Spatiotemporal Field Research Articles

Physics-informed neural networks for the Reynolds-Averaged Navier–Stokes modeling of Rayleigh–Taylor turbulent mixing

Recently, Physics-informed neural networks (PINNs) have proven to be an efficient machine-learning method for solving partial differential equations. However, this method can be quite challenging when solving complex problems with shock/material discontinuities or multi-scale features, such as turbulence. In this paper, we propose an improved PINNs framework for solving the Reynolds-averaged Navier–Stokes (RANS) equations for turbulent mixing induced by the Rayleigh–Taylor (RT) instability. The RANS model is based on the closure form of the K–L model. However, the transport equations of the turbulent kinetic energy K and turbulent length scale L are not included and are instead predicted directly by neural networks, thus resulting in an inverse problem. Several modifications are made to the original PINNs to improve its applicability to RT turbulent mixing and accelerate the training optimization process. We first examine the applicability of the PINNs for solving multi-material Euler equations without considering turbulence. Then, PINNs is applied to the RT turbulent mixing problem using training data from the traditional K–L model. The results confirm the ability of the PINNs to predict the entire spatiotemporal field using limited training data. Next, we further train the PINNs using data from the implicit large eddy simulation (ILES), which yields a PINN-based turbulence model that performs better than the traditional K–L model. These results shed light on further applications of PINNs for complex problems, particularly those with limited measurement data and unknown physical models.

Sensing Travel Source–Sink Spatiotemporal Ranges Using Dockless Bicycle Trajectory via Density-Based Adaptive Clustering

The travel source–sink phenomenon is a typical urban traffic anomaly that reflects the imbalanced dissipation and aggregation of human mobility activities. It is useful for pertinently balancing urban facilities and optimizing urban structures to accurately sense the spatiotemporal ranges of travel source–sinks, such as for public transportation station optimization, sharing resource configurations, or stampede precautions among moving crowds. Unlike remote sensing using visual features, it is challenging to sense imbalanced and arbitrarily shaped source–sink areas using human mobility trajectories. This paper proposes a density-based adaptive clustering method to identify the spatiotemporal ranges of travel source–sink patterns. Firstly, a spatiotemporal field is utilized to construct a stable neighborhood of origin and destination points. Then, binary spatiotemporal statistical hypothesis tests are proposed to identify the source and sink core points. Finally, a density-based expansion strategy is employed to detect the spatial areas and temporal durations of sources and sinks. The experiments conducted using bicycle trajectory data in Shanghai show that the proposed method can accurately extract significantly imbalanced dissipation and aggregation events. The travel source–sink patterns detected by the proposed method have practical reference, meaning that they can provide useful insights into the redistribution of bike-sharing and station resources.

Spatio-temporal solid-state electrocaloric effect exceeding twice the adiabatic temperature change

In an all-solid-state electrocaloric arrangement, an absolute temperature change which exceeds twice the electrocaloric adiabatic temperature change is locally realized, using just the distributed thermal capacitances and resistances and spatio-temporal distributed electric field control. First, simulations demonstrate surface temperature changes up to four times (400%) the electrocaloric adiabatic temperature change for several implementations of all-solid state distributed element configurations. Then, experimentally, an all-solid-state assembly is built from commercial electrocaloric capacitors with two independently-controlled parts, and the measured surface temperature change was 223% of the adiabatic electrocaloric temperature change, which clearly exceeds twice the adiabatic temperature change and verifies the practical feasibility of the approach. This allows a significant increase of the maximum temperature difference per stage in cascaded and thermal switch-based electrocaloric heat pumps, which was previously limited by the adiabatic electrocaloric temperature change (100%) under no-load conditions. Distributed thermal element simulations provide insight in the spatio-temporal temperatures within the all-solid-state electrocaloric element. Since only the distributed thermal capacitance and resistance is used to boost the temperature change, the maximum absolute temperature change occurs only in parts of the all-solid-state element, for example close to the surfaces. A trade-off of the approach is that the required electrocaloric capacitance increases more than the gained boost of the absolute temperature change, reducing the power density and electrical efficiency in heat pump systems. Nevertheless, the proposed approach enables to simplify electrocaloric heat pumps or to increasing the achievable temperature span, and might also improve other electrocaloric applications.

SequenceMorph: A Unified Unsupervised Learning Framework for Motion Tracking on Cardiac Image Sequences.

Modern medical imaging techniques, such as ultrasound (US) and cardiac magnetic resonance (MR) imaging, have enabled the evaluation of myocardial deformation directly from an image sequence. While many traditional cardiac motion tracking methods have been developed for the automated estimation of the myocardial wall deformation, they are not widely used in clinical diagnosis, due to their lack of accuracy and efficiency. In this paper, we propose a novel deep learning-based fully unsupervised method, SequenceMorph, for in vivo motion tracking in cardiac image sequences. In our method, we introduce the concept of motion decomposition and recomposition. We first estimate the inter-frame (INF) motion field between any two consecutive frames, by a bi-directional generative diffeomorphic registration neural network. Using this result, we then estimate the Lagrangian motion field between the reference frame and any other frame, through a differentiable composition layer. Our framework can be extended to incorporate another registration network, to further reduce the accumulated errors introduced in the INF motion tracking step, and to refine the Lagrangian motion estimation. By utilizing temporal information to perform reasonable estimations of spatio-temporal motion fields, this novel method provides a useful solution for image sequence motion tracking. Our method has been applied to US (echocardiographic) and cardiac MR (untagged and tagged cine) image sequences; the results show that SequenceMorph is significantly superior to conventional motion tracking methods, in terms of the cardiac motion tracking accuracy and inference efficiency.

Simulation of the dependence of the radiation pattern of a digital active phased array antenna on the main destabilizing factors

As for today digital active phased array antennas (DAPAA), based on the principle of functioning using digital diagram formation, are actively used as part of spacecraft and unmanned aerial vehicles in solving radio communication and radar problems. At the same time, for the purposes of radar, DAPAA allows you to perceive all the information contained in the structure of spatiotemporal electromagnetic fields in the opening of the array and transform it into data on the presence and parameters of objects, providing deep compensation for broadband interference signals, which, combined with the expansion of the dynamic range when accumulated during spatiotemporal processing, provides high noise immunity of radar stations. To solve communication problems, DAPAA allows you to form several beams simultaneously, which allows you to simultaneously serve several areas at once with the possibility of dynamically changing the bandwidth in the channels due to variations in partial power.

Spatio-temporal species kinetics, thermal and electrical field evolution in an argon EFCAP under different rates of nitrogen seeding: A one-dimensional simulation study

Nitrogen seeding is crucial in cold plasma devices for production of reactive nitrogen species. Excitation Frequency Controlled Cold Atmospheric Pressure Plasma (EFCAP) devices belong to recent concepts in cold plasma where discharge kinetics can be controlled via tuning of external field frequency. The study presents time dependent modelling of such an atmospheric pressure non-DBD argon discharge between two bare electrodes in one dimension under different rates on nitrogen seeding using commercial software COMSOL Multiphysics version 5.4. A square alternating high voltage power source of frequency 11 kHz and peak voltage of 500V drives the discharge in the model. In every half-period, there is an electrical breakdown. Spatio-temporal variations in the electron density, ion density, electric field, electric potential, and electron temperature are investigated. Observed unique spatial oscillations in the species densities, species temperature and distinct drift in the observed characteristics with different rates of nitrogen seeding are some of the appealing aspects revealed by the study. The excitation and dissociation of molecules, generation and losses of ions, plasma mediated reactions and collisional excitations are accounted elaborately in the model developed. The study could explain the origin of typical non-uniform discharge patterns reported experimentally under different excitation frequencies in EFCAP. Obtained results are expected to be useful for better understanding of device physics towards development of improved cold plasma sources with desired characteristics.

Four-wave mixing on thermal and resonant nonlinearities with feedback for object and signal waves

Background. The need to create highly efficient four-wave radiation converters in order to use them in adaptive optics systems, for real-time processing of complex spatio-temporal fields, in interferometry, quantum cryptography, etc. requires along with the use of traditional methods to increase the efficiency of such converters by increasing the interaction length, radiation power density, effective value of the nonlinear susceptibility of the development of new methods. One of these methods is a method based on the imposition of feedback on one or more interacting waves. Aim. The influence of feedback on the amplitude reflection coefficient of the degenerate four-wave radiation converter on thermal and resonant nonlinearities has been considered. Methods. The amplitude reflection coefficient of a degenerate four-wave radiation converter on thermal and resonant nonlinearities in the presence of feedback for both object and signal waves has been analyzed by a numerical method based on the multiple passage of the signal and object waves of the nonlinear layer in the ring resonator. Results. It was shown, that the difference in the reflection coefficients in the presence and absence of feedback for both object and signal waves increase monotonically with a growth in the pumping waves intensity and does not depend on the parameter characterizing the relationship between thermal and resonant nonlinearities at the approximation of a small reflection coefficient. Conclusion. The range of values of the absorption coefficient in which the imposition of feedback for both object and signal waves leads to an increase in the efficiency of the four-wave radiation converter has been established.

Convolutional neural network-based spatiotemporal prediction for deformation behavior of arch dams

Deformation directly reflects the behavior of arch dams, and deformation behavior models have been widely used for structural health monitoring (SHM) in accordance with monitoring data. The deformation field brings advantages to the SHM of arch dams in terms of the spatiotemporal scale. In this paper, a spatiotemporal deformation field behavior model based on a convolutional neural network (CNN) was proposed. The temperature field of the dam fusing the climatological data, including air temperature, weather conditions, and solar radiation, was introduced. Furthermore, the water pressure and constraint fields were also input into the CNN-based model. The physical law and structural continuity were considered, and the parameters of the CNN-based model were general and uniform for each predicted location. The accuracy and extrapolation ability of the proposed model were evaluated. The results illustrate that the CNN-based model predicts accurate deformation at the spatiotemporal scale of the arch dam. The accuracy of the prediction of single-point deformation time series from the CNN-based model is close to that from the traditional hydraulic-seasonal-time (HST) model and finite element model (FEM). For the prediction of the spatial deformation field, the mean MAE of the CNN-based model is 2.68 mm, while it is 5.66 mm for the FEM model, showing much higher prediction accuracy of the CNN-based model. The proposed globally uniform CNN-based model can derive a high-precision and high-density deformation field of arch dams with sparse monitoring data. It can also be continuously updated in real-time according to the latest monitoring data without inverse analysis and parameter adjustment like the FEM model.

Generalized central slice theorem perspective on Fourier-transform spectral imaging at a sub-Nyquist sampling rate.

Fourier-transform spectral imaging captures frequency-resolved images with high spectral resolution, broad spectral range, high photon flux, and low stray light. In this technique, spectral information is resolved by taking Fourier transformation of the interference signals of two copies of the incident light at different time delays. The time delay should be scanned at a high sampling rate beyond the Nyquist limit to avoid aliasing, at the price of low measurement efficiency and stringent requirements on motion control for time delay scan. Here we propose, what we believe to be, a new perspective on Fourier-transform spectral imaging based on a generalized central slice theorem analogous to computerized tomography, using an angularly dispersive optics decouples measurements of the spectral envelope and the central frequency. Thus, as the central frequency is directly determined by the angular dispersion, the smooth spectral-spatial intensity envelope is reconstructed from interferograms measured at a sub-Nyquist time delay sampling rate. This perspective enables high-efficiency hyperspectral imaging and even spatiotemporal optical field characterization of femtosecond laser pulses without a loss of spectral and spatial resolutions.

Deep learning method for super-resolution reconstruction of the spatio-temporal flow field

The high-resolution (HR) spatio-temporal flow field plays a decisive role in describing the details of the flow field. In the acquisition of the HR flow field, traditional direct numerical simulation (DNS) and other methods face a seriously high computational burden. To address this deficiency, we propose a novel multi-scale temporal path UNet (MST-UNet) model to reconstruct temporal and spatial HR flow fields from low-resolution (LR) flow field data. Different from the previous super-resolution (SR) model, which only takes advantage of LR flow field data at instantaneous (SLR) or in a time-series (MTLR), MST-UNet introduces multi-scale information in both time and space. MST-UNet takes the LR data at the current frame and the predicted HR result at the previous moment as the model input to complete the spatial SR reconstruction. On this basis, a temporal model is introduced as the inbetweening model to obtain HR flow field data in space and time to complete spatio-temporal SR reconstruction. Finally, the proposed model is validated by the spatio-temporal SR task of the flow field around two-dimensional cylinders. Experimental results show that the outcome of the MST-UNet model in spatial SR tasks is much better than those of SLR and MTLR, which can greatly improve prediction accuracy. In addition, for the spatio-temporal SR task, the spatio-temporal HR flow field predicted by the MST-UNet model has higher accuracy either.

Experimental and numerical investigation of surface streamers in a nanosecond pulsed packed bed reactor

Packed bed reactor (PBR) is the commonly used configuration in plasma catalysis, and its plasma characteristics have been extensively investigated. The filled catalysts in PBR make it challenging to carry out in-situ measurements of electric fields, and limited experimental data have been obtained. We investigated the surface streamer propagation and electric field distribution in a simplified PBR through simulations and experiments. The simplified PBR in the experiments is comprised of a blade-plate electrode structure filled with an Al2O3 column (ϵr = 9) in the discharge gap. An ICCD camera and an electric field diagnosis method called EFISH (electric field induced second harmonic generation) were employed, and a two-dimensional fluid model was established for the simulation. Four discharge types in the PBR were identified based on ICCD images and simulation results, including polar discharge at the contact areas, surface streamer along the dielectric column, expansion of surface discharge along the dielectric column, and surface ionization waves along the dielectric plate. Surface streamers with opposite propagation directions were found in the model, namely the forward streamer during the pulse rising time and the reverse streamer during the pulse falling time. Notably, the reverse streamer exhibits a significantly lower velocity compared to the forward streamer. Both experimental measurements and simulation were conducted to investigate the spatiotemporal electric field near the surface of the packing material. The results of both E exp and E sim showed peaks with opposite polarities, and exhibited similar trends. In the simulation, the forward streamer head showed a higher electric field compared to the reverse streamer head. Moreover, during the rest pulse time, the surface electric field was more intense at the contact areas than in other regions. The findings of this work provide valuable insights into the discharge mechanism and electric field on the catalytic material surface within the PBR.

A statistical significance test for spatio-temporal receptive field estimates obtained using spike-triggered averaging of binary pseudo-random sequences

A statistical significance test for spatio-temporal receptive field estimates obtained using spike-triggered averaging of binary pseudo-random sequences

Sea surface height data reconstruction via inter and intra layer features based on dual attention

Understanding of geoscience relies on spatio-temporal continuous fields, such as Sea Surface Height (SSH). Data reconstruction for restoring spatio-temporal continuous and gridded maps from incomplete observations and inaccuracy interpolation products has long been a crucial challenge in the marine geoscience. Despite remarkable progress, most existing learning-based reconstruction methods neglect to fully and discriminatively utilize the inter-layer and intra-layer features. The inter-layer semantics are complementary, and the significance of intra-layer components varies with frequency. To address these issues, we propose a multi-layer Feature Combination Network based on Attention mechanism (FCANet) for SSH data reconstruction. Specifically, a novel trainable Multi-layer Feature Combination Block (MFCB) is developed to enrich the features through inter-layer dependencies. Dual attention mechanism is introduced into the MFCB to enhance saliency of intra-layer features by adaptively rescaling the spatial-wise and channel-wise features. Furthermore, experimental results on SSH variable demonstrate the superiority of our FCANet over state-of-the-art reconstruction methods in the metrics of RMSE and SSIM.

Intra-Patient Lung CT Registration through Large Deformation Decomposition and Attention-Guided Refinement.

Deformable lung CT image registration is an essential task for computer-assisted interventions and other clinical applications, especially when organ motion is involved. While deep-learning-based image registration methods have recently achieved promising results by inferring deformation fields in an end-to-end manner, large and irregular deformations caused by organ motion still pose a significant challenge. In this paper, we present a method for registering lung CT images that is tailored to the specific patient being imaged. To address the challenge of large deformations between the source and target images, we break the deformation down into multiple continuous intermediate fields. These fields are then combined to create a spatio-temporal motion field. We further refine this field using a self-attention layer that aggregates information along motion trajectories. By leveraging temporal information from a respiratory cycle, our proposed methods can generate intermediate images that facilitate image-guided tumor tracking. We evaluated our approach extensively on a public dataset, and our numerical and visual results demonstrate the effectiveness of the proposed method.

Dynamic Mode Decomposition of merging wind turbine wakes

The design and operation of wind farms is significantly affected by the impact that upstream turbine wakes have on the power production and fatigue loading of subsequent turbines; often called the wake effect. In this work, two types of flows are considered: the wake of a single turbine with a laminar inflow and the combined wake of two turbines operating in-line where the upstream wake results in an unsteady inflow for the downstream turbine. Those two scenarios are simulated using large eddy simulation (LES) and the actuator line method (ALM). The spatio-temporal velocity fields are analyzed by means of high order dynamic mode decomposition (HODMD), a well established variant of the DMD. The results show that most of the higher frequencies characterizing the laminar case are instead dominated by the lower frequency modes in the combined wake. This suggests that structures emerging from the blade rotations in a wind turbine wake may be less significant for describing the wake dynamics when the rotor is operating in the unsteady wake of an upstream rotor.

Temporal and Spatial Variation Characteristics of SST in the North Pacific Ocean in Summer

Using Hadley Centre Sea Sea Surface Temperature data in the North Pacific region (0°N~60°N, 120°E~80°W) from 1950 to 2017, based on Empirical orthogonal function(EOF) analysis, the multi-year spatio-temporal field of SST in the North Pacific Ocean in summer into three main modes is decomposed into three modes. The temporal and spatial variation characteristics of SST in the North Pacific summer (June to August) are discussed in detail. The results show that the spatial distribution and time series of the first mode can reflect ENSO signal well. Compared with the first mode, the spatial field of the second mode has an inverse phase distribution. The spatial field distribution of the third mode is similar to the zonal distribution, and the whole sea area presents an oscillating structure of alternating cold and warm regions from south to north.

A Technology for Seismogenic Process Monitoring and Systematic Earthquake Forecasting

Earthquakes are a severe natural phenomenon that require continuous monitoring, analysis, and forecasting to mitigate their risks. Seismological data have long been used for this purpose, but geodynamic data from remote sensing of surface displacements have become available in recent decades. In this paper, we present a novel information technology for monitoring, analyzing seismogenic fields, and predicting earthquakes using Earth remote sensing data presented as a time series of surface displacement points for systematic regional earthquake prediction. We demonstrate, for the first time, the successful application of this technology and discuss the method of the minimum area of alarm, which was developed for machine learning and systematic earthquake prediction, as well as the architecture and tools of the GIS platform. Our technology is implemented as a network platform consisting of two GISs. The first GIS automatically loads earthquake catalog data and GPS time series, calculates spatiotemporal fields, performs systematic earthquake prediction in multiple seismically active regions, and provides intuitive mapping tools to analyze seismic processes. The second GIS is designed for scientific research of spatiotemporal processes, including those related to earthquake forecasting. We demonstrate the effectiveness of platform analysis tools that are intuitive and accessible to a wide range of users in solving problems of systematic earthquake prediction. Additionally, we provide examples of scientific research on earthquake prediction using the second GIS, including the effectiveness of using GPS data for forecasting earthquakes in California, estimating the density fields of earthquake epicenters using the adaptive weighted smoothing (AWS) method for predicting earthquakes in Kamchatka, and studying earthquake forecasts in the island part of the territory of Japan using the earthquake catalog and GPS. Our examples demonstrate that the method of the minimum area of alarm used for machine learning is effective for forecasting both catalog and remote sensing data.

Test and Visualization of Covariance Properties for Multivariate Spatio-Temporal Random Fields

The prevalence of multivariate space-time data collected from monitoring networks and satellites, or generated from numerical models, has brought much attention to multivariate spatio-temporal statistical models, where the covariance function plays a key role in modeling, inference, and prediction. For multivariate space-time data, understanding the spatio-temporal variability, within and across variables, is essential in employing a realistic covariance model. Meanwhile, the complexity of generic covariances often makes model fitting very challenging, and simplified covariance structures, including symmetry and separability, can reduce the model complexity and facilitate the inference procedure. However, a careful examination of these properties is needed in real applications. In the work presented here, we formally define these properties for multivariate spatio-temporal random fields and use functional data analysis techniques to visualize them, hence, providing intuitive interpretations. We then propose a rigorous rank-based testing procedure to conclude whether the simplified properties of covariance are suitable for the underlying multivariate space-time data. The good performance of our method is illustrated through synthetic data, for which we know the true structure. We also investigate the covariance of bivariate wind speed, a key variable in renewable energy, over a coastal and an inland area in Saudi Arabia. The supplementary material is available online, including the R code for our developed methods.

Synthesizing Audio from Tongue Motion During Speech Using Tagged MRI Via Transformer.

Investigating the relationship between internal tissue point motion of the tongue and oropharyngeal muscle deformation measured from tagged MRI and intelligible speech can aid in advancing speech motor control theories and developing novel treatment methods for speech related-disorders. However, elucidating the relationship between these two sources of information is challenging, due in part to the disparity in data structure between spatiotemporal motion fields (i.e., 4D motion fields) and one-dimensional audio waveforms. In this work, we present an efficient encoder-decoder translation network for exploring the predictive information inherent in 4D motion fields via 2D spectrograms as a surrogate of the audio data. Specifically, our encoder is based on 3D convolutional spatial modeling and transformer-based temporal modeling. The extracted features are processed by an asymmetric 2D convolution decoder to generate spectrograms that correspond to 4D motion fields. Furthermore, we incorporate a generative adversarial training approach into our framework to further improve synthesis quality on our generated spectrograms. We experiment on 63 paired motion field sequences and speech waveforms, demonstrating that our framework enables the generation of clear audio waveforms from a sequence of motion fields. Thus, our framework has the potential to improve our understanding of the relationship between these two modalities and inform the development of treatments for speech disorders.

Correlation-based sparse inverse Cholesky factorization for fast Gaussian-process inference

Gaussian processes are widely used as priors for unknown functions in statistics and machine learning. To achieve computationally feasible inference for large datasets, a popular approach is the Vecchia approximation, which is an ordered conditional approximation of the data vector that implies a sparse Cholesky factor of the precision matrix. The ordering and sparsity pattern are typically determined based on Euclidean distance of the inputs or locations corresponding to the data points. Here, we propose instead to use a correlation-based distance metric, which implicitly applies the Vecchia approximation in a suitable transformed input space. The correlation-based algorithm can be carried out in quasilinear time in the size of the dataset, and so it can be applied even for iterative inference on unknown parameters in the correlation structure. The correlation-based approach has two advantages for complex settings: It can result in more accurate approximations, and it offers a simple, automatic strategy that can be applied to any covariance, even when Euclidean distance is not applicable. We demonstrate these advantages in several settings, including anisotropic, nonstationary, multivariate, and spatio-temporal processes. We also illustrate our method on multivariate spatio-temporal temperature fields produced by a regional climate model.