Inverse Error Research Articles

Research on the properties of separable binary functions

PurposeAccording to the fact that the single function transformation which can both reduce the class ratio dispersion and keep the relative error no enlargement after the inverse transformation does not exist, this paper provides the separable binary function transformation . The authors select the appropriate and to get . The sequence can not only improve the modeling accuracy but also ensure that the inverse transformation relative error has no enlargement.Design/methodology/approachFirst of all, to meet that the sequence reduces the class ratio dispersion after binary function transformation, the sufficient and necessary condition of binary function transformation with reduced class ratio dispersion is obtained. Secondly, to meet the condition that the inverse transformation relative error is not enlarged, the necessary condition of separable binary function transformation is obtained respectively for monotonically increasing and monotonically decreasing function . Finally, the feasibility and correctness of this method are illustrated by example analysis and application.FindingsThe sufficient and necessary condition of binary function transformation with reduced class ratio dispersion and the necessary condition of separable binary function transformation with the inverse transformation relative error no enlargement.Practical implicationsAccording to the properties of separable binary function transformation provided in this paper, the grey prediction function model is established, which can improve the modeling accuracy.Originality/valueThis paper provides a binary function transformation, and researches the sufficient and necessary condition of binary function transformation with reduced class ratio dispersion and the necessary condition of separable binary function transformation with the inverse transformation relative error no enlargement. It is easy for scholars to carry out the pretest before selecting the separable binary function transformation. The binary function transformation is the further extension of single function transformation, which broadens and enriches the choice of function transformation.

Solving distributed low carbon scheduling problem for large complex equipment manufacturing using an improved hybrid artificial bee colony algorithm

Multi-agent collaborative manufacturing, high energy consumption and pollution, and frequent operation outsourcing are the three main characteristics of large complex equipment manufacturing enterprises. Therefore, the production scheduling problem of large complex equipment to be studied is a distributed flexible job shop scheduling problem involving operation outsourcing (Oos-DFJSP). Besides, the influences of each machine on carbon emission and job scheduling at different processing speeds are also involved in this research. Thus the Oos-DFJSP of large complex equipment consists of the following four sub-problems: determining the sequence of operations, assigning jobs to manufactories, assigning operations to machines and determining the processing speed of each machine. In the Oos-DFJSP, if a job is assigned to a manufactory of a group manufacturing enterprise, and the manufactory cannot complete some operations of the workpiece, then these operations will be assigned to other manufactories with related processing capabilities. Aiming at solving the problem, a multi-objective mathematical model including costs, makespan and carbon emission was established, in which energy consumption, power generation of waste heat and treatment capacity of pollutants were considered in the calculation of carbon emission. Then, a multi-objective improved hybrid genetic artificial bee colony algorithm was developed to address the above model. Finally, 45 groups of random comparison experiments were presented. Results indicate that the developed algorithm performs better than other multi-objective algorithms involved in the comparison experiments not only on quality of non-dominated solutions but also on Inverse Generational Distance and Error Ratio. That is, the proposed mathematical model and algorithm were proved to be an excellent method for solving the multi-objective Oos-DFJSP.

Purifier: Defending Data Inference Attacks via Transforming Confidence Scores

Neural networks are susceptible to data inference attacks such as the membership inference attack, the adversarial model inversion attack and the attribute inference attack, where the attacker could infer useful information such as the membership, the reconstruction or the sensitive attributes of a data sample from the confidence scores predicted by the target classifier. In this paper, we propose a method, namely PURIFIER, to defend against membership inference attacks. It transforms the confidence score vectors predicted by the target classifier and makes purified confidence scores indistinguishable in individual shape, statistical distribution and prediction label between members and non-members. The experimental results show that PURIFIER helps defend membership inference attacks with high effectiveness and efficiency, outperforming previous defense methods, and also incurs negligible utility loss. Besides, our further experiments show that PURIFIER is also effective in defending adversarial model inversion attacks and attribute inference attacks. For example, the inversion error is raised about 4+ times on the Facescrub530 classifier, and the attribute inference accuracy drops significantly when PURIFIER is deployed in our experiment.

ReGANIE: Rectifying GAN Inversion Errors for Accurate Real Image Editing

The StyleGAN family succeed in high-fidelity image generation and allow for flexible and plausible editing of generated images by manipulating the semantic-rich latent style space. However, projecting a real image into its latent space encounters an inherent trade-off between inversion quality and editability. Existing encoder-based or optimization-based StyleGAN inversion methods attempt to mitigate the trade-off but see limited performance. To fundamentally resolve this problem, we propose a novel two-phase framework by designating two separate networks to tackle editing and reconstruction respectively, instead of balancing the two. Specifically, in Phase I, a W-space-oriented StyleGAN inversion network is trained and used to perform image inversion and edit- ing, which assures the editability but sacrifices reconstruction quality. In Phase II, a carefully designed rectifying network is utilized to rectify the inversion errors and perform ideal reconstruction. Experimental results show that our approach yields near-perfect reconstructions without sacrificing the editability, thus allowing accurate manipulation of real images. Further, we evaluate the performance of our rectifying net- work, and see great generalizability towards unseen manipulation types and out-of-domain images.

Simulation and Error Analysis of Methane Detection Globally Using Spaceborne IPDA Lidar

Methane (CH4) is recognized as the second most important greenhouse gas. An accurate and precise monitoring of methane gas globally has a vital role in studying the carbon cycle and global warming. The spaceborne integrated path differential absorption (IPDA) lidar is one of the most effective payload for methane detection. The simulation and optimization of the lidar system parameters can create an important base for the development of spaceborne payloads. However, previous IPDA lidar simulations have mostly used standard atmospheric models at simulation conditions, and to the best of our knowledge, there is no literature yet which applies a wavelength optimization to the IPDA system. In this study, we have investigated the relationship between the IPDA lidar system, based on wavelength optimization, and error measurement for CH4 column-averaged concentration. By selecting the wavelengths with the lowest comprehensive error as on-line and off-line, the error has been minimized by 10 ppb approximately relative to before optimization. We have proposed an IPDA simulation model at real atmospheric conditions, combining with ERA-5 reanalysis data, to simulate methane concentration globally, and present the distribution of errors. Finally, after the optimization of the lidar system parameters, we have ensured that the maximum inversion error for CH4 measurement is less than 10 ppb, to provide a reference for designing spaceborne IPDA lidar systems for high-precision CH4 column-averaged concentration detection.

Prediction of Safety Risk Levels of Benzopyrene Residues in Edible Oils in China Based on the Variable-Weight Combined LSTM-XGBoost Prediction Model.

To assess and predict the food safety risk of benzopyrene (BaP) in edible oils in China, this study collected national sampling data of edible oils from 20 Chinese provinces and their prefectures in 2019, and constructed a risk assessment model of BaP in edible oils with consumption data. Initially, the k-means algorithm was used for risk classification; then the data were pre-processed and trained to predict the data using the Long Short-Term Memory (LSTM) and the eXtreme Gradient Boosting (XGBoost) models, respectively, and finally, the two models were combined using the inverse error method. To test the effectiveness of the prediction model, this study experimentally validated the model according to five evaluation metrics: root mean square error (RMSE), mean absolute error (MAE), precision, recall, and F1 score. The variable-weight combined LSTM-XGBoost prediction model proposed in this paper achieved a precision of 94.62%, and the F1 score value reached 95.16%, which is significantly better than other neural network models; the results demonstrate that the prediction model has certain stability and feasibility. Overall, the combined model used in this study not only improves the accuracy but also enhances the practicality, real-time capabilities, and expandability of the model.

Transfer Learning-Based Coupling of Smoothed Finite Element Method and Physics-Informed Neural Network for Solving Elastoplastic Inverse Problems

In practical engineering applications, there is a high demand for inverting parameters for various materials, and obtaining monitoring data can be costly. Traditional inverse methods often involve tedious computational processes, require significant computational effort, and exhibit slow convergence speeds. The recently proposed Physics-Informed Neural Network (PINN) has shown great potential in solving inverse problems. Therefore, in this paper, we propose a transfer learning-based coupling of the Smoothed Finite Element Method (S-FEM) and PINN methods for the inversion of parameters in elastic-plasticity problems. The aim is to improve the accuracy and efficiency of parameter inversion for different elastic-plastic materials with limited data. High-quality small datasets were synthesized using S-FEM and subsequently combined with PINN for pre-training purposes. The parameters of the pre-trained model were saved and used as the initial state for the PINN model in the inversion of new material parameters. The inversion performance of the coupling of S-FEM and PINN is compared with the coupling of the conventional Finite Element Method (FEM) and PINN on a small data set. Additionally, we compared the efficiency and accuracy of both the transfer learning-based and non-transfer learning-based methods of the coupling of S-FEM and PINN in the inversion of different material parameters. The results show that: (1) our method performs well on small datasets, with an inversion error of essentially less than 2%; (2) our approach outperforms the coupling of conventional FEM and PINN in terms of both computational accuracy and computational efficiency; and (3) our approach is at least twice as efficient as the coupling of S-FEM and PINN without transfer learning, while still maintaining accuracy. Our method is well-suited for the inversion of different material parameters using only small datasets. The use of transfer learning greatly improves computational efficiency, making our method an efficient and accurate solution for reducing computational cost and complexity in practical engineering applications.

Fourier spectral resolution enhancement algorithm based on linear prediction

Fourier transform infrared spectroscopy (FTIR) has been widely used for real-time monitoring of ambient gases, but for quantitative analysis of certain gases, higher spectral resolution is required to quantify more accurately. In this paper, a Fourier spectral resolution enhancement algorithm based on linear prediction is proposed. Firstly, the linear prediction model for interference signals is studied, utilizing the forward and backward linear prediction total least squares method for parameter estimation, minimum error criterion for determining the autoregressive (AR) model order, and sliding window technique for multi-step prediction. Then, the impact of the signal-to-noise ratio, enhancement factor, and initial resolution of the FTIR spectrum on the accuracy of the algorithm was studied through simulations. Finally, the algorithm is applied to spectral resolution enhancement and quantitative analysis of ammonia (NH3). The experimental results show that when the spectral resolution of NH3 is enhanced from 4 cm−1 to 2 cm−1 and 1 cm−1, the spectral error of the characteristic band is 0.16% and 0.26%, respectively. Additionally, the accuracy of concentration inversion is improved by 2.13% and 4.06%, respectively. The relative error of concentration inversion is 0.69% and 2.15%, respectively, when compared to the measured spectrum at corresponding resolutions. The algorithm proves effective in enhancing spectral resolution and improving the accuracy of quantitative analysis.

Particle size distribution measurement based on the angular scattering efficiency factor spectra inversion-simulation and experiment.

The quantification of the particle size distribution (PSD) within a particle system is significant to various domains, including atmospheric and environmental sciences, material science, civil engineering, and human health. The scattering spectrum reflects the PSD information of the particle system. Researchers have developed high-precision and high-resolution PSD measurements for monodisperse particle systems through scattering spectroscopy. However, for polydisperse particle systems, current methods based on light scattering spectrum and Fourier transform analysis can only obtain the information of the particle component, but cannot provide the relative content information of each component. In this paper, a PSD inversion method based on the angular scattering efficiency factors (ASEF) spectrum is proposed. By establishing a light energy coefficient distribution matrix, and then measuring the scattering spectrum of the particle system, PSD can be measured in conjunction with inversion algorithms. The simulations and experiments conducted in this paper substantiate the validity of the proposed method. Unlike the forward diffraction approach that measures the spatial distribution of scattered light I(θ) for inversion, our method uses the multi-wavelength distribution information of scattered light β(λ). Moreover, the influences of noise, scattering angle, wavelength, particle size range, and size discretization interval on PSD inversion are studied. The method of condition number analysis is proposed to identify the appropriate scattering angle, particle size measurement range, and size discretization interval, and it can reduce the root mean square error(RMSE) of PSD inversion. Furthermore, the method of wavelength sensitivity analysis is proposed to select the spectral band with higher sensitivity to particle size changes, thereby improving the computational speed and avoiding the problem of diminished accuracy caused by the reduction of the number of wavelengths used.

Nonlinear inversion of electrical resistivity sounding data for multi-layered 1-D earth model using global particle swarm optimization (GPSO)

Interpreting geophysical data requires solving nonlinear optimization problem(s) in inversion. Analytical methods such as least-square have some intrinsic limitations, which include slow convergence and dimensionality, making heuristic-based swarm intelligence a better alternative. Large-scale nonlinear optimization problems in inversion can be solved effectively using a technique within the swarm intelligence family called Particle Swarm Optimization (PSO). This study evaluates the inversion of geoelectrical resistivity data with global particle swarm optimization (GPSO). We attempted to invert field vertical electrical sounding data for a multi-layered 1-D earth model using the developed particle swarm optimization algorithm. The result of the PSO-interpreted VES data was compared with that of the least square inversion result from Winresist 1.0. According to the PSO-interpreted VES results, satisfactory solutions may be attained with a swarm of 200 or fewer particles, and convergence can be reached in fewer than 100 iterations. The GPSO inversion approach has a maximum capacity of 100 iterations, more than the least square inversion algorithm of the Winresist, which has a maximum capacity of 30 iterations. The misfit error of GPSO inversion is 6.14×10−7, much lower than that of the least square inversion of 4.0. The GPSO inversion model has lower and upper limit values of the geoelectric layer parameters model to fit the true model better. The limitations of the developed PSO inversion scheme include a slower execution time of the inversion procedures than the least-square inversion. There is a need for a priori knowledge of the number of layers from borehole reports in the study area. The PSO inversion scheme, however, estimates inverted models closer to the true solutions with greater accuracy than the least-square inversion scheme.

Performance of single empirical orthogonal function regression method in global sound speed profile inversion and sound field prediction

The sound speed profile (SSP) reflects the change in sound speed from the surface to the bottom of the seawater, which will have an important influence on underwater acoustic detection and communication. Depending on the inversion of sea surface data sets measured by satellite to obtain near-real-time and high-precision SSPs has become a research hotspot. In this paper, based on the Argo data and the sea surface data sets, we use the single empirical orthogonal function regression (sEOF-r) method to inverse the global SSPs and evaluate the performance of this method. There are also differences in the performance of inversed results at different sites and in different months at the global scale of the ocean. The eddy kinetic energy (EKE) affects the accuracy of inversion, we propose to add the EKE into the inversion formula at the same time to further optimize the inversed results and improve the accuracy, the global average inversion error after optimization reduces by 20%. Finally, we verify the effectiveness of the optimized method from the perspective of sound field prediction. In most cases, the correlation coefficient of the transmission loss (TL) calculated through the inversion SSP and Argo-SSP exceeds 0.7 and the error is controlled below 6 dB, which will have important implications for the actual sound field prediction and hydroacoustic communication.

Study on the Evolution Law of Overlying Strata Structure in Stope Based on “Space–Air–Ground” Integrated Monitoring Network and Discrete Element

The geological environmental damage caused by coal mining has become a hot issue in current research. Especially in the western mining area, the size of the mining working face is large, the mining intensity is high, while the surface movement and deformation are more intense and wider. Therefore, it is necessary to effectively monitor the surface using appropriate means and carrying out research on the overlying strata structure of the stope. In this paper, by using advantages of various subsidence monitoring technologies and the technical framework of the Internet of Things (IoT), a “space–air–ground” integrated collaborative monitoring network is constructed. The evolution law of overlying strata structure is studied based on discrete element simulations and theoretical analysis. Furthermore, a discrete element mechanical parameter inversion method is proposed. The main results, using numerical simulations, are as follows: The mean square error of monitoring surface subsidence is 33.2 mm, the mean square error of mechanical parameter inversion is 13.4 mm, and relative error is as low as 3.8%. The surface subsidence law of adjacent mining under different working face widths and interval coal pillar widths is revealed. The Boltzmann function model of surface subsidence ratio changing with width–depth ratio and the calculation formula of width reduction coefficient of adjacent mining working face are inverted. The critical failure width of the interval coal pillar is determined as 20.5 m. Based on the theory of “arch–beam” structure and numerical simulation results, the overlying strata structure model of adjacent mining in the mining area is constructed. The research results can provide technical support or theoretical reference for mining damage monitoring, subsidence control, and prediction in western mines.

A Secondary Particle Filter Photometric Data Inversion Method of Space Object Characteristics

A secondary particle filter (SPF) inversion method for geostationary space object characteristics based on ground photometric data is presented. The method combines the estimation results of the standard particle filter (PF) algorithm and the resampling algorithm of the particle generation process. SPF first generates N particles according to the standard PF process, and performs the standard PF without resampling. Particle weight is an important indicator to determine the closeness of particles to the real state. With the progress of PF, the weight of particles closer to the real state will gradually increase. SPF takes the particle weight value as an important basis to judge the closeness of particles to the real state. By setting a threshold, the particles closest to the real state are screened out and roughened. The SPF method in this paper uses a particle filter twice and it is a new particle filter method. The first particle filter identifies particles near the real state. Before the second particle filter, it is equivalent to the actual state distribution of the system is known, so that the distribution of initial particles can be set more efficiently and effectively, and the number of particles close to the real state of the system can be increased. Experiment results show that the estimation error and the RMSE of the inversion error of SPF are less than PF, which not only shows that the inversion result based on SPF is better than the inversion result based on PF, but also proves the effectiveness of the inversion method based on SPF.

Multiple Thermal Parameter Inversion for Concrete Dams Using an Integrated Surrogate Model

An efficient and accurate method for concrete thermal parameter inversion is essential to guarantee the reliable and prompt thermal analysis results of dams. Traditional inversion methods either suffer from low analysis efficiency or are limited in accuracy. Thus, this paper presents a method for multiple thermal parameter inversion based on an integrated surrogate model (ISM) and the Jaya algorithm. This method replaces finite element analysis with an ISM incorporating three machine learning algorithms, Kriging, support vector regression (SVR), and radial basis function (RBF), to describe the mapping relationship between thermal parameters and structure temperature responses. The input datasets for model training and testing are generated by a uniform design approach. Subsequently, a simple and efficient global optimization algorithm, Jaya, is used to identify the thermal parameters by minimizing the error between calculated and monitored temperatures. The effectiveness and practicality of this method are verified by applying monitored data of two strength grades of concrete in a dam. The verification results indicate that the proposed approach can obtain more accurate inversion results than the above individual models. Compared with these models, the inversion errors using ISM are reduced by 8.45%, 3.93% and 20.85%, respectively for C35 concrete, and by 6.53%, 23.82% and 44.43%, respectively for C40 concrete. Additionally, this approach maintains the powerful computational efficiency of surrogate-based optimization, and compared to the methods that directly invert using swarm intelligence algorithms, the analysis efficiency is improved by about 111.7 times.

A Modular Method for GPR Hyperbolic Feature Detection and Quantitative Parameter Inversion of Underground Pipelines

Ground penetrating radar (GPR) is widely used to inspect underground pipelines because it is non-destructive. When the scan line of GPR is perpendicular to the pipe, it will exhibit hyperbolic features in GPR B-scan images, which have no intuitive relationship with the geometric and physical parameters of the pipeline, making the interpretation of GPR images difficult. This paper proposes a modular detection and quantitative inversion method for the hyperbolic features in GPR B-scan images, which is divided into two steps. In the first step, the YOLOv7 object detection network is used to automatically detect the hyperbolic features in GPR images. In the second step, a two-stage curve fitting method is proposed based on the characteristics of the detection model. It uses a few key point annotations of the hyperbolic pattern and some parameters of the GPR system to quantitatively invert the depth and radius of pipes. Using the same hardware and data set, YOLOv7 achieves an 11.1% improvement in detection accuracy and an 18.2% improvement in speed compared to YOLOv5. The relative errors of the proposed method for the depth and radius of the synthetic data in homogeneous media are 0.6% and 4.4%, respectively, and 4.8% and 15% in non-homogeneous media. The relative error of the depth inversion of the measured data TU1208 is less than 10%. The results show that the method can effectively invert the depth and radius of underground pipelines and reduce the difficulty of GPR data interpretation.

Neural Network and Dynamic Inversion Based Adaptive Control for an HALE-UAV against Icing Effects

In the past few decades, in-flight icing has become a common problem for many missions, potentially leading to a reduction in control effectiveness and flight stability, which would threaten flight safety. One of the most popular methods to address this problem is adaptive control. This paper establishes a dynamic model of an iced high-altitude long-endurance unmanned aerial vehicle (HALE-UAV) with disturbance and measurement noise. Then, by combining multilayer perceptrons (MLP) with a nonlinear dynamic inversion (NDI) controller, we propose an MLP-NDI controller to compensate for online inversion errors and provide a brief proof of control stability. Two experiments were conducted: on one hand, we compared the MLP-NDI controller with other typical controllers; on the other hand, we evaluated its robustness and adaptiveness under different icing conditions. Results indicate that the MLP-NDI controller outperforms other typical controllers with higher tracking accuracy and exhibits strong robustness in the presence of icing errors and measurement noise, which has huge potential to ensure flight safety.

Compensating errors in inversions for subglacial bed roughness: same steady state, different dynamic response

Abstract. Subglacial bed roughness is one of the main factors controlling the rate of future Antarctic ice-sheet retreat and also one of the most uncertain. A common technique to constrain the bed roughness using ice-sheet models is basal inversion, tuning the roughness to reproduce the observed present-day ice-sheet geometry and/or surface velocity. However, many other factors affecting ice-sheet evolution, such as the englacial temperature and viscosity, the surface and basal mass balance, and the subglacial topography, also contain substantial uncertainties. Using a basal inversion technique intrinsically causes any errors in these other quantities to lead to compensating errors in the inverted bed roughness. Using a set of idealised-geometry experiments, we quantify these compensating errors and investigate their effect on the dynamic response of the ice sheet to a prescribed forcing. We find that relatively small errors in ice viscosity and subglacial topography require substantial compensating errors in the bed roughness in order to produce the same steady-state ice sheet, obscuring the realistic spatial variability in the bed roughness. When subjected to a retreat-inducing forcing, we find that these different parameter combinations, which per definition of the inversion procedure result in the same steady-state geometry, lead to a rate of ice volume loss that can differ by as much as a factor of 2. This implies that ice-sheet models that use basal inversion to initialise their model state can still display a substantial model bias despite having an initial state which is close to the observations.

Electrical signal reconstruction method of target-simulated minesweeper based on small unmanned boat platform

In recent years, with the continuous development of military unmanned boat technology, there has been a significant increase in interest in small unmanned boat-based minesweeper hunting technology. In this paper, an electrical signal reconstruction method based on time–frequency characteristics and used for small minesweeping gear is proposed. Compared with the existing methods, the method does not require measurement to obtain the complete electrical signal of the distribution and is applicable to both surface ships and submarines for signal reconstruction, which can complete the reconstruction of the original signal with high accuracy in the case of incomplete signal acquisition and can be applied to the signal reconstruction under the harsh marine acquisition environment or strong electromagnetic interference. In this paper, the mathematical model between the maximum sampling interval and the captain is established by extracting the time–frequency features of large ships, and the optimal size of the minesweeper and the optimal parameters of the point charge model are obtained based on the point charge model, and the performance of the method under low signal-to-noise ratio conditions is evaluated by depth permutation. Under the challenging signal-to-noise ratio conditions, the proposed method can accomplish the high-precision reconstruction of the electrical signal distribution of a large ship with the passage data collected by only one measurement node. From the results of simulation and ship model experiments, it can be seen that the electric signal can be simulated with a series unmanned boat array of one-tenth the size of a large ship, and the amplitude error of the reconstructed signal is less than 0.2 mV, the inversion error of EF(Electrostatic Field) is less than 10%, and the inversion error of SEF(shaft-frequency electric field) is less than 12%.

Spatial-temporal analysis of coal fire risk identification and suppression assessment with satellite time series mapping 2013-2020 in Midong coalfield, Xinjiang, China

ABSTRACT Spontaneous combustion of underground coal seam leads to significant loss of coal resource while causing serious geological disasters, environmental degradation and social security problems. The Midong Coalfield in Urumqi was selected to conduct research on dynamic detection and assessment of underground coal fires from 2013 to 2020 based on time series satellite imagery of Landsat-8. The land surface temperature (LST) was retrieved using RTE. The hotspot SFSE was proposed to map the spatial-temporal distribution of coal fires. The CTIR was also established to solve how to comprehensively evaluate the intensity and spatial variations of coal fire thermal island effect. Based on Sequence Overlap Analysis the integrated dynamic interpretation of thermal anomaly intensity, area and migration of coal fire hazard has been provided. In addition, the TADC was proposed to effectively reflect the active fire centre and aggregation tendency. The results show that: The RTE inversion error is within 4.6 °C, verified with the surveyed LST. The overall accuracy of fire thermal anomaly extraction by HSA by field-tested exceeds 65%. A feature can be judged to be a fire pixel when its recurrence reaches 75% or more of the total number of observation frequency. The maximum and minimum extent extracted of the total fire area is 65.6×105 and 46.6×105 m2, respectively. And the overall expansion rate is 1.29×105 m2 year−1, in 82% agreement with the measurement. The burning intensity of CTIR first increases 0.024 year−1 averagely, but then decreases at a rate of 0.0055 year−1. Fractures and faults in the fire-affected area play a critical role in fire induction and distribution. Frequent mining and excavation activities are confirmed to accelerate the further fire production and propagation. After suppression, the relevant fire area has shrunken by up to 60%, while the overall CTIR is reduced by more than 70%.

Optimal Hamiltonian simulation for time-periodic systems

The implementation of time-evolution operators U(t), called Hamiltonian simulation, is one of the most promising usage of quantum computers. For time-independent Hamiltonians, qubitization has recently established efficient realization of time-evolution U(t)=e−iHt, with achieving the optimal computational resource both in time t and an allowable error ε. In contrast, those for time-dependent systems require larger cost due to the difficulty of handling time-dependency. In this paper, we establish optimal/nearly-optimal Hamiltonian simulation for generic time-dependent systems with time-periodicity, known as Floquet systems. By using a so-called Floquet-Hilbert space equipped with auxiliary states labeling Fourier indices, we develop a way to certainly obtain the target time-evolved state without relying on either time-ordered product or Dyson-series expansion. Consequently, the query complexity, which measures the cost for implementing the time-evolution, has optimal and nearly-optimal dependency respectively in time t and inverse error ε, and becomes sufficiently close to that of qubitization. Thus, our protocol tells us that, among generic time-dependent systems, time-periodic systems provides a class accessible as efficiently as time-independent systems despite the existence of time-dependency. As we also provide applications to simulation of nonequilibrium phenomena and adiabatic state preparation, our results will shed light on nonequilibrium phenomena in condensed matter physics and quantum chemistry, and quantum tasks yielding time-dependency in quantum computation.