Parameter Space Research Articles

Real‐time topology optimization via learnable mappings

AbstractIn traditional topology optimization, the computing time required to iteratively update the material distribution within a design domain strongly depends on the complexity or size of the problem, limiting its application in real engineering contexts. This work proposes a multi‐stage machine learning strategy that aims to predict an optimal topology and the related stress fields of interest, either in 2D or 3D, without resorting to any iterative analysis and design process. The overall topology optimization is treated as regression task in a low‐dimensional latent space, that encodes the variability of the target designs. First, a fully‐connected model is employed to surrogate the functional link between the parametric input space characterizing the design problem and the latent space representation of the corresponding optimal topology. The decoder branch of an autoencoder is then exploited to reconstruct the desired optimal topology from its latent representation. The deep learning models are trained on a dataset generated through a standard method of topology optimization implementing the solid isotropic material with penalization, for varying boundary and loading conditions. The underlying hypothesis behind the proposed strategy is that optimal topologies share enough common patterns to be compressed into small latent space representations without significant information loss. Results relevant to a 2D Messerschmitt‐Bölkow‐Blohm beam and a 3D bridge case demonstrate the capabilities of the proposed framework to provide accurate optimal topology predictions in a fraction of a second.

Some specific wormhole solutions in extended f(R,G,T) gravity

This research work provides an exhaustive investigation of the viability of different coupled wormhole (WH) geometries with the relativistic matter configurations in the [Formula: see text] extended gravity framework. We consider a specific model in the context of [Formula: see text]-gravity for this purpose. Also, we assume a static spherically symmetric spacetime geometry and a unique distribution of matter with a set of shape functions ([Formula: see text]) for analyzing different energy conditions. In addition to this, we examined WH-models in the equilibrium scenario by employing anisotropic fluid. The corresponding results are obtained using numerical methods and then presented using different plots. In this case, [Formula: see text] gravity generates additional curvature quantities, which can be thought of as gravitational objects that maintain irregular WH-situations. Based on our findings, we conclude that in the absence of exotic matter, WH can exist in some specific regions of the parametric space using modified gravity model as [Formula: see text].

Meromorphic functions with a polar asymptotic value

This paper is part of a general program in complex dynamics to understand parameter spaces of transcendental maps with finitely many singular values. The simplest families of such functions have two asymptotic values and no critical values. These families, up to affine conjugation, depend on two complex parameters. Understanding their parameter spaces is key to understanding families with more asymptotic values, just as understanding quadratic polynomials was for rational maps more generally. The first such families studied were the one-dimensional slices of the exponential family, exp ⁡ ( z ) + a \exp (z) + a , and the tangent family λ tan ⁡ z \lambda \tan z . The exponential case exhibited phenomena not seen for rational maps: Cantor bouquets in both the dynamic and parameter spaces, and no bounded hyperbolic components. The tangent case, with its two finite asymptotic values ± λ i \pm \lambda i , is closer to the rational case, a kind of infinite degree version of the latter. In this paper, we consider a general family that interpolates between exp ⁡ ( z ) + a \exp (z) + a and λ tan ⁡ z \lambda \tan z . Our new family has two asymptotic values and a one-dimensional slice for which one of the asymptotic values is constrained to be a pole, the “polar asymptotic value” of the title. We show how the dynamic and parameter planes for this slice exhibit behavior that is a surprisingly delicate interplay between that of the exp ⁡ ( z ) + a \exp (z) + a and λ tan ⁡ z \lambda \tan z families.

CIME4R: Exploring iterative, AI-guided chemical reaction optimization campaigns in their parameter space

Chemical reaction optimization (RO) is an iterative process that results in large, high-dimensional datasets. Current tools allow for only limited analysis and understanding of parameter spaces, making it hard for scientists to review or follow changes throughout the process. With the recent emergence of using artificial intelligence (AI) models to aid RO, another level of complexity has been added. Helping to assess the quality of a model’s prediction and understand its decision is critical to supporting human-AI collaboration and trust calibration. To address this, we propose CIME4R—an open-source interactive web application for analyzing RO data and AI predictions. CIME4R supports users in (i) comprehending a reaction parameter space, (ii) investigating how an RO process developed over iterations, (iii) identifying critical factors of a reaction, and (iv) understanding model predictions. This facilitates making informed decisions during the RO process and helps users to review a completed RO process, especially in AI-guided RO. CIME4R aids decision-making through the interaction between humans and AI by combining the strengths of expert experience and high computational precision. We developed and tested CIME4R with domain experts and verified its usefulness in three case studies. Using CIME4R the experts were able to produce valuable insights from past RO campaigns and to make informed decisions on which experiments to perform next. We believe that CIME4R is the beginning of an open-source community project with the potential to improve the workflow of scientists working in the reaction optimization domain.Scientific contributionTo the best of our knowledge, CIME4R is the first open-source interactive web application tailored to the peculiar analysis requirements of reaction optimization (RO) campaigns. Due to the growing use of AI in RO, we developed CIME4R with a special focus on facilitating human-AI collaboration and understanding of AI models. We developed and evaluated CIME4R in collaboration with domain experts to verify its practical usefulness.

Gravitational wave effects and phenomenology of a two-component dark matter model

We study an extension of the Standard Model (SM) which could have two candidates for dark matter (DM) including a Dirac fermion and a vector dark matter (VDM) under a new U(1) gauge group in the hidden sector. The model is classically scale-invariant and the electroweak symmetry breaks because of loop effects. We investigate the parameter space allowed by current experimental constraints and phenomenological bounds. We probe the parameter space of the model in the mass range 1<MV<5000\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1< M_V<5000$$\\end{document} GeV and 1<Mψ<5000\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1<M_{\\psi }<5000$$\\end{document} GeV. It has been shown that there are many points in this mass range that are in agreement with all phenomenological constraints. The electroweak phase transition has been discussed and it has been shown that there is region in the parameter space of the model consistent with DM relic density and direct detection constraints that, at the same time, can lead to first-order electroweak phase transition. The gravitational waves produced during the phase transition could be probed by future space-based interferometers such as LISA and BBO.

Wake structure of an array of cylinders in shallow flow

Although there is a range of approaches for classifying the wake structure behind an array of obstacles, these approaches provide inconsistent results across different array systems. This motivates the present study to integrate and reconcile these approaches into one that is consistent across different systems. This new, transferable classification approach is based on the dimensionless flow blockage of the array and the wake stability parameter. To demonstrate this approach, a series of laboratory experiments was conducted to characterise the wake structure behind an array of emergent cylinders across a practically relevant parameter space that has not previously been explored. Two arrays with the same values of flow blockage and wake stability parameters but different sizes display the same wake structure, demonstrating the controlling influence of these two parameters on the wake structure. This approach classifies four different wake structures, which are distinct in that they display differences in instantaneous and time-averaged flow fields, temporal velocity oscillations, shear layer growth and the length of the steady wake region. The dependence of the wake structure on the two parameters is a consequence of (i) the controlling influence of blockage on the fraction of incident flow passing through the array and (ii) the ability of shallowness to suppress wake instabilities and, to a lesser extent, also influence the velocity through the array. This paper provides a predictive framework for the wake structure based on knowledge of the array geometry, and the depth and velocity of incident flow across the entire relevant practical parameter space.

On dynamical system modeling of Learned Primal-Dual with a linear operator $\mathcal{K}$: Stability and convergence properties

Abstract Learned Primal-Dual (LPD) is a deep learning based method for composite optimization problems that is based on unrolling/unfolding the primal-dual hybrid gradient algorithm. While achieving great successes in applications, the mathematical interpretation of LPD as a truncated iterative scheme is not necessarily sufficient to fully understand its properties. In this paper, we study the LPD with a general linear operator. We model the forward propagation of LPD as a system of difference equations and a system of differential equations in discrete- and continuous-time settings (for primal and dual variables/trajectories), which are named discrete-time LPD and continuous-time LPD, respectively. Forward analyses such as stabilities and the convergence of the state variables of the discrete-time LPD to the solution of continuous-time LPD are given. Moreover, we analyze the learning problems with/without regularization terms of both discrete-time and continuous-time LPD from the optimal control viewpoint. We prove convergence results of their optimal solutions with respect to the network state initialization and training data, showing in some sense the topological stability of the learning problems. We also establish convergence from the solution of the discrete-time LPD learning problem to that of the continuous-time LPD learning problem through a piecewise linear extension, under some appropriate assumptions on the space of learnable parameters. This study demonstrates theoretically the robustness of the LPD structure and the associated training process, and can induce some future research and applications.

Passive bionic motion of a flexible film in the wake of a circular cylinder: chaos and periodicity, flow–structure interactions and energy evolution

The self-sustained interactions between a flexible film and periodic vortices epitomize the spirit of fish swimming and flag flapping in nature, involving intricate patterns of flow–structure coupling. Here, we comprehensively investigate the multiple coupling states of a film in the cylinder wake mainly with experiments, complemented by theoretical solutions and nonlinear dynamical analyses. Four regimes of film motion states are identified in the parameter space spanned by the reduced velocity and the length ratio. These regimes are (i) keeping stationary, (ii) deflection flutter, (iii) hybrid flutter and (iv) periodic large-amplitude flapping, each governed by a distinct coupling mechanism, involving regular and irregular Kármán vortices, local instability of the elongated shear layers and 2P mode vortex shedding. The film futtering in regimes (ii) and (iii) is substantiated to be chaotic and bears a resemblance to the ‘entraining state’ of fish behind an obstacle in the river. The periodic flapping in regime (iv) manifests itself in an amalgam of standing and travelling waves, and has intrinsic relations to the ‘Kármán gaiting’ of fish in periodic vortices. With the spatiotemporal reconstruction for the periodic flapping, we procure the energy distributions on the film, revealing the energy transfer processes between the film and the large-scale vortices. The findings unequivocally indicate that the flow–structure interaction during the energy-release stage of the film is more intense than that during the energy-extraction stage. Given the similarities, the mathematical and physical methods presented in this work are also applicable to the research on biological undulatory locomotion.

Optimal parameter-space for stabilizing the ferroelectric phase of Hf0.5Zr0.5O2 thin-films under strain and electric fields

Abstract Hafnia-based ferroelectric materials, like Hf0.5Zr0.5O2 (HZO), have received tremendous attention owing to their potentials for building ultra-thin ferroelectric devices. The orthorhombic(O)-phase of HZO is ferroelectric but metastable in its bulk form under ambient conditions, which poses a considerable challenge to maintaining the operation performance of HZO-based ferroelectric devices. Here, we theoretically addressed this issue that provides parameter spaces for stabilizing the O-phase of HZO thin-films under various conditions. Three mechanisms were found to be capable of lowering the relative energy of the O-phase, namely, more significant surface-bulk portion of (111) surfaces, compressive c-axis strain, and positive electric fields. Considering these mechanisms, we plotted two ternary phase diagrams for HZO thin-films where the strain was applied along the in-plane uniaxial and biaxial, respectively. These diagrams indicate the O-phase could be stabilized by solely shrinking the film-thickness below 12.26 nm, ascribed to its lower surface energies. All these results shed considerable light on designing more robust and higher-performance ferroelectric devices.

Quark and lepton modular models from the binary dihedral flavor symmetry

Inspired by the structure of top-down derived models endowed with modular flavor symmetries, we investigate the yet phenomenologically unexplored binary dihedral group 2D3. After building the vector-valued modular forms in the representations of 2D3 with small modular weights, we systematically classify all (Dirac and Majorana) mass textures of fermions with fractional modular weights and all possible 2 + 1-family structures. This allows us to explore the parameter space of fermion models based on 2D3, aiming at a description of both quarks and leptons with a minimal number of parameters and best compatibility with observed data. We consider the separate possibilities of neutrino masses generated by either a type-I seesaw mechanism or the Weinberg operator. We identify a model that, besides fitting all known flavor observables, delivers predictions for six not-yet measured parameters and favors normal-ordered neutrino masses generated by the Weinberg operator. It would be interesting to figure out whether it is possible to embed our model within a top-down scheme, such as \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb{T}}^{2}/{\\mathbb{Z}}_{4}$$\\end{document} heterotic orbifold compactifications.

Holographic renormalization of Horndeski gravity

We study the renormalization of a particular sector of Horndeski theory. In particular, we focus on the nonminimal coupling of a scalar field to the Gauss-Bonnet term and its kinetic coupling to the Einstein tensor. Adopting a power expansion on the scalar function that couples the Gauss-Bonnet term, we find specific conditions on their coefficients such that the action and charges are finite. To accomplish the latter, we add a finite set of intrinsic boundary terms. The contribution of the nonminimal coupling generates an effective scalar mass, allowing us to recover a modified Breitenlohner-Freedman bound. Furthermore, we compute the holographic 1-point functions and Ward identities associated with the scalar field and the metric. We constrain the parameter space of the theory by taking into account the preservation of scaling symmetry at the boundary.

Wigner distributions of sea quarks in the light-cone quark model

We investigate the Wigner distributions of u¯ and d¯ quarks in a proton using the overlap representation within the light cone formalism. Using the light-cone wave functions which are obtained from the baryon-meson fluctuation model in terms of the |qq¯B⟩ Fock states, we calculate the Wigner distributions for the unpolarized/longitudinally polarized sea quarks in an unpolarized/longitudinally polarized proton. The Wigner distributions can be obtained through a Fourier transform on the generalized transverse-momentum dependent parton distributions (GTMDs). We also calculate the GTMDs of u¯ and d¯ quarks in the intermediate step. Numerical results for the Wigner distributions of u¯ and d¯ quarks in transverse momentum space, impact parameter space and the mixed plane are presented. We also study the orbital angular momentum and the spin-orbit correlations of the sea quarks. Published by the American Physical Society 2024

Polarization-engineered photon statistics and its tomography via optomagnonic interaction.

Cavity optomagnonics has received considerable research interest in recent years, due to the coherent magnetic Brillioun light scattering in the ferromagnetic material. Here, we theoretically propose and numerically verify a feasible scheme for the full polarization tomography on photon statistics in an optomagnonic whispering-gallery-mode microresonator system in the weak-coupling regime. By performing the polarization pre- and post-selections to manipulate the polarization states of the input and output photons, we find that the rich sub- and super-Poissonian photon statistics can be selectively generated, thanks to quantum interferences. In the parameter space of phase delay, the evolution from photon bunching to antibunching indicates the change from phase to amplitude squeezing. Our obtained result has potential applications in tunable quantum polarized light sources based on the cavity optomagnonic platform in micro-nano scale. It also offers a deeper understanding for full quantum cavity optomagnonics.

Computing eigenfrequency sensitivities near exceptional points

Exceptional points are spectral degeneracies of non-Hermitian systems where both eigenfrequencies and eigenmodes coalesce. The eigenfrequency sensitivities near an exceptional point are significantly enhanced, whereby they diverge directly at the exceptional point. Capturing this enhanced sensitivity is crucial for the investigation and optimization of exceptional-point-based applications, such as optical sensors. We present a numerical framework based on contour integration and algorithmic differentiation to accurately and efficiently compute eigenfrequency sensitivities near exceptional points. We demonstrate the framework for an optical microdisk cavity and derive a semianalytical solution to validate the numerical results. The computed eigenfrequency sensitivities are used to track the exceptional point along an exceptional surface in the parameter space. The presented framework can be applied to any kind of resonance problem, e.g., with arbitrary geometry or with exceptional points of arbitrary order. Published by the American Physical Society 2024

CURLING – I. The influence of point-like image approximation on the outcomes of cluster strong lens modeling

Abstract Cluster-scale strong lensing is a powerful tool for exploring the properties of dark matter and constraining cosmological models. However, due to the complex parameter space, pixelized strong lens modeling in galaxy clusters is computationally expensive, leading to the point-source approximation of strongly lensed extended images, potentially introducing systematic biases. Herein, as the first paper of the ClUsteR strong Lens modelIng for the Next-Generation observations (CURLING) program, we use lensing ray-tracing simulations to quantify the biases and uncertainties arising from the point-like image approximation for JWST-like observations. Our results indicate that the approximation works well for reconstructing the total cluster mass distribution, but can bias the magnification measurements near critical curves and the constraints on the cosmological parameters, the total matter density of the Universe Ωm, and dark energy equation of state parameter w. To mitigate the biases, we propose incorporating the extended surface brightness distribution of lensed sources into the modeling. This approach reduces the bias in magnification from 46.2 per cent to 0.09 per cent for μ ∼ 1000. Furthermore, the median values of cosmological parameters align more closely with the fiducial model. In addition to the improved accuracy, we also demonstrate that the constraining power can be substantially enhanced. In conclusion, it is necessary to model cluster-scale strong lenses with pixelized multiple images, especially for estimating the intrinsic luminosity of highly magnified sources and accurate cosmography in the era of high-precision observations.

Eliminating Non-Corner-Sharing Octahedral for Efficient and Stable Perovskite Solar Cells.

The metal halide (BX6)4- octahedron, where B represents a metal cation and X represents a halide anion, is regarded as the fundamental structural and functional unit of metal halide perovskites. However, the influence of the way the (BX6)4- octahedra connect to each other has on the structural stability and optoelectronic properties of metal halide perovskite is still unclear. Here, the octahedral connectivity, including corner-, edge-, and face-sharing, of various CsxFA1-xPbI3 (0≤x≤0.3) perovskite films is tuned and reliably characterized through compositional and additive engineering, and with ultralow-dose transmission electron microscopy. It is found that the overall solar cell device performance, the charge carrier lifetime, the open-circuit voltage, and the current density-voltage hysteresis are all improved when the films consist of corner-sharing octahedra, and non-corner sharing phases are suppressed, even in films with the same chemical composition. Additionally, it is found that the structural, optoelectronic, and device performance stabilities are similarly enhanced when non-corner-sharing connectivities are suppressed. This approach, combining macroscopic device tests and microscopic material characterization, provides a powerful tool enabling a thorough understanding of the impact of octahedral connectivity on device performance, and opens a new parameter space for designing high-performance photovoltaic metal halide perovskite devices.

Singlet-doublet fermion Dark Matter with Dirac neutrino mass, (g − 2)μ and ∆Neff

We study the possibility of generating light Dirac neutrino mass via scotogenic mechanism where singlet-doublet fermion Dark Matter (DM) plays non-trivial role in generating one-loop neutrino mass, anomalous magnetic moment of muon: (g − 2)μ as well as additional relativistic degrees of freedom ∆Neff within reach of cosmic microwave background (CMB) experiments. We show that the Dirac nature of neutrinos can bring interesting correlations within the parameter space satisfying the (g − 2)μ, DM relic density and the effective relativistic degrees of freedom ∆Neff. While we stick to thermal singlet-doublet DM with promising detection prospects, both thermal and non-thermal origin of ∆Neff have been explored. In addition to detection prospects of the model at DM, (g − 2)μ and other particle physics experiments, it remains verifiable at future CMB experiments like CMB-S4 and SPT-3G.

Evolving Improved Sampling Protocols for Dose–Response Modelling Using Genetic Algorithms with a Profile-Likelihood Metric

Practical limitations of quality and quantity of data can limit the precision of parameter identification in mathematical models. Model-based experimental design approaches have been developed to minimise parameter uncertainty, but the majority of these approaches have relied on first-order approximations of model sensitivity at a local point in parameter space. Practical identifiability approaches such as profile-likelihood have shown potential for quantifying parameter uncertainty beyond linear approximations. This research presents a genetic algorithm approach to optimise sample timing across various parameterisations of a demonstrative PK-PD model with the goal of aiding experimental design. The optimisation relies on a chosen metric of parameter uncertainty that is based on the profile-likelihood method. Additionally, the approach considers cases where multiple parameter scenarios may require simultaneous optimisation. The genetic algorithm approach was able to locate near-optimal sampling protocols for a wide range of sample number (n = 3–20), and it reduced the parameter variance metric by 33–37% on average. The profile-likelihood metric also correlated well with an existing Monte Carlo-based metric (with a worst-case r > 0.89), while reducing computational cost by an order of magnitude. The combination of the new profile-likelihood metric and the genetic algorithm demonstrate the feasibility of considering the nonlinear nature of models in optimal experimental design at a reasonable computational cost. The outputs of such a process could allow for experimenters to either improve parameter certainty given a fixed number of samples, or reduce sample quantity while retaining the same level of parameter certainty.

Fixed Point Results for Compatible Mappings in Extended Parametric Sb-Metric Spaces

This study aims to establish common fixed point theorems for a pair of compatible self-mappings within the framework of extended parametric Sb-metric spaces. To support our assertions, we provide corollaries and examples accompanied with graphical representations. Moreover, we leverage our principal outcome to guarantee the existence of a common solution to a system of integral equations.

Weak-formulated physics-informed modeling and optimization for heterogeneous digital materials

Abstract Numerical solutions to partial differential equations (PDEs) are instrumental for material structural design where extensive data screening is needed. However, traditional numerical methods demand significant computational resources, highlighting the need for innovative optimization algorithms to streamline design exploration. Direct gradient-based optimization algorithms, while effective, rely on design initialization and require complex, problem-specific sensitivity derivations. The advent of machine learning offers a promising alternative to handling large parameter spaces. To further mitigate data dependency, researchers have developed physics-informed neural networks (PINNs) to learn directly from PDEs. However, the intrinsic continuity requirement of PINNs restricts their application in structural mechanics problems, especially for composite materials. Our work addresses this discontinuity issue by substituting the PDE residual with a weak formulation in the physics-informed training process. The proposed approach is exemplified in modeling digital materials, which are mathematical representations of complex composites that possess extreme structural discontinuity. This paper also introduces an interactive process that integrates physics-informed loss with design objectives, eliminating the need for pre-trained surrogate models or analytical sensitivity derivations. The results demonstrate that our approach can preserve the physical accuracy in data-free material surrogate modeling but also accelerates the direct optimization process without model pre-training.