Search

Regression analysis is used for prediction and to understand the effect of independent variables on dependent variables. Symbolic regression (SR) automates the search for non-linear regression models, delivering a set of hypotheses that balances accuracy with the possibility to understand the phenomena. Many SR implementations return a Pareto front allowing the choice of the best trade-off. However, this hides alternatives that are close to non-domination, limiting these choices. Equality graphs (e-graphs) allow to represent large sets of expressions compactly by efficiently handling duplicated parts occurring in multiple expressions. E-graphs allow to store and query all SR solution candidates visited in one or multiple GP runs efficiently and open the possibility to analyse much larger sets of SR solution candidates. We introduce rEGGression, a tool using e-graphs to enable the exploration of a large set of symbolic expressions which provides querying, filtering, and pattern matching features creating an interactive experience to gain insights about SR models. The main highlight is its focus in the exploration of the building blocks found during the search that can help the experts to find insights about the studied phenomena.This is possible by exploiting the pattern matching capability of the e-graph data structure., Comment: 9 pages, 4 figures, 2 tables

The search for symbolic regression models with genetic programming (GP) has a tendency of revisiting expressions in their original or equivalent forms. Repeatedly evaluating equivalent expressions is inefficient, as it does not immediately lead to better solutions. However, evolutionary algorithms require diversity and should allow the accumulation of inactive building blocks that can play an important role at a later point. The equality graph is a data structure capable of compactly storing expressions and their equivalent forms allowing an efficient verification of whether an expression has been visited in any of their stored equivalent forms. We exploit the e-graph to adapt the subtree operators to reduce the chances of revisiting expressions. Our adaptation, called eggp, stores every visited expression in the e-graph, allowing us to filter out from the available selection of subtrees all the combinations that would create already visited expressions. Results show that, for small expressions, this approach improves the performance of a simple GP algorithm to compete with PySR and Operon without increasing computational cost. As a highlight, eggp was capable of reliably delivering short and at the same time accurate models for a selected set of benchmarks from SRBench and a set of real-world datasets., Comment: 10 pages, 5 figures, 5 tables

Symbolic regression is a machine learning method with the goal to produce interpretable results. Unlike other machine learning methods such as, e.g. random forests or neural networks, which are opaque, symbolic regression aims to model and map data in a way that can be understood by scientists. Recent advancements, have attempted to bridge the gap between these two fields; new methodologies attempt to fuse the mapping power of neural networks and deep learning techniques with the explanatory power of symbolic regression. In this paper, we examine these new emerging systems and test the performance of an end-to-end transformer model for symbolic regression versus the reigning traditional methods based on genetic programming that have spearheaded symbolic regression throughout the years. We compare these systems on novel datasets to avoid bias to older methods who were improved on well-known benchmark datasets. Our results show that traditional GP methods as implemented e.g., by Operon still remain superior to two recently published symbolic regression methods.

We analyse the search behaviour of genetic programming for symbolic regression in practically relevant but limited settings, allowing exhaustive enumeration of all solutions. This enables us to quantify the success probability of finding the best possible expressions, and to compare the search efficiency of genetic programming to random search in the space of semantically unique expressions. This analysis is made possible by improved algorithms for equality saturation, which we use to improve the Exhaustive Symbolic Regression algorithm; this produces the set of semantically unique expression structures, orders of magnitude smaller than the full symbolic regression search space. We compare the efficiency of random search in the set of unique expressions and genetic programming. For our experiments we use two real-world datasets where symbolic regression has been used to produce well-fitting univariate expressions: the Nikuradse dataset of flow in rough pipes and the Radial Acceleration Relation of galaxy dynamics. The results show that genetic programming in such limited settings explores only a small fraction of all unique expressions, and evaluates expressions repeatedly that are congruent to already visited expressions., Comment: This is an extended version of the article submitted to Parallel Problem Solving from Nature (PPSN) Conference 2024

Computing the matter power spectrum, $P(k)$, as a function of cosmological parameters can be prohibitively slow in cosmological analyses, hence emulating this calculation is desirable. Previous analytic approximations are insufficiently accurate for modern applications, so black-box, uninterpretable emulators are often used. We utilise an efficient genetic programming based symbolic regression framework to explore the space of potential mathematical expressions which can approximate the power spectrum and $\sigma_8$. We learn the ratio between an existing low-accuracy fitting function for $P(k)$ and that obtained by solving the Boltzmann equations and thus still incorporate the physics which motivated this earlier approximation. We obtain an analytic approximation to the linear power spectrum with a root mean squared fractional error of 0.2% between $k = 9\times10^{-3} - 9 \, h{\rm \, Mpc^{-1}}$ and across a wide range of cosmological parameters, and we provide physical interpretations for various terms in the expression. Our analytic approximation is 950 times faster to evaluate than camb and 36 times faster than the neural network based matter power spectrum emulator BACCO. We also provide a simple analytic approximation for $\sigma_8$ with a similar accuracy, with a root mean squared fractional error of just 0.1% when evaluated across the same range of cosmologies. This function is easily invertible to obtain $A_{\rm s}$ as a function of $\sigma_8$ and the other cosmological parameters, if preferred. It is possible to obtain symbolic approximations to a seemingly complex function at a precision required for current and future cosmological analyses without resorting to deep-learning techniques, thus avoiding their black-box nature and large number of parameters. Our emulator will be usable long after the codes on which numerical approximations are built become outdated., Comment: 9 pages, 5 figures. Accepted for publication in A&A

People with diabetes must carefully monitor their blood glucose levels, especially after eating. Blood glucose regulation requires a proper combination of food intake and insulin boluses. Glucose prediction is vital to avoid dangerous post-meal complications in treating individuals with diabetes. Although traditional methods, such as artificial neural networks, have shown high accuracy rates, sometimes they are not suitable for developing personalised treatments by physicians due to their lack of interpretability. In this study, we propose a novel glucose prediction method emphasising interpretability: Interpretable Sparse Identification by Grammatical Evolution. Combined with a previous clustering stage, our approach provides finite difference equations to predict postprandial glucose levels up to two hours after meals. We divide the dataset into four-hour segments and perform clustering based on blood glucose values for the twohour window before the meal. Prediction models are trained for each cluster for the two-hour windows after meals, allowing predictions in 15-minute steps, yielding up to eight predictions at different time horizons. Prediction safety was evaluated based on Parkes Error Grid regions. Our technique produces safe predictions through explainable expressions, avoiding zones D (0.2% average) and E (0%) and reducing predictions on zone C (6.2%). In addition, our proposal has slightly better accuracy than other techniques, including sparse identification of non-linear dynamics and artificial neural networks. The results demonstrate that our proposal provides interpretable solutions without sacrificing prediction accuracy, offering a promising approach to glucose prediction in diabetes management that balances accuracy, interpretability, and computational efficiency.

Reconfigurable Intelligent Surfaces (RIS) have been identified as a potential ingredient to enhance the performance of contemporary wireless communication and sensing systems. Yet, most of the existing devices are either costly or not available for reproduction. To close this gap, a Reconfigurable Intelligent Surface for the frequency range of 5 GHz WiFi is presented in this work. We describe the designed unit cell, which is optimized for the full frequency range of 5.15 to 5.875 GHz. Standard FR4 substrate is used for cost optimization. The measured reflection coefficient of a rectangular RIS prototype with 256 elements is used for RF performance evaluation. Fabrication data and firmware source code are made open source, which makes RIS more available in real measurement setups.

Channel Reciprocity-based Key Generation (CRKG) exploits reciprocal channel randomness to establish shared secret keys between wireless terminals. This new security technique is expected to complement existing cryptographic techniques for secret key distribution of future wireless networks. In this paper, we present a new attack, reconfigurable intelligent surface (RIS) jamming, and show that an attacker can prevent legitimate users from agreeing on the same key by deploying a malicious RIS to break channel reciprocity. Specifically, we elaborate on three examples to implement the RIS jamming attack: Using active nonreciprocal circuits, performing time-varying controls, and reducing the signal-to-noise ratio. The attack effect is then studied by formulating the secret key rate with a relationship to the deployment of RIS. To resist such RIS jamming attacks, we propose a countermeasure that exploits wideband signals for multipath separation. The malicious RIS path is distinguished from all separated channel paths, and thus the countermeasure is referred to as contaminated path removal-based CRKG(CRP-CRKG). We present simulation results, showing that legitimate users under RIS jamming are still able to generate secret keys from the remaining paths. We also experimentally demonstrate the RIS jamming attack by using commodity Wi-Fi devices in conjunction with a fabricated RIS prototype. In our experiments, we were able to increase the average bit disagreement ratio (BDR) of raw secret keys by 20%. Further, we successfully demonstrate the proposed CRP-CRKG countermeasure to tackle RIS jamming in wideband systems as long as the source of randomness and the RIS propagation paths are separable., Comment: 15 pages, 14 figures

We describe an approach for empirical modeling of steel phase kinetics based on symbolic regression and genetic programming. The algorithm takes processed data gathered from dilatometer measurements and produces a system of differential equations that models the phase kinetics. Our initial results demonstrate that the proposed approach allows to identify compact differential equations that fit the data. The model predicts ferrite, pearlite and bainite formation for a single steel type. Martensite is not yet included in the model. Future work shall incorporate martensite and generalize to multiple steel types with different chemical compositions., Comment: 24th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC 2022)

Describing dynamic medical systems using machine learning is a challenging topic with a wide range of applications. In this work, the possibility of modeling the blood glucose level of diabetic patients purely on the basis of measured data is described. A combination of the influencing variables insulin and calories are used to find an interpretable model. The absorption speed of external substances in the human body depends strongly on external influences, which is why time-shifts are added for the influencing variables. The focus is put on identifying the best timeshifts that provide robust models with good prediction accuracy that are independent of other unknown external influences. The modeling is based purely on the measured data using Sparse Identification of Nonlinear Dynamics. A differential equation is determined which, starting from an initial value, simulates blood glucose dynamics. By applying the best model to test data, we can show that it is possible to simulate the long-term blood glucose dynamics using differential equations and few, influencing variables., Comment: Submitted manuscript to be published in Computer Aided Systems Theory - EUROCAST 2022: 18th International Conference, Las Palmas de Gran Canaria, Feb. 2022

Industrial and scientific applications handle large volumes of data that render manual validation by humans infeasible. Therefore, we require automated data validation approaches that are able to consider the prior knowledge of domain experts to produce dependable, trustworthy assessments of data quality. Prior knowledge is often available as rules that describe interactions of inputs with regard to the target e.g. the target must be monotonically decreasing and convex over increasing input values. Domain experts are able to validate multiple such interactions at a glance. However, existing rule-based data validation approaches are unable to consider these constraints. In this work, we compare different shape-constrained regression algorithms for the purpose of data validation based on their classification accuracy and runtime performance., Comment: 9 pages, Submitted manuscript to be published in Computer Aided System Theory - EUROCAST 2022, Las Palmas de Gran Canaria, February 2022

Fast Function Extraction (FFX) is a deterministic algorithm for solving symbolic regression problems. We improve the accuracy of FFX by adding parameters to the arguments of nonlinear functions. Instead of only optimizing linear parameters, we optimize these additional nonlinear parameters with separable nonlinear least squared optimization using a variable projection algorithm. Both FFX and our new algorithm is applied on the PennML benchmark suite. We show that the proposed extensions of FFX leads to higher accuracy while providing models of similar length and with only a small increase in runtime on the given data. Our results are compared to a large set of regression methods that were already published for the given benchmark suite., Comment: Submitted manuscript to be published in Computer Aided Systems Theory - EUROCAST 2022: 18th International Conference, Las Palmas de Gran Canaria, Feb. 2022

Symbolic regression is a nonlinear regression method which is commonly performed by an evolutionary computation method such as genetic programming. Quantification of uncertainty of regression models is important for the interpretation of models and for decision making. The linear approximation and so-called likelihood profiles are well-known possibilities for the calculation of confidence and prediction intervals for nonlinear regression models. These simple and effective techniques have been completely ignored so far in the genetic programming literature. In this work we describe the calculation of likelihood profiles in details and also provide some illustrative examples with models created with three different symbolic regression algorithms on two different datasets. The examples highlight the importance of the likelihood profiles to understand the limitations of symbolic regression models and to help the user taking an informed post-prediction decision., Comment: 10 pages, 8 figures, 1 table, 3 algorithms. Submitted to IEEE Transactions on Evolutionary Computation

Gradient-based local optimization has been shown to improve results of genetic programming (GP) for symbolic regression. Several state-of-the-art GP implementations use iterative nonlinear least squares (NLS) algorithms such as the Levenberg-Marquardt algorithm for local optimization. The effectiveness of NLS algorithms depends on appropriate scaling and conditioning of the optimization problem. This has so far been ignored in symbolic regression and GP literature. In this study we use a singular value decomposition of NLS Jacobian matrices to determine the numeric rank and the condition number. We perform experiments with a GP implementation and six different benchmark datasets. Our results show that rank-deficient and ill-conditioned Jacobian matrices occur frequently and for all datasets. The issue is less extreme when restricting GP tree size and when using many non-linear functions in the function set., Comment: Submitted to International Symposium on Symbolic and Numeric Algorithms for Scientific Computing 2022 https://synasc.ro/

Particle-based modeling of materials at atomic scale plays an important role in the development of new materials and understanding of their properties. The accuracy of particle simulations is determined by interatomic potentials, which allow to calculate the potential energy of an atomic system as a function of atomic coordinates and potentially other properties. First-principles-based ab initio potentials can reach arbitrary levels of accuracy, however their aplicability is limited by their high computational cost. Machine learning (ML) has recently emerged as an effective way to offset the high computational costs of ab initio atomic potentials by replacing expensive models with highly efficient surrogates trained on electronic structure data. Among a plethora of current methods, symbolic regression (SR) is gaining traction as a powerful "white-box" approach for discovering functional forms of interatomic potentials. This contribution discusses the role of symbolic regression in Materials Science (MS) and offers a comprehensive overview of current methodological challenges and state-of-the-art results. A genetic programming-based approach for modeling atomic potentials from raw data (consisting of snapshots of atomic positions and associated potential energy) is presented and empirically validated on ab initio electronic structure data., Comment: Submitted to the GPTP XIX Workshop, June 2-4 2022, University of Michigan, Ann Arbor, Michigan

Intelligent reflecting surfaces (IRS) are a key enabler of various new applications in 6G smart radio environments. By utilizing an IRS prototype system, this paper aims to enhance self-interference (SI) cancellation for breath tracking with commodity WiFi devices. SI suppression is a crucial requirement for breath tracking with a single antenna site as the SI severely limits the radio sensing range by shadowing the received signal with its own transmit signal. To this end, we propose to assist SI cancellation by exploiting an IRS to form a suitable cancellation signal in the analog domain. Building upon a 256-element IRS prototype, we present results of breath tracking with IRS-assisted SI cancellation from a practical testbed. We use inexpensive WiFi hardware to extract the Channel State Information (CSI) in the 5~GHz band and analyze the phase change between a colocated transmitter and receiver with added local oscillator (LO) synchronization. We are able to track the breath of a test person regardless of the position in an indoor environment in a room-level range. The presented case study shows promising performance in both capturing the breath frequency as well as the breathing patterns., Comment: Submitted to IEEE Internet of Things Journal

The Galactic globular cluster system is incomplete, especially in the low latitude regions of the Galactic bulge and disk. We report the physical characterization of twelve star clusters in the Milky Way, most of which are explored here for the first time. Our aim is determining their main physical parameters, such as reddening and extinction, metallicity, age, total luminosity, mean cluster proper motions (PMs), distances, in order to unveil their physical nature. We study the clusters using optical and near-infrared (NIR) datasets. We use the Gaia Early Data Release 3 (EDR3) PMs in order to perform a PM-decontamination procedure and build final catalogues. We match the Gaia EDR3 with the VISTA Variables in the V\'ia L\'actea extended (VVVX) survey and Two Micron All Sky survey (2MASS) in the NIR, in order to construct complete colour-magnitude diagrams (CMDs) and investigate the clusters properties. The extinctions are evaluated using existing reddening maps, spanning $0.09\lesssim A_{Ks}\lesssim 0.86$ mag and $0.89 \lesssim A_{G}\lesssim 4.72$ mag in the NIR and optical, respectively. We obtain their heliocentric distances, that range from about 4 to 20 kpc, placing these clusters at $3\lesssim R_{G}\lesssim 14$ kpc from the Galactic centre. The best PARSEC isochrone fit yields a metallicity range of $-1.8<$[Fe/H]$<+0.3$ and an approximative age range of $2<$Age$<14$ Gyr. We find that all clusters have low-luminosities, with $-6.9

Wireless radio channels are known to contain information about the surrounding propagation environment, which can be extracted using established wireless sensing methods. Thus, today's ubiquitous wireless devices are attractive targets for passive eavesdroppers to launch reconnaissance attacks. In particular, by overhearing standard communication signals, eavesdroppers obtain estimations of wireless channels which can give away sensitive information about indoor environments. For instance, by applying simple statistical methods, adversaries can infer human motion from wireless channel observations, allowing to remotely monitor premises of victims. In this work, building on the advent of intelligent reflecting surfaces (IRSs), we propose IRShield as a novel countermeasure against adversarial wireless sensing. IRShield is designed as a plug-and-play privacy-preserving extension to existing wireless networks. At the core of IRShield, we design an IRS configuration algorithm to obfuscate wireless channels. We validate the effectiveness with extensive experimental evaluations. In a state-of-the-art human motion detection attack using off-the-shelf Wi-Fi devices, IRShield lowered detection rates to 5% or less.

In this chapter we take a closer look at the distribution of symbolic regression models generated by genetic programming in the search space. The motivation for this work is to improve the search for well-fitting symbolic regression models by using information about the similarity of models that can be precomputed independently from the target function. For our analysis, we use a restricted grammar for uni-variate symbolic regression models and generate all possible models up to a fixed length limit. We identify unique models and cluster them based on phenotypic as well as genotypic similarity. We find that phenotypic similarity leads to well-defined clusters while genotypic similarity does not produce a clear clustering. By mapping solution candidates visited by GP to the enumerated search space we find that GP initially explores the whole search space and later converges to the subspace of highest quality expressions in a run for a simple benchmark problem., Comment: Genetic Programming Theory and Practice XVI. Genetic and Evolutionary Computation. Springer

Symbolic regression is a powerful system identification technique in industrial scenarios where no prior knowledge on model structure is available. Such scenarios often require specific model properties such as interpretability, robustness, trustworthiness and plausibility, that are not easily achievable using standard approaches like genetic programming for symbolic regression. In this chapter we introduce a deterministic symbolic regression algorithm specifically designed to address these issues. The algorithm uses a context-free grammar to produce models that are parameterized by a non-linear least squares local optimization procedure. A finite enumeration of all possible models is guaranteed by structural restrictions as well as a caching mechanism for detecting semantically equivalent solutions. Enumeration order is established via heuristics designed to improve search efficiency. Empirical tests on a comprehensive benchmark suite show that our approach is competitive with genetic programming in many noiseless problems while maintaining desirable properties such as simple, reliable models and reproducibility., Comment: Genetic and Evolutionary Computation

Optimization networks are a new methodology for holistically solving interrelated problems that have been developed with combinatorial optimization problems in mind. In this contribution we revisit the core principles of optimization networks and demonstrate their suitability for solving machine learning problems. We use feature selection in combination with linear model creation as a benchmark application and compare the results of optimization networks to ordinary least squares with optional elastic net regularization. Based on this example we justify the advantages of optimization networks by adapting the network to solve other machine learning problems. Finally, optimization analysis is presented, where optimal input values of a system have to be found to achieve desired output values. Optimization analysis can be divided into three subproblems: model creation to describe the system, model selection to choose the most appropriate one and parameter optimization to obtain the input values. Therefore, optimization networks are an obvious choice for handling optimization analysis tasks., Comment: International Conference on Computer Aided Systems Theory, Eurocast 2017, pp 392-399

Multi-objective symbolic regression has the advantage that while the accuracy of the learned models is maximized, the complexity is automatically adapted and need not be specified a-priori. The result of the optimization is not a single solution anymore, but a whole Pareto-front describing the trade-off between accuracy and complexity. In this contribution we study which complexity measures are most appropriately used in symbolic regression when performing multi- objective optimization with NSGA-II. Furthermore, we present a novel complexity measure that includes semantic information based on the function symbols occurring in the models and test its effects on several benchmark datasets. Results comparing multiple complexity measures are presented in terms of the achieved accuracy and model length to illustrate how the search direction of the algorithm is affected., Comment: International Conference on Computer Aided Systems Theory, Eurocast 2015, pp 409-416

The growing volume of data makes the use of computationally intense machine learning techniques such as symbolic regression with genetic programming more and more impractical. This work discusses methods to reduce the training data and thereby also the runtime of genetic programming. The data is aggregated in a preprocessing step before running the actual machine learning algorithm. K-means clustering and data binning is used for data aggregation and compared with random sampling as the simplest data reduction method. We analyze the achieved speed-up in training and the effects on the trained models test accuracy for every method on four real-world data sets. The performance of genetic programming is compared with random forests and linear regression. It is shown, that k-means and random sampling lead to very small loss in test accuracy when the data is reduced down to only 30% of the original data, while the speed-up is proportional to the size of the data set. Binning on the contrary, leads to models with very high test error., Comment: International Conference on Computer Aided Systems Theory 2015, pp 378-386

The current development of today's production industry towards seamless sensor-based monitoring is paving the way for concepts such as Predictive Maintenance. By this means, the condition of plants and products in future production lines will be continuously analyzed with the objective to predict any kind of breakdown and trigger preventing actions proactively. Such ambitious predictions are commonly performed with support of machine learning algorithms. In this work, we utilize these algorithms to model complex systems, such as production plants, by focusing on their variable interactions. The core of this contribution is a sliding window based algorithm, designed to detect changes of the identified interactions, which might indicate beginning malfunctions in the context of a monitored production plant. Besides a detailed description of the algorithm, we present results from experiments with a synthetic dynamical system, simulating stable and drifting system behavior., Comment: International Conference on Computer Aided Systems Theory, Eurocast 2019, pp. 296-303

The typical methods for symbolic regression produce rather abrupt changes in solution candidates. In this work, we have tried to transform symbolic regression from an optimization problem, with a landscape that is so rugged that typical analysis methods do not produce meaningful results, to one that can be compared to typical and very smooth real-valued problems. While the ruggedness might not interfere with the performance of optimization, it restricts the possibilities of analysis. Here, we have explored different aspects of a transformation and propose a simple procedure to create real-valued optimization problems from symbolic regression problems.

In material science, models are derived to predict emergent material properties (e.g. elasticity, strength, conductivity) and their relations to processing conditions. A major drawback is the calibration of model parameters that depend on processing conditions. Currently, these parameters must be optimized to fit measured data since their relations to processing conditions (e.g. deformation temperature, strain rate) are not fully understood. We present a new approach that identifies the functional dependency of calibration parameters from processing conditions based on genetic programming. We propose two (explicit and implicit) methods to identify these dependencies and generate short interpretable expressions. The approach is used to extend a physics-based constitutive model for deformation processes. This constitutive model operates with internal material variables such as a dislocation density and contains a number of parameters, among them three calibration parameters. The derived expressions extend the constitutive model and replace the calibration parameters. Thus, interpolation between various processing parameters is enabled. Our results show that the implicit method is computationally more expensive than the explicit approach but also produces significantly better results., Comment: Preprint submitted to Applications in Engineering Sciences

With the increasing number of created and deployed prediction models and the complexity of machine learning workflows we require so called model management systems to support data scientists in their tasks. In this work we describe our technological concept for such a model management system. This concept includes versioned storage of data, support for different machine learning algorithms, fine tuning of models, subsequent deployment of models and monitoring of model performance after deployment. We describe this concept with a close focus on model lifecycle requirements stemming from our industry application cases, but generalize key features that are relevant for all applications of machine learning., Comment: International Conference on Computer Aided Systems Theory, Eurocast 2019, pp 263-270

We introduce in this paper a runtime-efficient tree hashing algorithm for the identification of isomorphic subtrees, with two important applications in genetic programming for symbolic regression: fast, online calculation of population diversity and algebraic simplification of symbolic expression trees. Based on this hashing approach, we propose a simple diversity-preservation mechanism with promising results on a collection of symbolic regression benchmark problems., Comment: International Conference on Computer Aided Systems Theory, EUROCAST 2019

We describe and analyze algorithms for shape-constrained symbolic regression, which allows the inclusion of prior knowledge about the shape of the regression function. This is relevant in many areas of engineering -- in particular whenever a data-driven model obtained from measurements must have certain properties (e.g. positivity, monotonicity or convexity/concavity). We implement shape constraints using a soft-penalty approach which uses multi-objective algorithms to minimize constraint violations and training error. We use the non-dominated sorting genetic algorithm (NSGA-II) as well as the multi-objective evolutionary algorithm based on decomposition (MOEA/D). We use a set of models from physics textbooks to test the algorithms and compare against earlier results with single-objective algorithms. The results show that all algorithms are able to find models which conform to all shape constraints. Using shape constraints helps to improve extrapolation behavior of the models., Comment: 33 pages, 6 figures

Friction systems are mechanical systems wherein friction is used for force transmission (e.g. mechanical braking systems or automatic gearboxes). For finding optimal and safe design parameters, engineers have to predict friction system performance. This is especially difficult in real-world applications, because it is affected by many parameters. We have used symbolic regression and genetic programming for finding accurate and trustworthy prediction models for this task. However, it is not straight-forward how nominal variables can be included. In particular, a one-hot-encoding is unsatisfactory because genetic programming tends to remove such indicator variables. We have therefore used so-called factor variables for representing nominal variables in symbolic regression models. Our results show that GP is able to produce symbolic regression models for predicting friction performance with predictive accuracy that is comparable to artificial neural networks. The symbolic regression models with factor variables are less complex than models using a one-hot encoding., Comment: Genetic and Evolutionary Computation Conference (GECCO), July 15th-19th, 2018

We describe a method for the identification of models for dynamical systems from observational data. The method is based on the concept of symbolic regression and uses genetic programming to evolve a system of ordinary differential equations (ODE). The novelty is that we add a step of gradient-based optimization of the ODE parameters. For this we calculate the sensitivities of the solution to the initial value problem (IVP) using automatic differentiation. The proposed approach is tested on a set of 19 problem instances taken from the literature which includes datasets from simulated systems as well as datasets captured from mechanical systems. We find that gradient-based optimization of parameters improves predictive accuracy of the models. The best results are obtained when we first fit the individual equations to the numeric differences and then subsequently fine-tune the identified parameter values by fitting the IVP solution to the observed variable values., Comment: The final authenticated publication is available online at https://doi.org/10.1007/978-3-030-45093-9

Reconfigurable intelligent surfaces (RIS) are a key enabler of various new applications in 6G smart radio environments. By utilizing an RIS prototype system, this paper aims to enhance self-interference (SI) cancellation for in-band full-duplex (FD) communication systems. SI suppression is a crucial requirement for FD communication as the SI severely limits the performance of a node by shadowing the received signal from a distant node with its own transmit signal. To this end, we propose to assist SI cancellation by exploiting an RIS to form a suitable cancellation signal in the analog domain. Building upon a 256-element RIS prototype, we present results of RIS-assisted SI cancellation from a practical testbed. Given an initial analog isolation of 44 dB provided by the antenna design, we are able to cancel the leaked signal by an additional 59 dB in the narrowband case, resulting in an overall SI suppression of 103 dB without additional digital cancellation. The presented case study shows promising performance to build an FD communication system on this foundation., Comment: 6 pages, 9 figures, Accepted for publication in IEEE International Conference on Communications (ICC) 2022

We present the identification of 34 likely binary central stars (CSs) of planetary nebulae (PNe) from {\it Kepler/K2} data, seven of which show eclipses. Of these, 29 are new discoveries. Two additional CSs with more complicated variability are also presented. We examined the light curves of all `possible', `likely' and `true' PNe in every {\it Kepler/K2} campaign (0 through 19) to identify CS variability that may indicate a binary CS. For Campaigns 0, 2, 7, 15, and 16 we find 6 likely or confirmed variables among 21 PNe. Our primary effort, though, was focused on Campaign 11 which targeted a Galactic bulge field containing approximately 183 PNe, in which we identified 30 candidate variable CSs. The periods of these variables range from 2.3~h to 30~d, and based on our analysis, most are likely to be close binary star systems. We present periods and preliminary classifications (eclipsing, double degenerate, or irradiated systems) for the likely binaries based on light curve shape. From our total sample of 204 target PNe, with a correction for incompleteness due to magnitude limits, we calculate a binary fraction of PN central stars to be 20.7 percent for all the observed PNe, or 23.5 percent if we limit our sample only to `true' PNe. However these fractions are almost certainly lower limits due to the large angular size of the \emph{Kepler} pixels, which leads to reduced sensitivity in detecting variability, primarily as a result of dilution and noise from the nebula and neighbouring stars. We discuss the binary population of CSs based on these results as part of the total known sample of close binary CSs., Comment: 21 pages, 11 figures, 4 tables. Accepted for publication in MNRAS

We investigate the addition of constraints on the function image and its derivatives for the incorporation of prior knowledge in symbolic regression. The approach is called shape-constrained symbolic regression and allows us to enforce e.g. monotonicity of the function over selected inputs. The aim is to find models which conform to expected behaviour and which have improved extrapolation capabilities. We demonstrate the feasibility of the idea and propose and compare two evolutionary algorithms for shape-constrained symbolic regression: i) an extension of tree-based genetic programming which discards infeasible solutions in the selection step, and ii) a two population evolutionary algorithm that separates the feasible from the infeasible solutions. In both algorithms we use interval arithmetic to approximate bounds for models and their partial derivatives. The algorithms are tested on a set of 19 synthetic and four real-world regression problems. Both algorithms are able to identify models which conform to shape constraints which is not the case for the unmodified symbolic regression algorithms. However, the predictive accuracy of models with constraints is worse on the training set and the test set. Shape-constrained polynomial regression produces the best results for the test set but also significantly larger models.

Physical layer key generation is a promising candidate for cryptographic key establishment between two wireless communication parties. It offers information-theoretic security and is an attractive alternative to public-key techniques. Here, the inherent randomness of wireless radio channels is used as a shared entropy source to generate cryptographic key material. However, practical implementations often suffer from static channel conditions which exhibit a limited amount of randomness. In the past, considerable research efforts have been made to address this fundamental limitation. However, current solutions are not generic or require dedicated hardware extensions such as reconfigurable antennas. In this paper, we propose a novel wireless key generation architecture based on randomized channel responses from an intelligent reflecting surface (IRS). Due to its passive nature, a cooperative IRS is well-suited to provide randomness for conventional resource-constrained radios. We conduct the first practical studies to successfully demonstrate IRS-based physical-layer key generation with an OFDM system. In a static environment, using a single subcarrier only, our IRS-assisted prototype system achieves a key generation rate (KGR) of 97.39 bps with 6.5% key disagreement rate (KDR) after quantization, while passing standard randomness tests.