Non-uniqueness Problem Research Articles

Efficient property-oriented design of composite layups via controllable latent features using generative VAE

Fiber-reinforced composites provide substantial tailoring potential, while the extensive parameters and complex coupling mechanisms pose formidable challenges to layup designs. This paper presents an efficient inverse design framework for composite layups utilizing a variational autoencoder (VAE), which is applicable to non-conventional laminates. By leveraging the VAE's exceptional feature extraction and generative capabilities, the decoder rapidly produces layups with desired properties through controllable feature vectors. Based on the stacking characteristics of layups, multi-scale one-dimensional convolutions precisely extract sequence features relevant to mechanical properties and specific manufacturing constraints. A customized loss function is formulated to constrain the latent features, while addressing the non-uniqueness problem for layups with certain mechanical properties. The developed property-oriented VAE can generate 100,000 layups in seconds, achieving an average success rate of 66.9% under comprehensive in-plane and bending stiffness design, and remains effective for 100-ply thick laminate. For comparison, the VAE model outperforms the genetic algorithm and the logic-based method in reinforced panel designs, reducing the retrieval error by 46.4% and 38.1%, respectively. The proposed approach demonstrates flexible and efficient design advantages using generative machine learning models, and is easily extendable to other inverse design scenarios.

Inverse design of ultranarrow and high-efficiency color filters based on tandem convolutional neural networks

In this paper, an ultranarrow, high-efficiency color filter based on a two-dimensional grating nanostructure array is realized by a tandem inverse design network. The tandem inverse designed network is generated by connecting an inverse network with a pre-trained forward network. The tandem convolutional neural network successfully overcame the non-uniqueness problem of the training data. The performance of the networks is verified by a test set of 2592 data points, and the average MSE of the prediction results of the tandem network is 1.01 × 10−3. Extremely low error indicates that the tandem network can learn and capture the distribution characteristics of the transmission spectrum and give a reasonable design of the structural parameters. Finally, we obtained multiple inverse-designed transmissive color filters with ultranarrow linewidths and high efficiency, with central wavelengths between 480 nm and 630 nm. The linewidth and efficiency of each kind of color filter are less than 10.6 nm and higher than 60%. Narrow linewidths and wide wavelength tunability result in high color accuracy and a broad color gamut of the filters. The filters with two-dimensional metallic nanostructure array also show polarization-independent characteristics. Compared with the traditional method, this method can quickly and accurately design the structural parameters corresponding to the spectral response, which provides a new method for the nanostructure design.

Tales of twin cities: what are climate analogues good for?

This article provides an epistemological assessment of climate analogue methods, with specific reference to the use of spatial analogues in the study of the future climate of target locations. Our contention is that, due to formal and conceptual inadequacies of geometrical dissimilarity metrics and the loss of relevant information, especially when reasoning from the physical to the socio-economical level, purported inferences from climate analogues of the spatial kind we consider here prove limited in a number of ways. Indeed, we formulate five outstanding problems concerning the search for best analogues, which we call the problem of non-uniqueness of the source, problem of non-uniqueness of the target, problem of average, problem of non-causal correlations and problem of inferred properties, respectively. In the face of such problems, we then offer two positive recommendations for a fruitful application of this methodology to the assessment of impact, adaptation and vulnerability studies of climate change, especially in the context of what we may prosaically dub “twin cities”. Arguably, such recommendations help decision-makers constrain the set of plausible climate analogues by integrating local knowledge relevant to the locations of interest.

A Two-Phase Flowback Type Curve with Fracture Damage Effects for Hydraulically Fractured Reservoirs

Summary Type curves are a powerful tool in characterizing hydraulic fracture (HF) and reservoir properties based on flowback and production data. We propose a type-curve method to evaluate HF characteristics and their dynamics for multifractured horizontal wells (MFHWs) in hydrocarbon reservoirs using flowback production data. The type curve incorporates the HF damage effect of choked-fracture skin factor in the two-phase flow in HF and matrix domains. The type-curve method can be applied to inversely estimate choked-fracture skin factor, s, HF pore volume (PV), Vfi, and HF initial permeability, kfi, by analyzing two-phase flowback production data. By introducing the new dimensionless parameters, the nonuniqueness problem of the type-curve analysis for two-phase flow is significantly reduced by incorporating the complexity of fracture dynamics into one set of curves. The accuracy of the type curve is examined against the results obtained from numerical simulations of shale gas and oil reservoirs. The validation results demonstrate a good match of analytical type curves and numerical data plots and confirm the accuracy of the proposed method in estimating the static and dynamic fracture properties. The results show that the relative errors in Vfi, kfi, and s estimations are all <10% for the simulated cases that are presented in this work. The flexibility and robustness of the proposed method are illustrated using the field example from a shale oil MFHW. The accuracy and applicability of the proposed type curve are also validated by comparing the calculated fracture properties from the field example using straightline analysis with Vfi and kfi of 705.3 Mcf and 245.2 md, type-curve analysis method (without skin effect) with Vfi and kfi of 751.9 Mcf and 249.8 md, and the type-curve method (with the choked fracture skin considered) with Vfi and kfi of 708.7 Mcf and 252.9 md, which showed that the results of each case are very close to one another. The interpreted results from the flowback analysis of the field example offer quantitative insight into HF properties and dynamics.

Branching-independent random utility model

This paper introduces a subclass of the Random Utility Model (RUM), called branching-independent RUM. In this subclass, the probability distribution over the ordinal rankings of alternatives satisfies the following property: for any k∈{1,…,n−1}, where n denotes the number of alternatives, when fixing the first k and the last n−k alternatives, the relative rankings of the first k and the last n−k alternatives are independent. Branching-independence is motivated by the classical example due to Fishburn (1998), which illustrates the non-uniqueness problem in random utility models. Surprisingly, branching-independent RUM is characterized by the Block-Marschak condition, which also characterizes general RUM. In fact, I show that a construction similar to the one used in Falmagne (1978) generates a branching-independent RUM. In addition, within the class of branching-independent RUMs, the probability distribution over preferences is uniquely determined. Hence, while branching-independent RUM has the same explanatory power as general RUM, it is uniquely identified.

A complex boundary wave superposition method for solving external acoustic problems

This paper proposes a complex boundary wave superposition method with a unique solution of full wavenumber based on the similarity between the acoustic wave superposition method (WSM) and the external excitation response of dynamic systems and combined with the idea that a damping system has a unique solution in dynamic theory. By placing the virtual equivalent source on the virtual boundary of complex space, the conventional WSM acquires damping properties comparable to those of the dynamical system. This approach successfully addresses the non-uniqueness of the solution at the eigenfrequency and is more efficient than the conventional combined layer potential method. The paper presents a comprehensive description of the proposed method, with a focus on theory, modeling, and parameter selection. The effectiveness of this method is evaluated by applying it to two types of acoustic problems, namely, radiation and scattering. The numerical results indicate that this method effectively addresses the non-unique problems encountered in conventional WSM. Furthermore, the proposed method is as accurate and efficient as the conventional WSM.

Relative uniqueness or uniqueness? A new cross-efficiency evaluation approach with weight priority strategy

Due to a large number of studies on cross-evaluation strategies, the theoretical problem of DEA cross-efficiency approach has been transformed from the non-uniqueness of the optimal solution to the relative uniqueness, because the existing cross-evaluation strategies can only reduce the possibility of non-unique solutions, but cannot prove the existence of a unique optimal solution. This paper illustrates the relative uniqueness of optimal solution of the cross-efficiency approach with traditional cross-evaluation strategies, and the graphic method and theoretical analysis are used to explain the reasons of relative uniqueness. Based on the data characteristic of inputs and outputs, the weight priority rule is made for constructing the new cross-evaluation strategy, and its optimal solution is proved to be unique. In addition, the weight priority strategy can also be introduced into traditional strategies as a supplementary strategy, and then the unique optimal solution can be obtained on the premise of preserving the characteristics of traditional strategies. In general, this paper solves the non-uniqueness and relative uniqueness problem of optimal solution in the DEA cross-efficiency approach, and then the reliability and robustness of the approach are thus improved.

A novel hybrid SBM-MFS methodology for acoustic wave propagation problems

In this paper, a novel hybrid meshless approach that combines the singular boundary method (SBM) and the method of fundamental solutions (MFS) to deal with two-dimensional (2D) exterior acoustic wave propagation problems is proposed and studied. The methodology is particularly devised to solve problems with complex boundary geometries containing geometric singularities such as corners and sharp edges. It employs the SBM to model intricate segments of these geometries and the MFS for the smooth ones. The proposed hybrid SBM-MFS method is studied in a 2D context in the framework of three benchmark examples involving acoustic radiation problems of circular-, square- and L-shaped objects in a full-space acoustic medium. In addition, the applicability of the proposed hybrid SBM-MFS methodology to predict the acoustic performance of a T-shaped thin barrier is also investigated. These examples are specifically designed to assess the feasibility, validity and accuracy of the hybrid SBM-MFS approach in comparison with the available analytical solutions and alternative numerical strategies such as the MFS, the SBM and the boundary element method (BEM). Numerical simulations demonstrate that the proposed method can match the level of accuracy of the MFS while keeps the robustness of the SBM when dealing with complex geometries, overcoming one the most important drawbacks of the traditional MFS. Moreover, the proposed hybrid SBM-MFS naturally avoids the non-uniqueness problem arising at the fictitious eigenfrequencies associated with the corresponding interior problems, a feature that neither the SBM nor the BEM inherently possesses.

Joint Inversion of Gravity and Magnetic Data based on the Modified Structural Similarity Index for the Structural Consistency Constraint

Joint inversion is a crucial approach to mitigate the non-uniqueness problem in geophysical inversion. Nevertheless, existing joint inversion methods fall short of meeting the stringent requirements of high-precision exploration, necessitating the development of new techniques. In this paper, we introduce the Structural Similarity Index (SSIM) as a novel structural consistency constraint for the joint inversion of gravity and magnetic data. Compared with the results of cross-gradient inversion, our method demonstrates outstanding performance and stability. SSIM inversion not only introduces a new class of joint inversion with structural constraints but also enhances the consistency of inversion results in the distribution of physical attribute values. The structural constraints of SSIM inversion are more comprehensive and robust, significantly improving the reliability of the inversion. Both synthetic and real data applications demonstrate that the proposed method can effectively handle both synthetic and real data, yielding outstanding results.

Inverse design of two-function transmission-type reconfigurable polarization control metasurfaces based on deep learning

Compared with single-function metasurfaces, the design difficulty of multi-function metasurfaces increases significantly. This paper introduces an inverse design method based on deep learning to address this challenge. By this method, a transmission-type reconfigurable polarization control metasurface (TRPCM) with two functions is rapidly designed. The network model used in the method consists of an electromagnetic parameter reconstruction network model and an inverse prediction network model. The combination of the two models can solve the problem of difficulty in defining high-dimensional inputs in traditional inverse design, and achieve accurate prediction of metasurface structure parameters under given design targets. To optimize the hyperparameters of the neural network model, a genetic algorithm was introduced. To solve the non-uniqueness problem of inverse design, a method for eliminating similar data by calculating Euclidean Distance was introduced. Both schemes further improve the predictive performance of the proposed network model. Finally, six design targets were set based on the TRPCM. The structural parameters of the metasurface were successfully predicted using two neural network models and achieved the required performance. On this basis, a set of parameters was selected for experimental validation. By controlling the ON or OFF of the PIN diodes, the fabricated metasurface achieves two functions: linear-to-circular polarization conversion and linear polarization maintenance in the range of 2–3.6 GHz. Study results show that the inverse design scheme proposed in the paper is feasible and practical for solving the rapid optimization design of complex multi-function metasurfaces.

Multi-headed tandem neural network approach for non-uniqueness in inverse design of layered photonic structures

Neural networks have proven to be an influential tool in assisting with the inverse design of nanophotonic structures. However, the issue of non-uniqueness poses a significant limitation to this approach, as disparate designs can produce nearly identical spectra. This problem can result in the neural network failing to converge or producing erroneous results. In this study, we propose a multi-headed tandem neural network (MTNN) approach to address this issue. This method enables the neural network to generate multiple sets of outputs and utilize tandem neural networks (TNNs), and self-attention mechanisms, among other techniques, to constrain the results, and let these multiple outputs be fitted separately to different results. This allows the neural network to converge without sacrificing the simplex solution in the face of multimodal solutions. We employ the MTNN approach to inverse engineer a multilayer photonic structure comprised of two sets of oxide films, and the multiple outputs provide numerous valuable solutions. Our approach presents an effective solution for the inverse design of photonic structures afflicted with non-uniqueness problems.

Joint inversion of potential field data with adaptive unstructured tetrahedral mesh

Inverting potential field data presents a significant challenge due to its ill-posed nature, often leading to nonunique model solutions. Addressing this, our work focuses on developing a robust joint inversion method for potential field data, aiming to achieve more accurate density and magnetic susceptibility distributions. Unlike most previous work that used regular meshes, our approach adopts an adaptive, unstructured tetrahedral mesh, offering enhanced capabilities in handling the inverse problem of potential field methods. During inversion, the tetrahedral mesh is refined in response to the model update rate. We integrate a Gramian constraint into the objective function, allowing the enforcement of model similarity in terms of either the model parameters or their spatial gradients on an unstructured mesh. In addition, we use the moving least-squares method for gradient operator computation, which is essential for model regularization. Our model studies indicate that this method effectively inverts potential field data, yielding reliable subsurface density and magnetic susceptibility distributions. The joint inversion approach, compared with individual data set inversion, produces coherent geophysical models with enhanced correlations. Notably, it significantly mitigates the nonuniqueness problem, with the recovered anomaly locations aligning more closely with actual ground truths. Applying our methodology and algorithm to field data from the Ring of Fire area in Canada, the joint inversion process has generated comprehensive geophysical models with robust correlations, offering potential benefits for mineral exploration in the region.

Searching for Features with Artificial Neural Networks in Science: The Problem of Non-Uniqueness

ABSTRACT Artificial neural networks and supervised learning have become an essential part of science. Beyond using them for accurate input-output mapping, there is growing attention to a new feature-oriented approach. Under the assumption that networks optimised for a task may have learned to represent and utilise important features of the target system for that task, scientists examine how those networks manipulate inputs and employ the features networks capture for scientific discovery. We analyse this approach, show its hidden caveats, and suggest its legitimate use. We distinguish three things that scientists call a ‘feature’: parametric, diagnostic, and real-world features. The feature-oriented approach aims for real-world features by interpreting the former two, which also partially rely on the network. We argue that this approach faces a problem of non-uniqueness: there are numerous discordant parametric and diagnostic features and ways to interpret them. When the approach aims at novel discovery, scientists often need to choose between those options, but they lack the background knowledge to justify their choices. Consequentially, features thus identified are not promised to be real. We argue that they should not be used as evidence but only used instrumentally. We also suggest transparency in feature selection and the plurality of choices.

The general set of Noetherian energy-momentum tensors in linearized gravity: mathematical framework

Energy-momentum tensors are foundational objects which are uniquely defined in standard physical field theories such as electrodynamics and Yang-mills theory. In general relativity, and in particular linearized gravity where symmetries required for an energy-momentum tensor derived from Noether’s first theorem are well defined, there exists a long standing non-uniqueness problem; numerous distinct energy-momentum expressions exist in the literature, and there is not consensus which, if any, is the unique expressions for the theory. Recently, the viability of the superpotential ‘improvement’ method was shown to be insufficient for addressing the non-uniqueness problem of energy-momentum tensors in linearized gravity. In the present article, the mathematical framework for the general set of Noetherian energy-momentum tensors in linearized gravity is derived using Noether’s first theorem, which consists of all possible energy-momentum tensors from the Noether current which yield the linearized Einstein field equations in the corresponding Euler-Lagrange equation of the Noether identity without introducing any ‘improvement’ terms. This result has several advantages in addition to not requiring ‘improvements’, such as the ability to impact the Lagrangian proportional piece of the energy-momentum tensor. Numerous common published gravitational energy-momentum expressions are then compared to these general results to assess which can be classified as Noetherian, and which cannot. Standard physical criteria such as symmetry and tracelessness are then used to prove that it is possible to directly obtain an energy-momentum tensor which is simultaneously symmetric and traceless from the Noether current; such an expression is derived from the general results. Consequences of these results and their relation to the aforementioned non-uniqueness problem are discussed.

Deep-learning-based inverse design of colloidal quantum dots

Because optical properties of colloidal quantum dots (QDs) greatly depend on their layer thicknesses at the sub-nanometer scale, accurately predicting optical properties based on these structural parameters can help streamline the development process. However, most of traditional inverse design approaches require time-consuming numerical simulations and optimization processes. In this simulation-only paper, we propose a deep-learning-based inverse design model for colloidal InP/ZnSe/ZnS QDs based on the structure parameters of layer thicknesses and optical properties of the emission and absorption spectrum. Four different deep neural network (DNN) structures are implemented and compared. A tandem DNN structure with the simultaneous use of both emission and absorption spectra as input data shows the best accuracy due to its ability to alleviate the non-uniqueness problem in the inverse design of colloidal QDs. Our inverse design model enables the prediction of layer thicknesses for QDs that exhibit on-demand optical emission/absorption spectra, which are particularly enhanced at the specific target wavelength region. Moreover, the weights and biases of the well-trained tandem DNN for InP/ZnSe/ZnS QDs can be transferred and tuned to implement a transfer-learning-assisted inverse design model for CdSe/ZnSe/ZnS QDs, where the amount of training data to achieve the average prediction accuracy of 99.3 % is reduced by a maximum of 71.4 %.

Bootstrap sampling style ensemble neural network for inverse design of optical nanoantennas

The process of machine learning-assisted nanophotonicsinverse design has been plagued by the problem of non-uniqueness for a long time, which is a problem worth studying. In this paper, we present a novel methodology for the design of bowtie optical nanoantennas (BONAs) by employing a Bootstrap Sampling Style Ensemble Neural Network (BSENN) model. Our approach combines a bagging algorithm with a tandem neural network to address the non-uniqueness challenge inherent in the inverse design process of BONAs. By splitting the data, training in batches, and integrating the results, our BSENN model is able to provide reliable predictions and offer a solution to the non-uniqueness problem. The main objective of our work is to explore diverse BONAs design structures that yield identical spectral responses, thereby providing a broader range of alternatives for the design of optical nanoantennas. Through the utilization of the BSENN model, we aim to enhance the design process and offer increased flexibility and versatility in the field of optical nanoantenna design.

Improved PVTOL Test Bench for the Study of Over-Actuated Tilt-Rotor Propulsion Systems

In recent years, applications exploiting the advantages of tilt-rotors and other vectored thrust propulsion systems have become widespread, particularly in many novel Vertical Takeoff and Landing (VTOL) configurations. These propulsion systems can provide additional control authority, enabling more complex flight modes, but the resulting control systems can be challenging to design due to the mismatch between the vehicle degrees of freedom and physical input variables. These propulsion systems present both advantages and difficulties because they can exert the same overall forces and moments in many different propulsive configurations. This leads to the traditional non-uniqueness problem when using the inverse dynamics control allocation approach, which is the basis of many popular VTOL control algorithms. In this article, a modified Planar VTOL (PVTOL) test bench configuration, which considers an arbitrary number of co-linear tilting rotors, is introduced as a benchmark for the study of the control allocation problem. The resulting propulsion system is then modeled and linearized in a closed and compact form. This allows a simple and systematic derivation of many of the currently used control allocation approaches. According to the proposed PVTOL configuration, a two-rotor test bench is implemented experimentally and a decoupling control allocation strategy based on Singular Value Decomposition (SVD) analysis is developed. The proposed approach is compared with a traditional input mixer algorithm based on physical intuition. The results show that the SVD-based solution achieves better cross-coupling reduction and preserves the main properties of the physically derived approach. Finally, it is shown that the proposed PVTOL configuration is effective for studying the control allocation problem experimentally in a controlled environment and could serve as a benchmark for comparing different approaches.

Stereophonic acoustic echo cancellation based on semi-blind source separation

The non-uniqueness problem embedded in stereophonic acoustic echo cancellation causes performance degradation. Usually, an additional decorrelation preprocessor is required, which is inevitably detrimental to the speech quality. In this paper, we propose a stereophonic acoustic echo cancellation method based on semi-blind source separation. By optimizing a dedicated demixing matrix rooted from stereophonic acoustic echo cancellation, the proposed method is insensitive to the inter-channel correlation between the far-end signals, resulting in better convergence behavior without any decorrelation preprocessing. Experimental results demonstrate the efficacy and robustness of the proposed method in the presence of inter-channel correlation, echo path changes, and double-talk.

A meshfree approach for vibro-acoustic analysis of combined composite laminated shells with variable thickness

The vibro-acoustic responses of combined composite laminated shell structures with variable thickness immersed in acoustic medium is investigated by using a meshfree method in this paper. The theoretical model of structural field is established by employing the energy principle in conjunction with the first-order shear deformation theory (FSDT) and the theoretical model of acoustic field are established by using Kirchhoff-Helmholtz integral equation. The displacement components of shell segments and the sound pressure variables of acoustic medium are described by using the meshfree Tchebychev point interpolation (TPIM) shape function and Double Fourier series in meridional and circumferential directions. The non-uniqueness problem of Kirchhoff-Helmholtz integral equation is overcome by adopting CHIEF method. The validation of the presented theoretical model is proved by comparing the results calculated by the proposed model with those results of existing literature and FEM/BEM. Based on the established theoretical model, vibro-acoustic responses of combined composite laminated shell structures with variable thickness immersed in acoustic medium are performed by analyzing the influences of thickness parameter, external load and boundary condition on the sound pressure level (SPL) and sound power level (SWL) of combined composite laminated shell structures. The above investigations can provide the theoretical thesis and technique guidance of preliminary design of combined composite laminated shell immersed in various acoustic medium.

A hybrid nearfield acoustic holography based on the mapping relationship and boundary element method

The nearfield acoustic holography (NAH) based on mapping relationship (MRS) had been developed. However, it is superior to the reconstructions on regular shapes by using the MRS-based NAH with spherical fundamental solutions (FS). In contrast, the boundary element method (BEM) based NAH is capable of handling complex shapes but requires relatively more measurement points. In this work, a hybrid method is developed by combing the MRS with spherical FS and the BEM. To circumvent the non-unique problems associated with the conventional BEM, the Burton-Miller formulation is adopted into the BEM based NAH. The merit of easy measurement setup, such as the determination of positions and number of microphones in the array is preserved in the hybrid method. Furthermore, it is possible to recast the reconstruction operation by the BEM-based NAH with sufficient measurements data on an artificial hologram that are implicitly interpolated by the MRS-based NAH. In conjunction with regularization techniques, results with improved accuracy are clearly observed in the velocity reconstructions for irregular shapes by the hybrid NAH. It is validated by numerical examples especially for an irregular box that the hybrid NAH is capable of producing reconstructions with significant improvement of accuracy even with small signal-to-noise ratio (SNR) as compared with the MRS-based NAH. An experiment is setup to further demonstrate the potential of the hybrid NAH for practical reconstruction of an irregular radiator. More robust and accurate reconstructions are achieved in contrast with the MRS-based NAH, which clearly illustrated advantages of the hybrid NAH.