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The Stochastic and Physical Monitoring Systems (SPMS) has been an annual international conference since 2010 with the aim to bring together students and researchers with areas of interest related to the following topics:
The SPMS 2024 conference will be held at Sokol Dobřichovice,
Czech Republic from 20th to 24th of June, 2024.
The meeting is organized by the Group of Applied Mathematics and Stochastics (GAMS), Department of Mathematics, Czech Technical University in Prague. Follow us on Instagram.
Voluntary trip for those registered in time
Time may change depending on the weather and sports activities.
Acoustic Emission (AE) is a crucial non-destructive testing method that captures ultrasonic stress waves in materials, aiding in the detection of fractures and wear. This study highlights AE's role in material integrity and predictive maintenance. Employing a specialized setup from the Institute of Thermomechanics of the Czech Academy of Sciences, we used various AE sensors and a USB oscilloscope to monitor emissions during steel plate drilling. Data was analyzed with machine learning to classify drill bit dullness, demonstrating AE's potential in industrial applications. This contribution presents the methodologies, setup, and implications of AE in enhancing material science practices.
This contribution presents the results of the past year of our research, the main objective of which was to identify, implement, and compare deep learning methods for the recognition of acoustic emission signals. Two experiments were conducted to obtain relevant data for comparing these methods. Initially, five selected architectures designed to work
directly with 1D signals as input data are presented. These models are compared based on their performance in a classification task using the data from the experiments. Additionally, an adapted version of the best-performing Pooled Inception Time network is utilized in a regression task to predict continuous dependent variable. Subsequently, we focused on the problem of estimating the shape of the probability distribution on the Preisach-Mayergoyz space from resulting hysteresis curves. We employed the neural networks introduced in the first part to predict the shape of the distribution mixture.
The main topic of this paper is the application of $\phi$-divergence in the field of non-destructive testing. The $\phi$-divergence is applied both in the framework of signal parameters and as part of the classification method. The application of $\phi$-divergence is verified both in an acoustic emission experiment and in a scatterer classification experiment in a water tank. In the latter experiment the principle of time reversal was also used, which is of great importance in the framework of non-destructive testing.
Modeling the behavior of materials under cyclic plastic loading is a crucial topic in the engineering design process for various applications. Numerous constitutive models have been developed for this purpose. In this paper, we have selected a specific material model with 12 parameters that must be fitted to measured data. This results in a non-convex optimization problem with many local minima. Conventional approaches, such as random search combined with Nelder-Mead optimization, are not dependable. This paper presents the application of the non-gradient Tensor Train Optimization method and custom-designed neural networks for the task at hand. Both methods were extended with Nelder-Mead optimization and validated on synthetic data and measured experiments. The results show that both methods are comparable and outperform random search.
The nonlinear behavior of consolidated granular materials includes three distinct phenomena: classical nonlinearity, hysteresis, and slow dynamics. Despite the occurrence of these phenomena simultaneously, they have been studied separately, resulting in the development of independent theoretical models.
In our recent work, we have proposed the concept of non-equilibrium strain, which we have introduced into the classical acoustoelastic theory. This theory states that the relative velocity variation is proportional to the sum of the applied strain and the non-equilibrium strain: $\delta v_{ij}=\beta_{ij} \left(\varepsilon+\varepsilon_\mathrm{neq}\right).$
The non-equilibrium strain builds up as the material is subjected to loading, and slowly relaxes to zero as the applied strain is removed. We demonstrate that the non-equilibrium strain can be used to describe both slow dynamics and hysteresis. In fact, hysteresis can be seen as a consequence of slow dynamics.
The non-equilibrium strain can be expressed as a superposition of components with different relaxation times, resulting in a multirelaxation process with a given distribution.
A viscoelastic model for non-equilibrium strain is proposed, and it is demonstrated that short relaxation times are responsible for the cubic nonlinearity, moderate relaxation times cause hysteresis, and long relaxation times allow for the accumulation of velocity variation.
Finite mixtures of probability densities with components from exponential family serve as flexible parametric models of high-dimensional systems. However, with a few specialized exceptions, these dynamic models assume data-independent weights of mixture components. Their use is illogical and restricts the modelling applicability. The requirement for closeness with respect to conditioning, the basic learning operation, leads to a novel class of models: the mixture ratios. This work justifies them and shows their ability to model truly dynamic systems.
Computational and statistical techniques are imperative to experiments in physics. This presentation explores the potential applications of some computational methods. More specifically, I will focus on a recent ongoing project where we attempt to simulate the effect of cities on the surrounding environment mechanically, with the main aim being to study the extent of the effects of urban heat islands on surrounding temperature and how to limit such effects. As the project is still in its infancy where we do not have meaningful results, I will point out some places where computational and statistical techniques could be applied to further the project. Additionally, I will also mention some possibilities for similar pre-existing numerical simulations as future goals to complement our experiments[1]. This presentation will emphasise the importance of these mathematical techniques in these sorts of experiments in hopes to encourage the audience to get involved.
[1] K. Gunawardena, T. Kershaw, and K. Steemers, “Simulation pathway for estimating heat island influence on urban/suburban building space-conditioning loads and response to facade material changes,” Building and Environment, vol. 150, pp. 195–205, Mar. 2019, doi: https://doi.org/10.1016/j.buildenv.2019.01.006.
This contribution formulates the problem of portfolio management as a decision process and applies multivariate regression techniques on gathered real-world data. The aim is to determine whether this approach can yield a sufficiently accurate predictor for decision-making and later optimization.
Classical decision theory is in a strong conflict with the observed experimental data coming from cognitive and descriptive decision making research. This conflict yields different paradoxes and inconsistencies. It was shown that quantum-like approach to decision making solves these problems, but the reasons why it does so far stayed unknown.
This contribution presents new framework that i) introduces more general formalisation of decision making task ii) step-by-step shows, that under realistic assumptions a solution is found without prior definition of probability iii) shows quantum nature of uncertainty and claims that quantum models are inevitable for decision making.
The work addresses the issue of decreased utility of future rewards, referred to as discounting, while utilizing fully probabilistic design (FPD) of decision strategies. FPD obtains the optimal strategy for decision tasks using only probability distributions, which is its main asset. The standard way of solving decision tasks is provided by Markov decision processes (MDP), which FPD covers as a special case. Methods of solving discounted MDPs have already been introduced. However, the use of FPD might be advantageous when solving tasks with an unknown system model. Due to its probabilistic nature, FPD is able to obtain a more precise estimation of this model. After previously introducing discounting and system model estimation to FPD, the thesis now examines the effect of discounting on decision processes and its possible advantages when dealing with an unknown system model.
Recovering a source and an amount of an emitted substance from distant measurement is an ill-posed problem. In this contribution, two methods based on Bayes theorem will be compared on a realistic toy problem with microplastics. First of them is a Bayesian neural network pretrained to mimic a lognormal process and second one is hierarchical variational model, where the parameters of the posterior distribution are modeled by a convolutional neural network. Both these approaches allow to incorporate spatial dependency of the locations of the source and offer an estimate of uncertainty to assess the reliability of the method.
The presentation will cover the new 4D-STEM PNBD (Powder Nano Beam Diffraction) analytical method developed in collaboration with UTIA, UMCH and UPT. In the introduction we will explain the principle of the method itself, its advantages, importance and limitations. One of the major limitations is the low accelerating voltage of scanning electron microscopes, which results in heavily noisy diffractograms with a high degree of blur. We will discuss the possibility of using deconvolution algorithms to improve the quality of diffractograms, reduce the effect of noise and improve the overall crystallographic analysis. We will briefly introduce the deconvolution algorithms used and their principle. Furthermore, a number of methods for estimating the impulse response of an electron microscope will be presented. Existing results will be discussed and we will also briefly introduce the possibility of using segmentation neural networks for analysis, trained on synthetically generated data.
This research delves into the dispersion of point sets within a unit cube
$[0,1]^𝑑$, a measure of how well-distributed points are in a space. Building on the work of Hlawka and Niederreiter, we present improved lower bounds for minimal dispersion by constructing specific sets called restriction sets. Our approach involves analyzing test boxes, uncoverable sets, and cover-free families, leading to new bounds and insights into point distribution. Additionally, we introduce a generalized framework for restriction sets and uncoverable intersections, enhancing the understanding of high-dimensional integration. This research also has practical applications in data mining, particularly in exploring empty regions within datasets.
This presentation is about applications of potential theory. We delve into the use of quadratic forms on d-dimensional torus, emphasizing boundary conditions and the calculation of their minimal values through rigorous mathematical methods. Then we show the application of Feynman-Kac lemma and formulas within the context of potential theory, showcasing their utility in handling complex Gaussian models and perturbations.
Detecting fraudulent financial transactions is crucial for the financial industry, where traditional methods often fall short. This presentation introduces the complexities of fraud detection. We begin by addressing the challenges in fraud detection, followed by an overview of the dataset used for analysis. Finally, we compare the performance of three AI models - SVM, Random Forest and neural network. The results of these models are first analyzed separately and then compared with each other.
Time may change depending on the weather and sports activities.
The number of wildfires in Mediterranean countries is quite high but they are mainly concentrated around summer months. Due to seasonality, there are territories where the number of fires is zero in some months and is overdispersed in others. Zero-inflated negative binomial mixed models are adapted to this type of data because they allow to describe the patterns that explain both number of fires and its non-occurrence, as well as provide good prediction tools. In addition to model-based predictions, a parametric bootstrap method is applied for estimating mean squared errors and constructing prediction intervals. The statistical methodology and developed software are applied to model and predict number of wildfires in Spain between 2002 and 2015 by provinces and months.
This contribution presents a new statistical methodology for the small area estimation of the proportion of employed, unemployed and inactive people, and of unemployment rates. The novel empirical best and plug-in predictors are based on a multinomial mixed model that is fitted to unit-level data. Model parameters are estimated by maximum likelihood and mean squared errors by parametric bootstrap. A detailed application to real data from the first Spanish Labour Force Survey of 2021 is included, where the target is to map labour force indicators by province, sex and age group.
One-dimensional partice hopping with constrained variance is a well known model of Brownian motion and therefore the traditional particle diffusion. Model analysis is possible using the Central Limit Theorem (CLT) which produces Einstein formula. Another strategies of heavy tile hopping with discrete Pareto distribution can be studied by the Generalized CLT (GCLT). Doing the same using only Fourier transform and l'Hospital rule without CLT or GCLT is the main subject of presentation.
A novel computational approach is introduced as a robust alternative to Monte Carlo simulations for diffusive processes over fractal sets. Unlike stochastic methods, introduced constrained convolution schema (CCS) is a deterministic numerical algorithm tailored for grid-based set models, including random sets, ensuring reproducibility and computational efficiency. CCS is designed to yield the complete distribution of diffusion processes within a specified timeframe, offering comprehensive insights into the dynamics of diffusion phenomena. This contribution not only outlines the theoretical framework of CCS but also provides illustrative examples demonstrating its applicability across a diverse range of fractal sets. Through its deterministic nature and versatility, CCS emerges as a valuable tool for exploring diffusion phenomena in complex systems with enhanced precision and computational tractability.
Anomaly detection has numerous applications across various fields, including the space industry. A spacecraft must continuously monitor the health of its subsystems to detect non-nominal situations, but transmitting all telemetry data to the ground for analysis is not feasible due to limited transmission capacity and potential delays. Therefore, autonomous fault and anomaly detection is essential for timely response to unexpected events and ensuring the mission’s success. The conventional approach in Space Operations involves using Out-of-Limits (OOL) alarms for anomaly detection, which may prove insufficient in identifying and responding to complex anomalies or unforeseen novelties within the range of nominal values. This talk proposes a Machine Learning approach for anomaly/novelty detection embedded into the radiation-tolerant LEON 3 processor for the HERA mission.
The research focuses on the study of special variants of heterogeneous balance particle systems and their properties. Based on the knowledge gained, we will show analytically derived descriptions and characteristics for systems described by specifically chosen probability densities, while supporting the theoretical conclusions by numerical computation on synthetic data. We also apply the theory of heterogeneous particle balance systems to traffic data. We will emphasize the comparison of the differences in the analysis outputs for homogeneous and heterogeneous particle balance systems and discuss the advantages and disadvantages of the two approaches, respectively.
We investigate which distribution is most appropriate for modeling returns of cryptocurrencies. We study distribution of both unconditional returns and conditional returns. Four well-known heavy-tailed distributions Generalized Normal, Student t-, Normal Inverse Gaussian, Alpha stable and two recently suggested distributions and four GARCH models plain GARCH, range GARCH, TGARCH and EGARCH are studied. The results estimated for Bitcoin, Binance Coin, Ethereum, Solana and Ripple are unambiguous. For each cryptocurrency, the most appropriate distribution is the generalized normal distribution. This conclusion holds not only for returns, but also for conditional returns (residuals from a conditional mean model in the presence of heteroscedasticity), and for all considered volatility models. The most suitable GARCH model is the EGARCH model, and the range GARCH model performs very well in some cases.
Fast detector simulations have been of interest in the high energy physics community because of the increasing data intake. Among different deep learning techniques, transformer networks stand out thanks to the lack of inductive bias and their potential to learn complex data structures. We present a study on representation learning of transformers using the calorimeter showers and an image completion task with data preprocessing inspired by the Vision Transformer.
In high-energy physics, detecting rare events and computing their properties demand precise and reliable statistical methods, with uncertainty quantification being crucial. Today, most research relies on machine learning methods, where calibrating output probabilities can be complex. How can we then draw conclusions with the required five sigma statistical significance, which is essential for validating new findings?
The significance of calibrating the output probabilities of machine learning methods is immense. Accurate calibration ensures that predicted probabilities reflect the true likelihood of events, allowing for more robust decision-making and reliable interpretation of results. Poor calibration can lead to erroneous conclusions, particularly in high-stakes fields like high-energy physics where rare event detection is critical.
Conformal prediction methods are becoming a primary approach in both academia and industry to quantify uncertainty, calculate confidence intervals in regression tasks, and calibrate probabilities in classification tasks. This presentation will introduce the fundamental principles of conformal prediction and discuss data exchangeability and conformity scores.
This contribution introduces a new ML framework designed to distinguish between signal and background in a high-energy physics experiment. Employing a dataset processed through the Constrained Flood Fill Algorithm, this framework utilizes a multimodal approach which integrates modified ResNet models via a late fusion technique and implements a gating mechanism for each readout plane. Promising performance in signal discrimination by the late fusion model has been demonstrated, showing favorable comparisons with previous methods where preselection cuts were combined with Boosted Decision Trees (BDT), including features derived from a CNN. A principal advantage of the presented ML framework is its capacity to directly analyze raw detector outputs, eliminating the necessity for track reconstruction. This approach effectively tackles the challenge of incomplete association of particles with reconstructed tracks and the issue of background events being mis-reconstructed as signal events.
This paper investigates the consistency and efficiency of generalized Cramér–von Mises (GCM) minimum distance estimators in the context of statistical estimation, focusing particularly on the L$_1$ norm and the expected L$_1$ norm. It presents new inequality between Kolmogorov and generalized Cramér–von Mises distances, leading to the proof of consistency of Cramér–von Mises estimator with the convergence rate of $n^{-1/3}$, and consistency of GCM of the order of $n^{-p/2(p+q)}$ in the (expected) L$_1$ norm. Through theoretical analysis and computer simulations, the study explores practical application of these estimators across various distribution types, contributing to the understanding of minimum distance estimation in statistical analysis. The computer simulation also suggests further possible improvements of proven L$_1$ convergence rate of GCM up to $n^{-1/2}$.
We enrich the theory of φ-divergences and statistical distances. Specifically, we explore the property of robustness of our measures used, e.g., in defectoscopy classification tasks for constructing new spectral signal attributes or in newly designed classification tree algorithm. Since almost all datasets are surely contaminated by a certain portion of some kind of noise (electronics, experimental environment, non-homogenous material, other conditions), the resistance of algorithmic decisions against possible errors or outliers is crucial. We consider the general problem of discrimination of the true statistical model or of the true data source identification under the frame of minimum distance estimators (MDE). They are increasingly being used when the classical maximum likelihood theory breaks down and because they have better robustness properties. Specifically, the power-type I$_\alpha$ and blended Le Cam φ-divergences LC$_\beta$ under six data source distributions (Uniform, Normal, Logistic, Laplace, Cauchy, 3-parametric Weibull) will be applied for sample sizes n = 10, 20, 50, 120, 250. The simulation experiment deals with the discrimination/classification capability within a semi-parametric model treated under different types of data source distributions. This simulation is based on the previously developed software package IF-M for the evaluation of different types of AMD estimators adapted for our purposes on robustness in correspondence with proven theorems.