Continuous Parameter Space Research Articles

TWO-DIMENSIONAL HYPERCHAOTIC MAP FOR CHAOTIC OSCILLATIONS

This manuscript explores a two-dimensional hyperchaotic map for generating chaotic oscillations. Hyperchaotic maps are finding increasing applications in various scientific and technological fields due to the unique properties of their generated oscillations. The studied map, based on two interconnected piecewise-linear functions, is one of the simplest for generating oscillations with a predetermined distribution of values across a continuous parameter space. This simplicity allows for wide applicability in various contexts. The paper presents simulation results demonstrating control over the parameters of the dynamic modes. Building upon these modeling results, a two-dimensional hyperchaotic system is implemented using an electric circuit. The chosen map is attractive due to its inherent simplicity and ease of parameter control. By adjusting these parameters, the distribution of the generated signal's values can be manipulated. The circuit consists of two symmetrical sections connected via feedback loops, employing four amplifiers with variable gain. The gain values act as the circuit's implementation of the control parameters. Chaotic oscillations are generated by applying a delayed clock signal from an external square wave generator to circuit elements. The obtained experimental results exhibit excellent agreement with the simulation data.

Empi: GPU-Accelerated Matching Pursuit with Continuous Dictionaries

This article introduces an effective approach to performing matching pursuit calculations with continuous (quasi-infinite) dictionaries. Simulating continuous parameter space is accomplished by combining optimal dictionary construction as introduced previously with local parameter optimization. At the same time, the calculations can be performed not only with Gabor atoms, but with any type of oscillating atoms, or even multiple types of atoms at once. The proposed method is confirmed by introducing a first stable version of a high-performance implementation empi , supporting calculations with continuous as well as discrete dictionaries, further accelerated by the use of multi-threading and GPU support.

Film hole layout optimization for multi-row film cooling plate in continuous parameter space under non-uniform inlet temperature distribution

Film cooling is an advanced external cooling technology for protecting gas turbine blades from excessive temperatures. To counteract non-uniform heat loads caused by hot streak and swirl effects at the combustion chamber outlet, fine design of film hole positions is necessary. However, the complexity due to the numerous film holes and their positional parameters presents challenges in the independent optimization of film hole positions in a continuous parameter space. This study proposed an optimization method grounded in the divide and conquer approach to address optimization for film hole layout. The film hole layout was decomposed into multiple single rows and optimized systematically by iteratively refining the single-row film hole layout along the streamwise direction using the expectation maximization algorithm. Optimized layouts for five different inlet temperature distributions were obtained using the proposed method and adiabatic wall temperature distributions were compared and analyzed for optimized and staggered layouts. Additionally, the cooling performance of the optimized layout was evaluated against the staggered layout under conjugate heat transfer conditions and the robustness of the optimized layout under various blowing ratios and peak temperature positions was tested. The results demonstrated that the proposed method can optimize the positions of 52 film holes within 0.3h, and it was generalized to various inlet temperature distributions. By enhancing lateral interactions among downstream film jets, the lifting effect of kidney vortex in the optimized layout was weakened, bringing the film jets closer to the wall and significantly increasing coolant coverage during streamwise development. Comparative analysis reveals the superior cooling performance of the optimized layout at the blowing ratio of 1.0, evidenced by a 15.1% reduction in total input heat transfer rate and a 12.3% enhancement in overall cooling efficiency relative to the staggered layout. Under conditions with blowing ratios ranging from 0.5 to 1.5 and peak temperature position deviations, the average wall temperature of the optimized layout consistently remained lower than the staggered layout, indicating the robustness of the optimized layout to variations in blowing ratio and hot streak position.

A new strategy optimisation method for underwater flapping foil propulsion based on Twin-Delayed Deep Deterministic and Gaussian process regression

In complex sea environments, underwater bionic flapping foils exhibit significant nonlinear characteristics across a high-dimensional parameter space. This study introduces a novel optimisation paradigm, G-TD3, integrating Twin-Delayed Deep Deterministic (TD3) reinforcement learning with Gaussian process regression (GPR). An automatic experimental device was developed, using which a series of flapping foil propulsion experiments were conducted, exploring both symmetric and asymmetric flutter modes. Utilizing GPR, we characterized the flapping foil's operational environment from experimental data. In addition, the TD3 algorithm was deployed to exploit this environment, enabling interactive learning in high-dimensional, continuous parameter spaces. Our integrated approach facilitates comprehensive exploration-exploitation dynamics. The optimized propulsion strategy, fine-tuned through maximizing acquisition rewards, demonstrates G-TD3's superiority over traditional brute-force methods, requiring less data for optimising both symmetric and asymmetric flutter strategies. This research provides a new optimisation method for nonlinear systems and offers valuable insights into the practical applications of bionic flapping foils.

Concurrent geometrico-topological tuning of nanoengineered auxetic lattices fabricated by material extrusion for enhancing multifunctionality: Multiscale experiments, finite element modeling and data-driven prediction

This study demonstrates the multifunctional performance of innovative 2D auxetic lattices through a combination of multiscale experiments, finite element modeling and data-driven prediction. A geometric modeling approach utilizing Voronoi partitioning and a unique branch-stem-branch (BSB) structure, patterned according to 2D wallpaper symmetries, enables precise concurrent geometric and topological tuning of lattices across a continuous parameter space. Selected architectures are physically realized via material extrusion of polylactic acid (PLA) infused with carbon black (CB). Experimental characterizations, supported by Finite Element modeling, reveal the significant influence of BSB structure's design parameters on mechanical and piezoresistive performance under tensile loading, with a remarkable Poisson’s ratio of -0.74, accompanied by a 15-fold increase in elastic stiffness and a 34-fold increase in strain sensitivity. Additionally, architecturally, and topologically tailored lattice structures exhibit tunable damage sensitivity, reflecting the rate of conductive network destruction within the lattice. This offers insights into the rapidity of cell wall failure, with a steeper slope of the piezoresistance curve in the inelastic regime indicating a faster breakdown and quicker onset of mechanical failure. Integration of Gaussian Process Regression enables accurate exploration of the design space beyond realized structures, highlighting the potential of these intelligent lattice structures for applications such as sensors and in situ health monitoring, marking a significant advancement in multifunctional materials.

A solver for subsonic flow around airfoils based on physics-informed neural networks and mesh transformation

Physics-informed neural networks (PINNs) have recently become a new popular method for solving forward and inverse problems governed by partial differential equations. However, in the flow around airfoils, the fluid is greatly accelerated near the leading edge, resulting in a local sharper transition, which is difficult to capture by PINNs. Therefore, PINNs are still rarely used to solve the flow around airfoils. In this study, we combine physical-informed neural networks with mesh transformation, using a neural network to learn the flow in the uniform computational space instead of physical space. Mesh transformation avoids the network from capturing the local sharper transition and learning flow with internal boundary (wall boundary). We successfully solve inviscid flow and provide an open-source subsonic flow solver for arbitrary airfoils. Our results show that the solver exhibits higher-order attributes, achieving nearly an order of magnitude error reduction over second-order finite volume method (FVM) on very sparse meshes. Limited by the learning ability and optimization difficulties of the neural network, the accuracy of this solver will not improve significantly with mesh refinement. Nevertheless, it achieves comparable accuracy and efficiency to second-order FVM on fine meshes. Finally, we highlight the significant advantage of the solver in solving parametric problems, as it can efficiently obtain solutions in the continuous parameter space about the angle of attack.

Physics-informed neural networks for parametric compressible Euler equations

The numerical approximation of solutions to the compressible Euler and Navier–Stokes equations is a crucial but challenging task with relevance in various fields of science and engineering. Recently, methods from deep learning have been successfully employed for solving partial differential equations by incorporating the equations into a loss function that is minimized during the training of a neural network. This approach yields a so-called physics-informed neural network. It is not based upon classical discretizations, such as finite-volume or finite-element schemes, and can even address parametric problems in a straightforward manner. This has raised the question, whether physics-informed neural networks may be a viable alternative to conventional methods for computational fluid dynamics. In this article we introduce an adaptive artificial viscosity reduction procedure for physics-informed neural networks enabling approximate parametric solutions for forward problems governed by the stationary two-dimensional Euler equations in sub- and supersonic conditions. To the best of our knowledge, this is the first time that the concept of artificial viscosity in physics-informed neural networks is successfully applied to a complex system of conservation laws in more than one dimension. Moreover, we highlight the unique ability of this method to solve forward problems in a continuous parameter space. The presented methodology takes the next step of bringing physics-informed neural networks closer towards realistic compressible flow applications.

Electron Beams on the Brillouin Zone: A Cohomological Approach via Sheaves of Fourier Algebras

Topological states of matter can be classified only in terms of global topological invariants. These global topological invariants are encoded in terms of global observable topological phase factors in the state vectors of electrons. In condensed matter, the energy spectrum of the Hamiltonian operator has a band structure, meaning that it is piecewise continuous. The energy in each continuous piece depends on the quasi-momentum which varies in the Brillouin zone. Thus, the Brillouin zone of quasi-momentum variables constitutes the base localization space of the energy eigenstates of electrons. This is a continuous topological parameter space bearing the homotopy of a torus. Since the base localization space has the homotopy of a torus, if we vary the quasi-momentum in a direction, when the edge of the zone is reached, we obtain a closed path. Then, if we lift this loop from the base space to the sections of the sheaf-theoretic fibration induced by the localization of the energy eigenfunctions, we obtain a global topological phase factor which encodes the topological structure of the Brillouin zone. Because it is homotopically equivalent to a torus, the global phase factor turns out to be quantized, taking integer values. The experimental significance of this model stems from the recent discovery that there are observable global topological phase factors in fairly ordinary materials. In this communication, we show that it is the unitary representation theory of the discrete Heisenberg group in terms of commutative modular symplectic variables, giving rise to a joint commutative representation space endowed with an integral and Z2-invariant symplectic form that articulates the specific form of the topological conditions characterizing both the quantum Hall effect and the spin quantum Hall effect under a unified sheaf-theoretic cohomological framework.

Application of Pure Birth to the Phenomenon of Covid-19 Infected Cases in Indonesia with A Time Interval (0, 24) Hours from June to September 2020

Since the emergence of the 2019 novel coronavirus (2019-nCoV) in Wuhan City, China, in 2019, many countries in the world have been infected with the virus with very serious cases. This has caused a slump, especially for Indonesia, with a lower-middle-class society of 115 million people or 45% of the total population. The virus's rapid spread through droplets resulted in the Indonesian government implementing a lockdown called Large-scale Social Restrictions within months. This system is an effort to break the chain of virus spread. A pure birth process can be called a stochastic process with a continuous parameter space and a discrete state space. This research will focus on the application of the Pure Birth Process, which is expected to provide scientific studies on Covid-19 in Indonesia, become a new reference for the development of mathematics, and provide information on research results so that they can be used in policymaking to overcome and overcome the spread of Covid-19. 19. At the end of this study, it was known that the spread of Covid-19 in Indonesia was very drastic, which had a rate of increase in cases as big as a person/hour or person/day, which is a very significant increase. Based on calculations using Pure Birth, it is hoped that it can be used in policymaking for the government and the community to overcome and overcome the spread of Covid-19.

Exact electronic states with shallow quantum circuits from global optimisation

Quantum computers promise to revolutionise molecular electronic simulations by overcoming the exponential memory scaling. While electronic wave functions can be represented using a product of fermionic unitary operators, the best ansatz for strongly correlated electronic systems is far from clear. In this contribution, we construct universal wave functions from gate-efficient, spin symmetry-preserving fermionic operators by introducing an algorithm that globally optimises the wave function in the discrete ansatz design and continuous parameter spaces. Our approach maximises the accuracy that can be obtained with near-term quantum circuits and provides a practical route for designing ansätze in the future. Numerical simulations for strongly correlated molecules, including water and molecular nitrogen, and the condensed-matter Hubbard model, demonstrate the improved accuracy of gate-efficient quantum circuits for simulating strongly correlated chemistry.

A gradient set matching pursuit algorithm with anti-base mismatch ability for sparse reconstruction under low SNR

This paper is concerned with designing an effective algorithm for recovering mismatched sparse signals from noise underdetermined measurements. The sparse recovery problem is formulated as the gradient optimization model of the residual cost function in a multidimensional continuous parameter space. The mismatched atoms of the discrete dictionary matrix are recovered as the accurate target sparse coefficient by solving a gradient descent algorithm with a hyperparameters joint adaptive adjustment function. To estimate the target parameters of frequency agile radar, we propose a gradient set matching pursuit algorithm. The algorithm uses the prior knowledge of resolution of the two-dimensional ambiguity function to build a discrete dictionary and obtains the support set according to the orthogonal matching pursuit principle. We divide the gradient set space in the neighborhood of the support set and calculate the mean gradient as the judgment direction and iteration step of the initial optimization process to overcome the residual function distortion and gradient error caused by random noise. The iterative convergence process of the proposed algorithm in the support set vector space is more robust, and the problem of falling into local optimum is avoided. Compared with the conventional sparse recovery algorithm and gradient descent algorithm, the proposed algorithm boosts its reconstruction performance of target parameters in the scenario of low SNR and mismatch of multiple scattering points. Simulation results show the effectiveness of the proposed algorithm.

Targeted Discovery of Low-Coordinated Crystal Structures via Tunable Particle Interactions

Particles interacting via isotropic, multiwell pair potentials have been shown to self-assemble into a range of crystal structures, yet how the characteristics of the underlying interaction potential give rise to the resultant structure remains largely unknown. We have thus developed a functional form for the interaction potential in which all features can be tuned independently. We perform continuous parameter space searches by systematically changing pairs of parameters, controlling the various features of the interaction potential. By enforcing a repulsive first well (controlling particle interactions of the first neighbor shell), we stimulate the formation of low-coordinated assemblies. We report the self-assembly of 20 previously unknown crystal structure types, 14 of which have low coordination numbers. Despite limiting the search to a small region of the vast parameter space of possible particle interactions, a wealth of complexity and symmetry is apparent within these crystal structures, which include clathrates with empty cages and low-symmetry structures. Our findings suggest that an unknown number of previously undiscovered crystal structure configurations are possible through self-assembly, which can serve as interesting design targets for soft condensed matter synthesis.

Machine Learning Assisted Analysis of Electrochemical H2O2 Production

The two-electron water oxidation reaction (2e– WOR) provides an option for on-site production of the valuable chemical hydrogen peroxide (H2O2). A major challenge for the 2e– WOR is the need to improve its selectivity toward H2O2 over O2 production through the oxygen evolution reaction. Electrolyte engineering has shown great promise in improving the selectivity and production rates toward H2O2. However, experimental efforts in optimizing the electrolyte only yield results at discrete conditions, which does not provide a complete picture of performance over the entire parameter range. Here, we apply a machine learning assisted prediction to map out the performance of electrochemical H2O2 production over the continuous parameter space of electrolyte composition and applied potential. We collected experimental data of faradaic efficiencies (FEH2O2) and current densities toward H2O2 (JH2O2) as functions of the applied potential and carbonate ion mole fractions (HCO3– and CO32–) in the electrolyte. The data were then used to train a support vector regression model with 5-fold cross-validation. The accuracy of the model was verified against additional experimental results. The model identified that a maximum H2O2 current density of 2.16 mA/cm2 can be achieved from an optimized bicarbonate ion mole fraction of 0.225 at an applied potential of 3.25 V vs RHE. Lastly, the continuous model enables us to evaluate the thermal efficiency, H2O2 electricity cost, and time needed to produce a set amount of H2O2 over a broad range of electrolytes and applied potential conditions. This work demonstrates how machine learning enables the use of discrete experimental points to construct a continuous picture of electrochemical H2O2 production with high accuracy.

An improved orthogonal matching pursuit method for denoising high-frequency ultrasonic detection signals of flip chips

Noise suppression of an echo signal plays an important role in high-frequency ultrasonic testing of flip chips. This paper proposes an orthogonal matching pursuit (OMP) method optimized by an improved artificial bee colony (ABC) algorithm for denoising high-frequency ultrasonic testing signals of flip chips. We add adaptive learning factors to change the way the ABC randomly selects the search direction, which speeds up the convergence speed of the algorithm. The improved ABC, named adaptive artificial bee colony (AABC), replaces the greedy search process of OMP. Instead of searching for the atom that best matches the echo signal, the improved OMP algorithm searches for the optimal parameter and replaces the atom with a set of parameters with practical physical significance. The introduction of the AABC changes the search space of OMP from discrete dictionary space to continuous parameter space, which minimizes the error between the atom and echo signal and leads to an accurate approximation. Additionally, the AABC reduces the search times of OMP and improves the convergence speed. Then, the wavelet transform thresholding technology is combined with the attenuation characteristic of high-frequency ultrasound to eliminate the influence of error decomposition caused by noise and inaccurate sparsity setting. We present the noise suppression experimental results of high-frequency ultrasonic simulation and real testing signals of flip chips, including Gaussian white noise and correlated noise, and compare the proposed method with other sparse representation methods, including matching pursuit (MP) and OMP. The results demonstrate the superior performance of the proposed method.

Statistical Significance Testing for Mixed Priors: A Combined Bayesian and Frequentist Analysis.

In many hypothesis testing applications, we have mixed priors, with well-motivated informative priors for some parameters but not for others. The Bayesian methodology uses the Bayes factor and is helpful for the informative priors, as it incorporates Occam’s razor via the multiplicity or trials factor in the look-elsewhere effect. However, if the prior is not known completely, the frequentist hypothesis test via the false-positive rate is a better approach, as it is less sensitive to the prior choice. We argue that when only partial prior information is available, it is best to combine the two methodologies by using the Bayes factor as a test statistic in the frequentist analysis. We show that the standard frequentist maximum likelihood-ratio test statistic corresponds to the Bayes factor with a non-informative Jeffrey’s prior. We also show that mixed priors increase the statistical power in frequentist analyses over the maximum likelihood test statistic. We develop an analytic formalism that does not require expensive simulations and generalize Wilks’ theorem beyond its usual regime of validity. In specific limits, the formalism reproduces existing expressions, such as the p-value of linear models and periodograms. We apply the formalism to an example of exoplanet transits, where multiplicity can be more than . We show that our analytic expressions reproduce the p-values derived from numerical simulations. We offer an interpretation of our formalism based on the statistical mechanics. We introduce the counting of states in a continuous parameter space using the uncertainty volume as the quantum of the state. We show that both the p-value and Bayes factor can be expressed as an energy versus entropy competition.

Decoding the Mechanisms of Phase Transitions from In Situ Microscopy Observations.

Analysis of the temperature- and stimulus-dependent imaging data toward elucidation of the physical transformations is an ubiquitous problem in multiple fields. Here, temperature-induced phase transition in BaTiO3 is explored using the machine learning analysis of domain morphologies visualized via variable-temperature scanning transmission electron microscopy (STEM) imaging data. This approach is based on the multivariate statistical analysis of the time or temperature dependence of the statistical descriptors of the system, derived in turn from the categorical classification of observed domain structures or projection on the continuous parameter space of the feature extraction-dimensionality reduction transform. The proposed workflow offers a powerful tool for the exploration of the dynamic data based on the statistics of image representation as a function of the external control variable to visualize the transformation pathways during phase transitions and chemical reactions. This can include the mesoscopic STEM data as demonstrated here, but also optical, chemical imaging, etc., data. It can further be extended to the higher dimensional spaces, for example, analysis of the combinatorial libraries of materials compositions.

Intrinsic superflat bands in general twisted bilayer systems

Twisted bilayer systems with discrete magic angles, such as twisted bilayer graphene featuring moiré superlattices, provide a versatile platform for exploring novel physical properties. Here, we discover a class of superflat bands in general twisted bilayer systems beyond the low-energy physics of magic-angle twisted counterparts. By considering continuous lattice dislocation, we obtain intrinsic localized states, which are spectrally isolated at lowest and highest energies and spatially centered around the AA stacked region, governed by the macroscopic effective energy potential well. Such localized states exhibit negligible inter-cell coupling and support the formation of superflat bands in a wide and continuous parameter space, which can be mimicked using a twisted bilayer nanophotonic system. Our finding suggests that general twisted bilayer systems can realize continuously tunable superflat bands and the corresponding localized states for various photonic, phononic, and mechanical waves.

Signal-to-noise-ratio and maximum-signal-to-noise-ratio detection statistics in template-bank searches for exotic physics transients with networks of quantum sensors

Quantum sensor networks such as the existing networks of atomic clocks and magnetometers offer intriguing capabilities in searches for transient signals such as dark matter or fields sourced by powerful astrophysical events. The common matched-filter technique relies on the signal-to-noise-ratio (SNR) detection statistic to probe such transients. For macroscopic dark matter objects, the network would register a sweeping signal as the object propagates through at galactic velocities. A potential event is registered when the SNR from a specific template exceeds a threshold set by a desired false positive rate. Generically, to span the continuous parameter space for the network-exotic-physics encounter, one has to deal with multiple templates. In such template-bank searches, the natural generalization of the SNR statistic is the maximum-signal-to-noise-ratio (SNR-max) statistic, defined as the maximum of the absolute values of SNRs determined from individual template matching. While individual SNR realizations are Gaussian distributed, SNR-max probability distribution is non-Gaussian. Moreover, as the individual template-bank SNRs are computed using the same network data streams, SNRs become correlated between the templates. Cross-template correlations have a sizable effect on the SNR-max probability and cumulative distributions, and on the threshold SNR-max values. Computing threshold SNR-max values for large template banks is computationally prohibitive and we develop analytic approaches to computing properties of the SNR-max statistic. This is done for cases when the template bank is nearly orthogonal (small cross-template correlations) and for banks with cross-template correlation coefficient distribution ``squeezed'' about the most probable cross-template correlation value. Since the cross-template correlation coefficients quantify the similarity of templates, increasing correlations tend to decrease SNR-max thresholds for specific values of false positive rates. Increasing the number of templates in the bank increases the SNR-max thresholds. Our derivations are carried out for networks that may exhibit colored noise and cross-node correlations. Specific applications are illustrated with a dark matter search with atomic clocks onboard satellites of a Global Positioning System and with a ``toy'' planar network with cyclic rotational symmetry.

A new CASE for complementary materials science categorization

A new CASE for complementary materials science categorization

Inference of ventricular activation properties from non-invasive electrocardiography

The realisation of precision cardiology requires novel techniques for the non-invasive characterisation of individual patients’ cardiac function to inform therapeutic and diagnostic decision-making. Both electrocardiography and imaging are used for the clinical diagnosis of cardiac disease. The integration of multi-modal datasets through advanced computational methods could enable the development of the cardiac ‘digital twin’, a comprehensive virtual tool that mechanistically reveals a patient's heart condition from clinical data and simulates treatment outcomes. The adoption of cardiac digital twins requires the non-invasive efficient personalisation of the electrophysiological properties in cardiac models. This study develops new computational techniques to estimate key ventricular activation properties for individual subjects by exploiting the synergy between non-invasive electrocardiography, cardiac magnetic resonance (CMR) imaging and modelling and simulation. More precisely, we present an efficient sequential Monte Carlo approximate Bayesian computation-based inference method, integrated with Eikonal simulations and torso-biventricular models constructed based on clinical CMR imaging. The method also includes a novel strategy to treat combined continuous (conduction speeds) and discrete (earliest activation sites) parameter spaces and an efficient dynamic time warping-based ECG comparison algorithm. We demonstrate results from our inference method on a cohort of twenty virtual subjects with cardiac ventricular myocardial-mass volumes ranging from 74 cm3 to 171 cm3 and considering low versus high resolution for the endocardial discretisation (which determines possible locations of the earliest activation sites). Results show that our method can successfully infer the ventricular activation properties in sinus rhythm from non-invasive epicardial activation time maps and ECG recordings, achieving higher accuracy for the endocardial speed and sheet (transmural) speed than for the fibre or sheet-normal directed speeds.