Temporal Error Research Articles

Unconditional stability and error estimates of the modified characteristics FEMs for the Micropolar Navier–Stokes Equations

In this paper, the unconditional stability and optimal error estimate of the velocity, pressure and angular velocity for the modified characteristics FEMs of the unsteady Micropolar Naiver–Stokes Equations (MNSE) are presented. In this method, the nonlinear equation is linearized by the characteristic finite element method for dealing with the time derivative term and the convection term. Basing on the characteristic time-discrete system, the error function is split into a temporal error and a spatial error. With a rigorous analysis to the characteristic time-discrete system, we prove that the error between the numerical solution and the solution of the time-discrete system is τ-independent, where τ denotes the time stepsize. The stability results and optimal error estimates in L2 norm and H1 norm will be given. Finally, some numerical results will be provided to confirm our theoretical analysis.

IMU-Based Real-Time Estimation of Gait Phase Using Multi-Resolution Neural Networks.

This work presents a real-time gait phase estimator using thigh- and shank-mounted inertial measurement units (IMUs). A multi-rate convolutional neural network (CNN) was trained to estimate gait phase for a dataset of 16 participants walking on an instrumented treadmill with speeds varying between 0.1 to 1.9 m/s, and conditions such as asymmetric walking, stop-start, and sudden speed changes. One-subject-out cross-validation was used to assess the robustness of the estimator to the gait patterns of new individuals. The proposed model had a spatial root mean square error of 5.00±1.65%, and a temporal mean absolute error of 2.78±0.97% evaluated at the heel strike. A second cross-validation was performed to show that leaving out any of the walking conditions from the training dataset did not result in significant performance degradation. A 2-sample Kolmogorov-Smirnov test showed that there was no significant increase in spatial or temporal error when testing on the abnormal walking conditions left out of the training set. The results of the two cross-validations demonstrate that the proposed model generalizes well across new participants, various walking speeds, and gait patterns, showcasing its potential for use in investigating patient populations with pathological gaits and facilitating robot-assisted walking.

Attention and feature binding in the temporal domain.

Previous studies have shown that illusory conjunction can emerge for both spatially and temporally proximal objects. However, the mechanisms involved in binding in the temporal domain are not yet fully understood. In the current study, we investigated the role of attentional processes in correct and incorrect temporal binding, and specifically how feature binding is affected by the speed of attentional engagement. In two experiments, participants searched for a target in a rapid serial visual presentation stream and reported its colour and alphanumeric identity. Temporal binding errors were frequent. Critically, when participants reported the identity of a distractor instead of a target, they were also more likely to report the colour of this distractor. This association was observed both within and between individuals. These findings suggest that attentional engagement facilitates the binding of temporally co-occurring features. We discuss these results within a 'diachronic' framework of selective attention, and also consider other factors that contribute to temporal binding errors.

Consistent Individual Tendencies in Motor Speed-Accuracy Trade-Off.

The literature on speed-accuracy trade-off (SAT) in motor control has evidenced individuality in how individuals trade moments (e.g.,mean and variance) of spatial and temporal errors. These individual tendencies could grasp tendencies of the system given previous experiences and constraints of the organism, a signature of the system control. Nonetheless, such tendency must be robust to small perturbations. Thirty participants performed nine conditions with different time and spatial criteria over 2days (scanning). In between these scanning conditions, individuals performed a practice condition that required modifications of the individuals' preferred spatial and temporal tendency in the SAT. Our results demonstrated that there were no systematic effects of practice in SAT preferences. However, individual analyses demonstrated significant changes for 25 out of 30 individuals. The latter either attests against a consistent preference or to a more complex characterization of individual SAT tendencies.

Concrete acoustic emission signal augmentation method based on generative adversarial networks

With the development of concrete structure health monitoring (SHM), the utilization of acoustic emission (AE) as an effective non-destructive testing method has attracted increasing attention among researchers. However, the acquisition of concrete AE signals in real-world scenarios is often limited, which poses challenges to the training as well as the practical application of deep learning (DL) models. To address this problem, a concrete acoustic emission signal augmentation method based on generative adversarial networks (GAN) is proposed in this paper. This method features a unique architecture where both the generator and discriminator are built upon a Bidirectional Long Short-Term Memory (BiLSTM) network. Additionally, the generator integrates an attention mechanism between the BiLSTM layers, enhancing its ability to capture the temporal dynamics of AE signals. To improve the local details of the generated signals, a temporal difference mean square error (TD-MSE) regularization is incorporated into the loss function. Experimental results demonstrate that the method not only substantially increases the amount of data available but also significantly enhances the model’s generalization capabilities and classification accuracy.

Sentinel-2 Reference Fire Perimeters for the Assessment of Burned Area Products over Latin America and the Caribbean for the Year 2019

The increasing availability of products generating burned area (BA) maps in recent years necessitates the creation of more accurate reference perimeters to validate these products and provide users with information about their accuracy. For this purpose, reference perimeters were created using Sentinel-2 images in Latin America and the Caribbean (LAC) for the year 2019. The sampling was adapted to the peculiarities of the Sentinel-2 tiling grid system, and statistically representative sample units were selected for biomes and fire activity through stratified random sampling. Fire perimeters were extracted using a Random Forest supervised classification and results were manually supervised and refined. Efforts were made to maximize the temporal length covered by the reference perimeters for each sample, aiming to minimize temporal errors when using the perimeters for validation. The dataset covers 569,214.2 km2 (3.5% burned, 88.7% unburned, and 7.8% unobserved). These perimeters were compared with higher spatial resolution PlanetScope-derived perimeters, resulting in 8.4% commission errors and 3.8% omission errors. As a validation exercise, MCD64A1 and FireCCI51 global burned area products were validated using the Sentinel-2 reference dataset created, confirming that the temporal extent of the reference perimeters significantly affects the validation of such products. The reference fire perimeters are publicly available in the Burned Area Reference Database (BARD).

Application of immersive virtual reality for assessing chronic neglect in individuals with stroke: the immersive virtual road-crossing task

ABSTRACT Background Neglect can be a long-term consequence of chronic stroke that can impede an individual’s ability to perform daily activities, but chronic and discrete forms can be difficult to detect. We developed and evaluated the “immersive virtual road-crossing task” (iVRoad) to identify and quantify discrete neglect symptoms in chronic stroke patients. Method The iVRoad task requires crossing virtual intersections and placing a letter in a mailbox placed either on the left or right. We tested three groups using the HTC Vive Pro Eye: (1) chronic right hemisphere stroke patients with (N = 20) and (2) without (N = 20) chronic left-sided neglect, and (3) age and gender-matched healthy controls (N = 20). We analyzed temporal parameters, errors, and head rotation to identify group-specific patterns, and applied questionnaires to measure self-assessed pedestrian behavior and usability. Results Overall, the task was well-tolerated by all participants with fewer cybersickness-induced symptoms after the VR exposure than before. Reaction time, left-sided errors, and lateral head movements for traffic from left most clearly distinguished between groups. Neglect patients committed more dangerous crossings, but their self-rated pedestrian behavior did not differ from that of stroke patients without neglect. This demonstrates their reduced awareness of the risks in everyday life and highlights the clinical relevance of the task. Conclusions Our findings suggest that a virtual road crossing task, such as iVRoad, has the potential to identify subtle symptoms of neglect by providing virtual scenarios that more closely resemble the demands and challenges of everyday life. iVRoad is an immersive, naturalistic virtual reality task that can measure clinically relevant behavioral variance and identify discrete neglect symptoms.

Unconditional optimal first‐order error estimates of a full pressure segregation scheme for the magnetohydrodynamics equations

AbstractIn this article, a first‐order linear fully discrete pressure segregation scheme is studied for the time‐dependent incompressible magnetohydrodynamics (MHD) equations in three‐dimensional bounded domain. Based on an incremental pressure projection method, this scheme allows us to decouple the MHD system into two sub‐problems at each time step, one is the velocity‐magnetic field system, the other is the pressure system. Firstly, a coupled linear elliptic system is solved for the velocity and the magnetic field. Next, a Poisson‐Neumann problem is treated for the pressure. We analyze the temporal error and the spatial error, respectively, and derive the temporal‐spatial error estimates of for the velocity and the magnetic field in the discrete space and for the pressure in the discrete space without imposing constraints on the mesh width and the time step size . Finally, some numerical results are presented to confirm the theoretical predictions and demonstrate the efficiency of the method.

Prioritized experience replay based on dynamics priority

Experience replay has been instrumental in achieving significant advancements in reinforcement learning by increasing the utilization of data. To further improve the sampling efficiency, prioritized experience replay (PER) was proposed. This algorithm prioritizes experiences based on the temporal difference error (TD error), enabling the agent to learn from more valuable experiences stored in the experience pool. While various prioritized algorithms have been proposed, they ignored the dynamic changes of experience value during the training process, merely combining different priority criteria in a fixed or linear manner. In this paper, we present a novel prioritized experience replay algorithm called PERDP, which employs a dynamic priority adjustment framework. PERDP adaptively adjusts the weights of each criterion based on average priority level of the experience pool and evaluates experiences’ value according to current network. We apply this algorithm to the SAC model and conduct experiments in the OpenAI Gym experimental environment. The experiment results demonstrate that the PERDP exhibits superior convergence speed when compared to the PER.

Research on decision making of intelligent vehicle based on composite priority experience replay

To address the problems of underutilization of samples and unstable training for intelligent vehicle training in the Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm, a TD3 algorithm based on the Composite Prioritized Experience Replay (CPR-TD3) mechanism is proposed. It considers experience immediate reward value and Temporal Difference error (TD-error) based and respectively to construct priorities to rank the samples. Subsequently composite average ranking of the samples to recalculate the priorities for sampling, uses the collected samples to train the target network. Then introduces the minimum lane change distance and the variable headway time distance to improve the reward function. Finally, the improved algorithm is proved to be effective by comparing it with the traditional TD3 on the highway scenario, and the CPR-TD3 algorithm improves the training efficiency of intelligent vehicles.

Image based automatic wind velocity profiler for adaptive optics

Abstract Adaptive optics (AO) systems correct optical phase aberrations of the incoming light generated by the atmosphere. To do so simultaneous estimators of the atmospheric turbulence parameters are required. For the family of wide-field AO systems (WFAO), this information must be stratified in altitude. Among these vectorized estimations, wind profiling in altitude is needed for the reduction of temporal errors in AO loops or for the estimation of turbulence coherence time. This paper proposes a turbulence wind profiler called image processing based peak tracking algorithm (IPTA). IPTA is an image-processing based approach that automatically and reliably estimates wind velocity for several turbulent layers along the line of sight. The estimation of each wind layer is achieved by tracking peaks produced in cross-correlation maps from pairs of wavefront sensors (WFSs) slopes using the technique known as SLODAR (slope detection and ranging). Results for simulated and on-sky WFS datasets demonstrate that IPTA outperforms one of the state of the art wind profiler methods (the profiler covariance parametrization of wind velocity (CAW)) in terms of accuracy and speed. Results also show that, in terms of execution time, our method scales better when the number of WFS lenslets is increased. Being an open source and reliable tool, we believe IPTA can be a useful wind profiler for the adaptive optics community.

Frontal Norepinephrine Represents a Threat Prediction Error Under Uncertainty

BackgroundTo adapt to threats in the environment, animals must predict them and engage in defensive behavior. While the representation of a prediction error signal for reward has been linked to dopamine, a neuromodulatory prediction error for aversive learning has not been identified. MethodsWe measured and manipulated norepinephrine release during threat learning using optogenetics and a novel fluorescent norepinephrine sensor. ResultsWe found that norepinephrine response to conditioned stimuli reflects aversive memory strength. When delays between auditory stimuli and footshock are introduced, norepinephrine acts as a prediction error signal. However, temporal difference prediction errors do not fully explain norepinephrine dynamics. To explain noradrenergic signaling, we used an updated reinforcement learning model with uncertainty about time and found that it explained norepinephrine dynamics across learning and variations in temporal and auditory task structure. ConclusionsNorepinephrine thus combines cognitive and affective information into a predictive signal and links time with the anticipation of danger.

Testing temporal transferability of remote sensing models for large area monitoring

Applying remote sensing models outside the temporal range of their training data, referred to as temporal model transfer, has become common practice for large area monitoring projects that extrapolate models for hindcasting or forecasting to time periods lacking reference data. However, the development of appropriate validation methods for temporal transfer has lagged behind its rapid adoption. Breaking temporal transfer's assumption of temporal consistency in both remote sensing and reference data and their relationship to each other could lead to biased pixel-level predictions and small area estimators, compromising the operational validity of large area monitoring products. Few studies using temporal transfer have evaluated its effects on model accuracy at the pixel/plot level, and the propensity for biased small area estimators and trends resulting from temporal transfer remains unexplored. We present a framework for evaluating temporal transferability by combining temporal cross-validation with a multiscale map assessment to aid in identifying where and when biased model predictions could scale to small area estimates and affect predicted trends.This validation framework is demonstrated in a case study of annual percent tree canopy cover mapping in Michigan. We tested and compared temporal transferability of random forest models of canopy cover derived from 2010 to 2016 systematic dot-grid photo-interpretations at Forest Inventory and Analysis plots with Landsat spectral indices fit with the LandTrendr temporal segmentation algorithm serving as the primary predictor variables. The temporal cross-validation error (mean RMSE = 13.9% cover) was higher than the common validation approach of considering all time periods of testing data together (RMSE = 13.6% cover) and lower than models trained and tested within the same year (mean RMSE = 14.2% cover). However, the bias of model predictions and small area estimators for individual years was higher with temporal transfer models than when applying models within the same year as their training data. We also evaluated how training models using different temporal subsets and with and without LandTrendr fitting affected predictions of Michigan's 1984–2020 predicted annual mean cover. The mean cover from LandTrendr-based models followed expected and consistent trends and had less difference between models trained with different temporal subsets (max difference = 5.8% cover). While those from Landsat had high interannual variations and greater difference between temporal models (max difference = 11.2% cover). The results of this case study demonstrate that evaluation of temporal transferability is necessary for establishing the operational validity of large area monitoring products, even when using time series algorithms that improve temporal consistency.

Optimal Adaptive Tracking Control of Partially Uncertain Nonlinear Discrete-Time Systems Using Lifelong Hybrid Learning.

This article addresses a multilayer neural network (MNN)-based optimal adaptive tracking of partially uncertain nonlinear discrete-time (DT) systems in affine form. By employing an actor-critic neural network (NN) to approximate the value function and optimal control policy, the critic NN is updated via a novel hybrid learning scheme, where its weights are adjusted once at a sampling instant and also in a finite iterative manner within the instants to enhance the convergence rate. Moreover, to deal with the persistency of excitation (PE) condition, a replay buffer is incorporated into the critic update law through concurrent learning. To address the vanishing gradient issue, the actor and critic MNN weights are tuned using control input and temporal difference errors (TDEs), respectively. In addition, a weight consolidation scheme is incorporated into the critic MNN update law to attain lifelong learning and overcome catastrophic forgetting, thus lowering the cumulative cost. The tracking error, and the actor and critic weight estimation errors are shown to be bounded using the Lyapunov analysis. Simulation results using the proposed approach on a two-link robot manipulator show a significant reduction in tracking error by 44% and cumulative cost by 31% in a multitask environment.

Temporal Error Correlations in a Terrestrial Carbon Cycle Model Derived by Comparison to Carbon Dioxide Eddy Covariance Flux Tower Measurements

AbstractAtmospheric CO2 flux inversions require as input an estimate of spatial and temporal correlations of errors in their estimate of the prior mean. Some previous studies have used the differences in CO2 daily average flux estimates produced by terrestrial carbon cycle models and eddy covariance measurements to constrain the flux error correlations. Since inversions are starting to resolve the daily cycle, we set out to examine the correlations at sub‐daily time scales, as well as the correlations across years. To this end, we examine the autocorrelations in the difference between net ecosystem‐atmosphere exchange measurements from 75 AmeriFlux towers and temporally downscaled high‐spatial‐resolution flux estimates from the Carnegie‐Ames‐Stanford Approach (CASA) terrestrial carbon cycle model. We find that the daily cycle is prominent in these hourly autocorrelations and that these autocorrelations persist across years. We propose a family of functions to model these temporal correlations in atmospheric inversions, and use cross validation to determine which of the correlation functions best fits autocorrelation data from towers not in the training set. Correlation functions with a component that attempts to model the daily cycle in the differences match correlations from other towers better than those without. Those models that reproduce the same correlation structures at 1‐year intervals while modulating the amplitudes of the correlations between those intervals improve the fit still further.

Temporal Information Processing in the Cerebellum and Basal Ganglia.

Temporal information processing in the range of a few hundred milliseconds to seconds involves the cerebellum and basal ganglia. In this chapter, we present recent studies on nonhuman primates. In the studies presented in the first half of the chapter, monkeys were trained to make eye movements when a certain amount of time had elapsed since the onset of the visual cue (time production task). The animals had to report time lapses ranging from several hundred milliseconds to a few seconds based on the color of the fixation point. In this task, the saccade latency varied with the time length to be measured and showedstochastic variability from one trial to the other. Trial-to-trial variability under the same conditions correlated well with pupil diameter and the preparatory activity in the deep cerebellar nuclei and the motor thalamus. Inactivation of these brain regions delayed saccades when asked to report subsecond intervals. These results suggestthat the internal state, which changes with each trial, may cause fluctuations in cerebellar neuronal activity, thereby producing variations in self-timing. When measuring different time intervals, the preparatory activity in the cerebellum always begins approximately 500ms before movements, regardless of the length of the time interval being measured. However, the preparatory activity in the striatum persists throughout the mandatory delay period, which can be up to 2s, with different rate of increasing activity. Furthermore, in the striatum, the visual response and low-frequency oscillatory activity immediately before time measurement were altered by the length of the intended time interval. These results indicate that the state of the network, including the striatum, changes with the intended timing, which lead to different time courses of preparatory activity. Thus, the basal ganglia appear to be responsible for measuring time in the range of several hundred milliseconds to seconds, whereas the cerebellum is responsible for regulating self-timing variability in the subsecond range. The second half of this chapter presents studies related to periodic timing. During eye movements synchronized with alternating targets at regular intervals, different neurons in the cerebellar nuclei exhibit activity related to movement timing, predicted stimulus timing, and the temporal error of synchronization. Among these, the activity associated with target appearance is particularly enhanced during synchronized movements and may represent an internal model of the temporal structure of stimulus sequence. We also considered neural mechanism underlying the perception of periodic timing in the absence of movement. During perception of rhythm, we predict the timing of the next stimulus and focus our attention on that moment. In the missing oddball paradigm, the subjects had to detect the omission of a regularly repeated stimulus. When employed in humans, the results show that the fastest temporal limit for predicting each stimulus timing is about 0.25s (4Hz). In monkeys performing this task, neurons in the cerebellar nuclei, striatum, and motor thalamus exhibit periodic activity, with different time courses depending on the brain region. Since electrical stimulation or inactivation of recording sites changes the reaction time to stimulus omission, these neuronal activities must be involved in periodic temporal processing. Future research is needed to elucidate the mechanism of rhythm perception, which appears to be processed by both cortico-cerebellar and cortico-basal ganglia pathways.

Quantifying and eliminating the time delay in stabilization exponential time differencing Runge–Kutta schemes for the Allen–Cahn equation

Although the stabilization technique is favorable in designing unconditionally energy stable or maximum-principle-preserving schemes for gradient flow systems, the induced time delay is intractable in computations. In this paper, we propose a class of delay-free stabilization schemes for the Allen–Cahn gradient flow system. Considering the Fourier pseudo-spectral spatial discretization for the Allen–Cahn equation with either the polynomial or the logarithmic potential, we establish a semi-discrete, mesh-dependent maximum principle by adopting a stabilization technique. To unconditionally preserve the mesh-dependent maximum principle and energy stability, we investigate a family of exponential time differencing Runge–Kutta (ETDRK) integrators up to the second-order. After reformulating the ETDRK schemes as a class of parametric Runge–Kutta integrators, we quantify the lagging effect brought by stabilization, and eliminate delayed convergence using a relaxation technique. The temporal error estimate of the relaxation ETDRK integrators in the maximum norm topology is analyzed under a fixed spatial mesh. Numerical experiments demonstrate the delay-free and structure-preserving properties of the proposed schemes.

Temporal covariance of spatial soil moisture variations: A mechanistic error modeling approach

AbstractWhen estimating field‐scale average soil moisture from sensors measuring at fixed positions, spatial variability in soil moisture leads to “measurement errors” of the spatial mean, which may persist over time due to persistent soil moisture patterns resulting in autocorrelated measurement errors. The uncertainty of parameters that are derived from such measurements may be underestimated when they are assumed to be independent. Temporal autocorrelation models assume stationary random errors, but such error models are not necessarily applicable to soil moisture measurements. As an alternative, we propose a mechanistic error model that is based on the spatial variability of the water retention curve and assumes a uniform water potential. We tested whether spatial soil moisture variability and its temporal covariance could be predicted based on (1) mean soil moisture, (2) water retention variability, and (3) (co)variances of the van Genuchten parameters using a first‐order expansion of the retention curve. The proposed models were tested in a numerical and a field experiment. For the field experiment, in situ sensor measurements and water retention curves were obtained in a field plot. Both experiments showed that water retention variability under a uniform water potential is a good predictor for spatial soil moisture variability, and that soil moisture errors are strongly correlated in time and neglecting them would be an incorrect assumption. The temporal error covariance could be predicted as a function of the mean moisture contents at two observation times. Further research is required to assess the impact of these temporal correlations on soil moisture predictions.

An Actor-Critic Hierarchical Reinforcement Learning Model for Course Recommendation

Online learning platforms provide diverse course resources, but this often results in the issue of information overload. Learners always want to learn courses that are appropriate for their knowledge level and preferences quickly and accurately. Effective course recommendation plays a key role in helping learners select appropriate courses and improving the efficiency of online learning. However, when a user is enrolled in multiple courses, existing course recommendation methods face the challenge of accurately recommending the target course that is most relevant to the user because of the noise courses. In this paper, we propose a novel reinforcement learning model named Actor-Critic Hierarchical Reinforcement Learning (ACHRL). The model incorporates the actor-critic method to construct the profile reviser. This can remove noise courses and make personalized course recommendations effectively. Furthermore, we propose a policy gradient based on the temporal difference error to reduce the variance in the training process, to speed up the convergence of the model, and to improve the accuracy of the recommendation. We evaluate the proposed model using two real datasets, and the experimental results show that the proposed model significantly outperforms the existing recommendation models (improving 3.77% to 13.66% in terms of HR@5).

VT-IO: A Virtual Time System Enabling High-fidelity Container-based Network Emulation for I/O Intensive Applications

Network emulation allows unmodified code execution on lightweight containers to enable accurate and scalable networked application testing. However, such testbeds cannot guarantee fidelity under high workloads, especially when many processes concurrently request resources (e.g., CPU, disk I/O, GPU, and network bandwidth) that are more than the underlying physical machine can offer. A virtual time system enables the emulated hosts to maintain their own notion of virtual time. A container can stop advancing its time when not running (e.g., in an idle or suspended state). The existing virtual time systems focus on precise time management for CPU-intensive applications but are not designed to handle other operations, such as disk I/O, network I/O, and GPU computation. In this paper, we develop a lightweight virtual time system that integrates precise I/O time for container-based network emulation. We model and analyze the temporal error during I/O operations and develop a barrier-based time compensation mechanism in the Linux kernel. We also design and implement Dynamic Load Monitor (DLM) to mitigate the temporal error during I/O resource contention. VT-IO enables accurate virtual time advancement with precise I/O time measurement and compensation. The experimental results demonstrate a significant improvement in temporal error with the introduction of DLM. The temporal error is reduced from 7.889 seconds to 0.074 seconds when utilizing the DLM in the virtual time system. Remarkably, this improvement is achieved with an overall overhead of only 1.36% of the total execution time.