arXiv subjects

Giacomo Borghi

Publications and source records attributed to Giacomo Borghi.

At least 37 records · Page 2Linked to original sources

arXiv2024

A particle consensus approach to solving nonconvex-nonconcave min-max problems

We propose a zero-order optimization method for sequential min-max problems based on two populations of interacting particles. The systems are coupled so that one population aims to solve the inner maximization problem, while the other aims to solve the outer minimization problem. The dynamics are characterized by a consensus-type interaction with additional stochasticity to promote exploration of the objective landscape. Without relying on convexity or concavity assumptions, we establish theoretical convergence guarantees of the algorithm via a suitable mean-field approximation of the particle systems. Numerical experiments illustrate the validity of the proposed approach. In particular, the algorithm is able to identify a global min-max solution, in contrast to gradient-based methods, which typically converge to possibly suboptimal stationary points.

math.OC↗

arXiv2024

Dynamics of measure-valued agents in the space of probabilities

Motivated by the development of dynamics in probability spaces, we propose a novel multi-agent dynamic of consensus type where each agent is a probability measure. The agents move instantaneously towards a weighted barycenter of the ensemble according to the 2-Wasserstein metric. We mathematically describe the evolution as a system of measure differential inclusions and show the existence of solutions for compactly supported initial data. Inspired by the consensus-based optimization, we apply the multi-agent system to solve a minimization problem over the space of probability measures. In the small numerical example, each agent is described by a particle approximation and aims to approximate a target measure.

math.AP↗

arXiv2023

Model predictive control strategies using consensus-based optimization

Model predictive control strategies require to solve in an sequential manner, many, possibly non-convex, optimization problems. In this work, we propose an interacting stochastic agent system to solve those problems. The agents evolve in pseudo-time and in parallel to the time-discrete state evolution. The method is suitable for non-convex, non-differentiable objective functions. The convergence properties are investigated through mean-field approximation of the time-discrete system, showing convergence in the case of additive linear control. We validate the proposed strategy by applying it to the control of a stirred-tank reactor non-linear system.

math.OC↗

arXiv2023

Characterization of iLGADs using soft X-rays

Experiments at synchrotron radiation sources and X-ray Free-Electron Lasers in the soft X-ray energy range ($250$eV--$2$keV) stand to benefit from the adaptation of the hybrid silicon detector technology for low energy photons. Inverse Low Gain Avalanche Diode (iLGAD) sensors provide an internal gain, enhancing the signal-to-noise ratio and allowing single photon detection below $1$keV using hybrid detectors. In addition, an optimization of the entrance window of these sensors enhances their quantum efficiency (QE). In this work, the QE and the gain of a batch of different iLGAD diodes with optimized entrance windows were characterized using soft X-rays at the Surface/Interface:Microscopy beamline of the Swiss Light Source synchrotron. Above $250$eV, the QE is larger than $55\%$ for all sensor variations, while the charge collection efficiency is close to $100\%$. The average gain depends on the gain layer design of the iLGADs and increases with photon energy. A fitting procedure is introduced to extract the multiplication factor as a function of the absorption depth of X-ray photons inside the sensors. In particular, the multiplication factors for electron- and hole-triggered avalanches are estimated, corresponding to photon absorption beyond or before the gain layer, respectively.

physics.ins-det↗

arXiv2023

Kinetic description and convergence analysis of genetic algorithms for global optimization

Genetic Algorithms (GA) are a class of metaheuristic global optimization methods inspired by the process of natural selection among individuals in a population. Despite their widespread use, a comprehensive theoretical analysis of these methods remains challenging due to the complexity of the heuristic mechanisms involved. In this work, relying on the tools of statistical physics, we take a first step towards a mathematical understanding of GA by showing how their behavior for a large number of individuals can be approximated through a time-discrete kinetic model. This allows us to prove the convergence of the algorithm towards a global minimum under mild assumptions on the objective function for a popular choice of selection mechanism. Furthermore, we derive a time-continuous model of GA, represented by a Boltzmann-like partial differential equation, and establish relations with other kinetic and mean-field dynamics in optimization. Numerical experiments support the validity of the proposed kinetic approximation and investigate the asymptotic configurations of the GA particle system for different selection mechanisms and benchmark problems.

math.OC↗

arXiv2023

Consensus based optimization with memory effects: random selection and applications

In this work we extend the class of Consensus-Based Optimization (CBO) metaheuristic methods by considering memory effects and a random selection strategy. The proposed algorithm iteratively updates a population of particles according to a consensus dynamics inspired by social interactions among individuals. The consensus point is computed taking into account the past positions of all particles. While sharing features with the popular Particle Swarm Optimization (PSO) method, the exploratory behavior is fundamentally different and allows better control over the convergence of the particle system. We discuss some implementation aspects which lead to an increased efficiency while preserving the success rate in the optimization process. In particular, we show how employing a random selection strategy to discard particles during the computation improves the overall performance. Several benchmark problems and applications to image segmentation and Neural Networks training are used to validate and test the proposed method. A theoretical analysis allows to recover convergence guarantees under mild assumptions on the objective function. This is done by first approximating the particles evolution with a continuous-in-time dynamics, and then by taking the mean-field limit of such dynamics. Convergence to a global minimizer is finally proved at the mean-field level.

math.OC↗

arXiv2022

Repulsion dynamics for uniform Pareto front approximation in multi-objective optimization problems

Scalarization allows to solve a multi-objective optimization problem by solving many single-objective sub-problems, uniquely determined by some parameters. In this work, we propose several adaptive strategies to select such parameters in order to obtain a uniform approximation of the Pareto front. This is done by introducing a heuristic dynamics where the parameters interact through a binary repulsive potential. The approach aims to minimize the associated energy potential which is used to quantify the diversity of the computed solutions. A stochastic component is also added to overcome non-optimal energy configurations. Numerical experiments show the validity of the proposed approach for bi- and tri-objectives problems with different Pareto front geometries.

math.OC↗

arXiv2022

Development of LGAD sensors with a thin entrance window for soft X-ray detection

We show the developments carried out to improve the silicon sensor technology for the detection of soft X-rays with hybrid X-ray detectors. An optimization of the entrance window technology is required to improve the quantum efficiency. The LGAD technology can be used to amplify the signal generated by the X-rays and to increase the signal-to-noise ratio, making single photon resolution in the soft X-ray energy range possible. In this paper, we report first results obtained from an LGAD sensor production with an optimized thin entrance window. Single photon detection of soft X-rays down to 452~eV has been demonstrated from measurements, with a signal-to-noise ratio better than 20.

physics.ins-det↗

arXiv2022

A Compensated Design of the LGAD Gain Layer

In this contribution, we present an innovative design of the Low-Gain Avalanche Diode (LGAD) gain layer, the p$^+$ implant responsible for the local and controlled signal multiplication. In the standard LGAD design, the gain layer is obtained by implanting $\sim$ 5E16/cm$^3$ atoms of an acceptor material, typically Boron or Gallium, in the region below the n$^{++}$ electrode. In our design, we aim at designing a gain layer resulting from the overlap of a p$^+$ and an n$^+$ implants: the difference between acceptor and donor doping will result in an effective concentration of about 5E16/cm$^3$, similar to standard LGADs. At present, the gain mechanism of LGAD sensors under irradiation is maintained up to a fluence of $\sim$ 1-2E15/cm$^2$, and then it is lost due to the acceptor removal mechanism. The new design will be more resilient to radiation, as both acceptor and donor atoms will undergo removal with irradiation, but their difference will maintain constant. The compensated design will empower the 4D tracking ability typical of the LGAD sensors well above 1E16/cm$^2$.

physics.ins-det↗

arXiv2022

An adaptive consensus based method for multi-objective optimization with uniform Pareto front approximation

In this work we are interested in stochastic particle methods for multi-objective optimization. The problem is formulated using parametrized, single-objective sub-problems which are solved simultaneously. To this end a consensus based multi-objective optimization method on the search space combined with an additional heuristic strategy to adapt parameters during the computations is proposed. The adaptive strategy aims to distribute the particles uniformly over the image space by using energy-based measures to quantify the diversity of the system. The resulting metaheuristic algorithm is mathematically analyzed using a mean-field approximation and convergence guarantees towards optimal points is rigorously proven. In addition, a gradient flow structure in the parameter space for the adaptive method is revealed and analyzed. Several numerical experiments shows the validity of the proposed stochastic particle dynamics and illustrate the theoretical findings.

math.OC↗

arXiv2022

Characterization of timing and spacial resolution of novel TI-LGAD structures before and after irradiation

The characterization of spacial and timing resolution of the novel Trench Isolated LGAD (TI-LGAD) technology is presented. This technology has been developed at FBK with the goal of achieving 4D pixels, where an accurate position resolution is combined in a single device with the precise timing determination for Minimum Ionizing Particles (MIPs). In the TI-LGAD technology, the pixelated LGAD pads are separated by physical trenches etched in the silicon. This technology can reduce the interpixel dead area, mitigating the fill factor problem. The TI-RD50 production studied in this work is the first one of pixelated TI-LGADs. The characterization was performed using a scanning TCT setup with an infrared laser and a $^{90}$Sr source setup.

physics.ins-det↗

arXiv2022

A consensus-based algorithm for multi-objective optimization and its mean-field description

We present a multi-agent algorithm for multi-objective optimization problems, which extends the class of consensus-based optimization methods and relies on a scalarization strategy. The optimization is achieved by a set of interacting agents exploring the search space and attempting to solve all scalar sub-problems simultaneously. We show that those dynamics are described by a mean-field model, which is suitable for a theoretical analysis of the algorithm convergence. Numerical results show the validity of the proposed method.

math.OC↗

arXiv2022

Binary interaction methods for high dimensional global optimization and machine learning

In this work we introduce a new class of gradient-free global optimization methods based on a binary interaction dynamics governed by a Boltzmann type equation. In each interaction the particles act taking into account both the best microscopic binary position and the best macroscopic collective position. In the mean-field limit we show that the resulting Fokker-Planck partial differential equations generalize the current class of consensus based optimization (CBO) methods. For the latter methods, convergence to the global minimizer can be shown for a large class of functions. Algorithmic implementations inspired by the well-known direct simulation Monte Carlo methods in kinetic theory are derived and discussed. Several examples on prototype test functions for global optimization are reported including applications to machine learning.

math.OC↗

arXiv2022

Optimization of the Gain Layer Design of Ultra-Fast Silicon Detectors

In the past few years, the need of measuring accurately the spatial and temporal coordinates of the particles generated in high-energy physics experiments has spurred a strong R\&D in the field of silicon sensors. Within these research activities, the so-called Ultra-Fast Silicon Detectors (UFSDs), silicon sensors optimized for timing based on the Low-Gain Avalanche Diode (LGAD) design, have been proposed and adopted by the CMS and ATLAS collaborations for their respective timing layers. The defining feature of the Ultra-Fast Silicon Detectors (UFSDs) is the internal multiplication mechanism, determined by the gain layer design. In this paper, the performances of several types of gain layers, measured with a telescope instrumented with a $^{90}$Sr $β$-source, are reported and compared. The measured sensors are produced by Fondazione Bruno Kessler (FBK) and Hamamatsu Photonics (HPK). The sensor yielding the best performance, both when new and irradiated, is an FBK 45\mum-thick sensor with a carbonated deep gain implant, where the carbon and the boron implants are annealed concurrently with a low thermal load. This sensor is able to achieve a time resolution of 40~ps up to a radiation fluence of~\fluence{2.5}{15}, delivering at least 5~fC of charge.

physics.ins-det↗

arXiv2021

Constrained consensus-based optimization

In this work we are interested in the construction of numerical methods for high dimensional constrained nonlinear optimization problems by particle-based gradient-free techniques. A consensus-based optimization (CBO) approach combined with suitable penalization techniques is introduced for this purpose. The method relies on a reformulation of the constrained minimization problem in an unconstrained problem for a penalty function and extends to the constrained settings the class of CBO methods. Exact penalization is employed and, since the optimal penalty parameter is unknown, an iterative strategy is proposed that successively updates the parameter based on the constrained violation. Using a mean-field description of the the many particle limit of the arising CBO dynamics, we are able to show convergence of the proposed method to the minimum for general nonlinear constrained problems. Properties of the new algorithm are analyzed. Several numerical examples, also in high dimensions, illustrate the theoretical findings and the good performance of the new numerical method.

math.OC↗

arXiv2021

The XGIS instrument on-board THESEUS: the detection plane and on-board electronics

The X and Gamma Imaging Spectrometer instrument on-board the THESEUS mission (selected by ESA in the framework of the Cosmic Vision M5 launch opportunity, currently in phase A) is based on a detection plane composed of several thousands of single active elements. Each element comprises a 4.5x4.5x30 mm 3 CsI(Tl) scintillator bar, optically coupled at both ends to Silicon Drift Detectors (SDDs). The SDDs acts both as photodetectors for the scintillation light and as direct X-ray sensors. In this paper the design of the XGIS detection plane is reviewed, outlining the strategic choices in terms of modularity and redundancy of the system. Results on detector-electronics prototypes are also described. Moreover, the design and development of the low-noise front-end electronics is presented, emphasizing the innovative architectural design based on custom-designed Application-Specific Integrated Circuits (ASICs).

astro-ph.IM↗

arXiv2021

The X/Gamma-ray Imaging Spectrometer (XGIS) on-board THESEUS: design, main characteristics, and concept of operation

THESEUS is one of the three missions selected by ESA as fifth medium class mission (M5) candidates in its Cosmic Vision science program, currently under assessment in a phase A study with a planned launch date in 2032. THESEUS is designed to carry on-board two wide and deep sky monitoring instruments for X/gamma-ray transients detection: a wide-field soft X-ray monitor with imaging capability (Soft X-ray Imager, SXI, 0.3 - 5 keV), a hard X-ray, partially-imaging spectroscopic instrument (X and Gamma Imaging Spectrometer, XGIS, 2 keV - 10 MeV), and an optical/near-IR telescope with both imaging and spectroscopic capability (InfraRed Telescope, IRT, 0.7 - 1.8 $μ$m). The spacecraft will be capable of performing fast repointing of the IRT to the error region provided by the monitors, thus allowing it to detect and localize the transient sources down to a few arcsec accuracy, for immediate identification and redshift determination. The prime goal of the XGIS will be to detect transient sources, with monitoring timescales down to milliseconds, both independently of, or following, up SXI detections, and identify the sources performing localisation at < 15 arcmin and characterize them over a broad energy band, thus providing also unique clues to their emission physics. The XGIS system consists of two independent but identical coded mask cameras, arranged to cover 2 steradians . The XGIS will exploit an innovative technology coupling Silicon Drift Detectors (SDD) with crystal scintillator bars and a very low-noise distributed front-end electronics (ORION ASICs), which will produce a position sensitive detection plane, with a large effective area over a huge energy band (from soft X-rays to soft gamma-rays) with timing resolution down to a few $μ$s.Here is presented an overview of the XGIS instrument design, its configuration, and capabilities.

astro-ph.IM↗

arXiv2018

The enhanced X-ray Timing and Polarimetry mission - eXTP

In this paper we present the enhanced X-ray Timing and Polarimetry mission - eXTP. eXTP is a space science mission designed to study fundamental physics under extreme conditions of density, gravity and magnetism. The mission aims at determining the equation of state of matter at supra-nuclear density, measuring effects of QED, and understanding the dynamics of matter in strong-field gravity. In addition to investigating fundamental physics, eXTP will be a very powerful observatory for astrophysics that will provide observations of unprecedented quality on a variety of galactic and extragalactic objects. In particular, its wide field monitoring capabilities will be highly instrumental to detect the electro-magnetic counterparts of gravitational wave sources. The paper provides a detailed description of: (1) the technological and technical aspects, and the expected performance of the instruments of the scientific payload; (2) the elements and functions of the mission, from the spacecraft to the ground segment.

astro-ph.IM↗