroscopic properties of two different polymers. Systematically coarse-grained models were developed to study the viscoelastic stress response of polyurea, a copolymer that segregates into rigid and viscous phases, at time scales characteristic of blast and impact loading. With the application of appropriate scaling parameters, the coarse-grained models can predict viscoelastic properties with a speed up of 5-6 orders of magnitude relative to the atomistic MD models. Coarse-grained models of polyethylene were also created to investigate the thermomechanical material response under shock loading. As structure-based coarse-grained methods are generally not transferable to states different from which they were calibrated at, their applicability for modeling non-equilibrium processes such as shock and impact is highly limited. To address this problem, a new model is developed that incorporates many-body interactions and is calibrated across a range of different thermodynamic states using a least square minimization scheme. The new model is validated by comparing shock Hugoniot properties with atomistic and experimental data for polyethylene. Lastly, a high fidelity coarse-grained model of polyethylene was constructed that reproduces the joint-probability distributions of structural variables such as the distributions of bond lengths and bond angles between sequential coarse-grained sites along polymer chains. This new model accurately represents the structure of both the amorphous and crystal phases of polyethylene and enabling investigation of how polymer processing such as cold-drawing and bulk crystallization affect material structure at significantly larger time and length scales than traditional molecular simulations.Dissertation/ThesisDoctoral Dissertation Mechanical Engineering 201

Understanding the Nanotube Growth Mechanism: A Strategy to Control Nanotube Chirality during Chemical Vapor Deposition Synthesis

For two decades, single-wall carbon nanotubes (SWCNTs) have captured the attention of the research community, and become one of the flagships of nanotechnology. Due to their remarkable electronic and optical properties, SWCNTs are prime candidates for the creation of novel and revolutionary electronic, medical, and energy technologies. However, a major stumbling block in the exploitation of nanotube-based technologies is the lack of control of nanotube structure (chirality) during synthesis, which is intimately related to the metallic or semiconductor character of the nanotube. Incomplete understanding of the nanotube growth mechanism hinders a rationale and cost-efficient search of experimental conditions that give way to structural (chiral) control. Thus, computational techniques such as density functional theory (DFT), and reactive molecular dynamics (RMD) are valuable tools that provide the necessary theoretical framework to guide the design of experiments. The nanotube chirality is determined by the helicity of the nanotube and its diameter. DFT calculations show that once a small nanotube 'seed' is nucleated, growth proceeds faster if the seed corresponds to a high chiral angle nanotube. Thus, a strategy to gain control of the nanotube structure during chemical vapor deposition synthesis must focus on controlling the structure of the nucleated nanotube seeds. DFT and RMD simulations demonstrate the viability of using the structures of catalyst particles over which nanotube growth proceeds as templates guiding nanotube growth toward desired chiralities. This effect occurs through epitaxial effects between the nanocatalyst and the nanotube growing on it. The effectiveness of such effects has a non-monotonic relationship with the size of the nanocatalyst, and its interaction with the support, and requires fine-tuning reaction conditions for its exploitation. RMD simulations also demonstrate that carbon bulk-diffusion and nanoparticle supersaturation are not needed to promote nanotube growth, hence reaction conditions that increase nanoparticle stability, but reduce carbon solubility, may be explored to achieve nanotube templated growth of desired chiralities. The effect of carbon dissolution was further demonstrated through analyses of calculated diffusion coefficients. The metallic nanocatalyst was determined to be in viscous solid state throughout growth, but with a less solid character during the induction/nucleation stage

Unsupervised inference methods for protein sequence data

L'abstract è presente nell'allegato / the abstract is in the attachmen

Out of equilibrium Statistical Physics of learning

In the study of hard optimization problems, it is often unfeasible to achieve a full analytic control on the dynamics of the algorithmic processes that find solutions efficiently. In many cases, a static approach is able to provide considerable insight into the dynamical properties of these algorithms: in fact, the geometrical structures found in the energetic landscape can strongly affect the stationary states and the optimal configurations reached by the solvers. In this context, a classical Statistical Mechanics approach, relying on the assumption of the asymptotic realization of a Boltzmann Gibbs equilibrium, can yield misleading predictions when the studied algorithms comprise some stochastic components that effectively drive these processes out of equilibrium. Thus, it becomes necessary to develop some intuition on the relevant features of the studied phenomena and to build an ad hoc Large Deviation analysis, providing a more targeted and richer description of the geometrical properties of the landscape. The present thesis focuses on the study of learning processes in Artificial Neural Networks, with the aim of introducing an out of equilibrium statistical physics framework, based on the introduction of a local entropy potential, for supporting and inspiring algorithmic improvements in the field of Deep Learning, and for developing models of neural computation that can carry both biological and engineering interest

Multiscale Simulations of Intrinsically Disordered Proteins

Intrinsically disordered proteins (IDPs) lack stable secondary and/or tertiary structures under physiological conditions. The have now been recognized to play important roles in numerous biological processes, particularly cellular signaling and regulation. Mutation of IDPs are frequently associated with human diseases, such as cancers and neuron degenerative diseases. Therefore, it is important to understand the structure, dynamics, and interactions of IDPs, so as to establish the mechanistic basis of how intrinsic disorder mediates versatile functions and how such mechanisms may fail in human diseases. However, the heterogeneous structural ensembles of IDPs are not amenable to high resolution characterization solely through experimental measurements, and molecular modelling and simulation are required to study IDP structures, dynamics, and interactions at the atomistic levels. Here, we first applied the state-of-the-art explicit solvent atomistic simulations to an anti-apoptotic protein Bcl-xL and demonstrated how inherent structural disorder may provide a physical basis of protein regulated unfolding in signaling transduction. We have also constructed a series of efficient coarse-grained models to directly simulate the interactions between IDPs and unveiled how the preexisting structural elements accelerate binding of ACTR to NCBD by promoting efficient folding upon encounter. These studies shed important light on how IDPs perform functions in the cellular regulatory network, but also reveal the necessity of new sampling techniques for more efficient simulations of IDPs. We have thus developed a novel sampling technique, called multiscale enhanced sampling (MSES). MSES couples the atomistic model with coarse-grained ones, to accelerate the sampling of atomistic conformational space. Bias from coupling to a coarse-grained model can be removed using Hamiltonian replica exchange. To achieve the best possible efficiency of MSES simulations, we have developed a new hybrid resolution protein model that could capture the essential features of IDP structures, so as to generate local and long-range fluctuations that are largely consistent with those at the atomistic level. We have also developed an advanced replica exchange protocol, to allow the fast conformational transitions observed in the coupled conditions to be rapidly exchanged to the unbiased limit. Application of these strategies to characterize the structural ensembles of a few non-trivial IDPs shows that faster convergence rate can be achieved, demonstrating the great potential of MSES for atomistic simulations of larger and more complex IDPs