Efficient Forward Model Research Articles

Learning Structured Representations of Spatial and Interactive Dynamics for Trajectory Prediction in Crowded Scenes

Context plays a significant role in the generation of motion for dynamic agents in interactive environments. This work proposes a modular method that utilises a learned model of the environment for motion prediction. This modularity explicitly allows for unsupervised adaptation of trajectory prediction models to unseen environments and new tasks by relying on unlabelled image data only. We model both the spatial and dynamic aspects of a given environment alongside the per agent motions. This results in more informed motion prediction and allows for performance comparable to the state-of-the-art. We highlight the model's prediction capability using a benchmark pedestrian prediction problem and a robot manipulation task and show that we can transfer the predictor across these tasks in a completely unsupervised way. The proposed approach allows for robust and label efficient forward modelling, and relaxes the need for full model re-training in new environments.

Dynamic simulation of falling weight deflectometer tests on flexible transversely isotropic layered pavements

Developing an accurate and efficient forward model of the dynamic response of pavement structure is of great significance for obtaining the design parameters of the layered pavement structure through inverse calculation based on the measured pavement data. Based on the spectral element method, this study proposes an accurate and efficient numerical dynamic model of falling weight deflectometer tests for the transversely isotropic layered pavement structure. The developed algorithm considerably enhances the efficiency of the model in solving the dynamic response of transversely isotropic layered media by avoiding the infinite integration in integral transformation. Moreover, numerical examples verify the accuracy and efficiency of the algorithm developed in this study. At the same time, an extensive parametric studies have been carried out to clarify the effects of the Young's modulus in the vertical direction and thickness of the layered pavement structure as well as the elastic modulus of the thin interlayer on the dynamic response of the pavement, which provides a reliable, numerical, theoretical basis for the design of pavement structure.

A nonlinear spectral element model for the simulation of traffic speed deflectometer tests of asphalt pavements

ABSTRACT A non-destructive testing method suitable for network-level pavement structural evaluation is the traffic speed deflectometer (TSD) test. However, the analysis of TSD measurements still needs a proper parameter back-calculation procedure, which requires an accurate and efficient forward calculation model. As a first step to solving this issue, a nonlinear spectral element model which can simulate TSD tests of asphalt pavements is developed. The model is used to investigate the characteristics and parameter sensitivity of the response of asphalt pavements caused by the TSD loading. The results indicate that the vertical deflection curve along the direction of movement observed on the asphalt pavement surface is slightly asymmetric, and the maximum deflection appears behind the centre of the loading area. In addition, the slope curve of vertical deflection is highly sensitive to the magnitude of the applied force, the moduli of the base layer and subgrade, and the thicknesses of the asphalt layer and base layer. Furthermore, the slope curve is relatively sensitive to the glassy modulus of the asphalt layer. Because of its good predictive capability and high computational efficiency, the proposed model has the desired characteristics to be used as the computational kernel for parameter back-calculation procedures of TSD measurements.

Numerical Modelling of Borehole-Surface CSEM Response of Onshore Gas Hydrate Deposit with Higher Order Finite Difference Method

The recent increase in energy demand has propelled research on the discovery of unconventional energy sources as conventional oil and gas reservoirs are been depleted. Hence, in this study, we investigate the feasibility of using the Borehole Controlled Source Electromagnetic (BSCSEM) method for gas hydrate exploration in Qilian Mountain, China. To achieve this, we developed an accurate and efficient forward modeling code for the simulation of electromagnetic diffusion problems based on the total field formulation using the Frequency Domain Finite Difference (FDFD) approach. We used large grid sizes to reduce the computational cost of simulating the borehole to surface responses and also examined the effect of applying the Perfectly Matched Layer (PML) on the BSCSEM computational area. Subsequently, we investigate the effects of the higher and lower-order approximations and used spatial operators of the lower order and first-order accuracy in substantial parts of the computational domain including but not limited to layer boundaries during the solution process. We also investigate responses from different source orientations and source length, with a focus on the electric dipoles for 2D and 3D models of buried resistive targets. Finally, we performed 2D modeling to detect onshore gas hydrate deposit for known scenarios using a suitable BSCSEM configuration for 200 m borehole dipole with an average current of 10 A. Our results generally indicate that the BSCSEM responses from the vertical transmitters were highly effective in characterizing the resistive layers as well as the measurement of the vertical component of the electric field. By changing the depth of the vertical dipole sources, we found out that BSCSEM showed the ability to gain information about the subsurface medium from different angles. Hence, we conclude that in a complex environment, the combined use of the horizontal and the vertical transmitters to acquire three component (3C) field data and the joint analysis of their electric responses helps to delineate the subsurface structure more clearly.

Non-line-of-sight Reconstruction Using Efficient Transient Rendering

Being able to see beyond the direct line of sight is an intriguing prospect and could benefit a wide variety of important applications. Recent work has demonstrated that time-resolved measurements of indirect diffuse light contain valuable information for reconstructing shape and reflectance properties of objects located around a corner. In this article, we introduce a novel reconstruction scheme that, by design, produces solutions that are consistent with state-of-the-art physically based rendering. Our method combines an efficient forward model (a custom renderer for time-resolved three-bounce indirect light transport) with an optimization framework to reconstruct object geometry in an analysis-by-synthesis sense. We evaluate our algorithm on a variety of synthetic and experimental input data, and show that it gracefully handles uncooperative scenes with high levels of noise or non-diffuse material reflectance.

An efficient forward model based on the Lattice Boltzmann method for optical tomography

Optical tomography is a powerful tool for preclinical and clinical biomedical research, which enables quantitative observation and precise localization of regions of interest within biological tissues. However, the excessive time caused by the forward model of optical tomography is the main limitation of its application in many fields, such as the dynamic imaging. In this paper, we present an efficient forward model based on the Lattice Boltzmann method (LBM), which is realized by radiation transfer equation discretization to simplify the mathematical structures and apply it for optical tomography. To demonstrate the feasibility of the proposed model for optical tomography, we carried out numerical cylinder simulation to validate the simulated light source distribution. To evaluate the performance of the proposed model for optical tomography, we performed a numerical phantom and a physical phantom experiments on a hybrid fluorescence diffuse optical tomography/X-CT imaging system to observe the tomographic reconstruction, by using the simulated phantom data and the experimental phantom data, respectively. The results showed that our proposed forward model obtained similar light source distribution comparing with the standard Monte Carlo method and the cosine similarity was about 96%. Further, our proposed forward model greatly improves the efficiency of optical tomography without a degradation of quality. The LBM provided about 5 times speed enhancement for phantom experiment and 2 times contrast-to-noise ratio boost for physical phantom experiment. Experimental results showed that our proposed model has large potential for performance improvement in optical tomography.

Spheroidal forward modelling of the gravitational fields of 1 Ceres and the Moon

A novel, explicit, and efficient forward modelling of the spheroidal harmonic spectra of external planetary gravitational fields is developed in this article. We introduce the oblate spheroidal coordinate system and derive the mathematical apparatus for the analysis of the spheroidal harmonic spectrum from the volumetric bulk density and geometry of a gravitating body. We discretise the volume integral and formulate a new and efficient numerical algorithm for the spheroidal forward modelling. We provide complete sets of recursions for calculating the associated Legendre functions of the first kind and their integrals in the Supplementary material. We also develop a computer program that implements the numerical algorithm and we test its performance. For this purpose, we consider synthetic gravitational fields of 1 Ceres (a significantly flattened asteroid) and of the Moon (a nearly spherical body). These tests prove high numerical accuracy and applicability of the spheroidal forward modelling up to degree and order 2519. We finally apply our spheroidal forward modelling and its simpler spherical counterpart for computing global gravitational field models up to degree and order 2519 generated by realistic topographic mass distributions of 1 Ceres and of the Moon. These models are compared in the spatial and spectral domains to manifest an enhanced applicability of the spheroidal approach with respect to the spherical one. In particular, we show an extended convergence space when using the spheroidal forward modelling and the corresponding harmonic representation for the oblate 1 Ceres.

Modelling ground‐penetrating radar wave propagation using graphics processor unit parallel implementation of the symplectic Euler method

ABSTRACTInversion of ground‐penetrating radar signals requires accurate and efficient forward modelling. The symplectic Euler method promises good results when simulating ground‐penetrating radar wave propagation in substructures, but its computational efficiency is limited by the same Courant–Friedrichs–Lewy stability condition as the finite‐difference time‐domain method. A two‐dimensional graphics processor unit–accelerated parallel symplectic Euler algorithm is used to simulate ground‐penetrating radar wave propagation. We compared the reflection waveforms as well as the simulation time of the complex underground structure models simulated by the parallel symplectic Euler method with traditional finite‐difference time‐domain method. Results show that the parallel symplectic Euler algorithm achieves the same level of accuracy as the standard finite‐difference time‐domain method. Moreover, it significantly improves the computational efficiency, as the calculation speed is improved by more than 21 times. We verify the performance of the proposed algorithm through a map of the single‐track radar data for a three‐layered pavement model and a simulation wiggle map for a structural damage pavement model. This provides a theoretical basis for accurately interpreting ground‐penetrating radar detection data and efficient forward modelling for the next step of inversion imaging.

Perturbing beyond the shallow amplitude regime: Green’s function scattering formalism with Bloch modes

We present a Bloch modes' based Green's function scattering formalism for cost efficient forward modelling of disordered binary surface textures. The usage of Bloch modes of an unperturbed reference ordered system as ansatz allows our formalism to address surface scattering beyond the shallow amplitude regime. The main advantage of our formalism is the possibility to utilize a small amount of plane waves to represent the assumed Bloch modes thereby reducing computational costs, while still allowing one to estimate the scattering response to all channels accessible by the disordered system. Benchmarking calculations discussed in the paper demonstrate how the usage of our Bloch modes ansatz provides an excellent estimate of the scattering response over an important regime of disorder. As an example of our method's strength, we examine an electrically decoupled binary light trapping texture and demonstrate how introducing disorder may improve light incoupling into the considered solar cell structure.

Efficient 3‐D Large‐Scale Forward Modeling and Inversion of Gravitational Fields in Spherical Coordinates With Application to Lunar Mascons

AbstractAn efficient forward modeling algorithm for calculation of gravitational fields in spherical coordinates is developed for 3‐D large‐scale gravity inversion problems. The 3‐D Gauss‐Legendre quadrature (GLQ) is used to calculate the gravitational fields of mass distributions discretized into tesseroids. Equivalence relations in the kernel matrix of the forward modeling are exploited to decrease storage and computation time. The numerical tests demonstrate that the computation time of the proposed algorithm is reduced by approximately 2 orders of magnitude, and the memory requirement is reduced by N′λ times compared with the traditional GLQ method, where N′λ is the number of the model elements in the longitudinal direction. These significant improvements in computational efficiency and storage make it possible to calculate and store the dense Jacobian matrix in 3‐D large‐scale gravity inversions. The equivalence relations can be applied to the Taylor series method or combined with the adaptive discretization to ensure high accuracy. To further illustrate the capability of the algorithm, we present a regional synthetic example. The inverted results show density distributions consistent with the actual model. The computation took about 6.3 hr and 0.88 GB of memory compared with about a dozen days and 245.86 GB for the traditional 3‐D GLQ method. Finally, the proposed algorithm is applied to the gravity field derived from the latest lunar gravity model GL1500E. Three‐dimensional density distributions of the Imbrium and Serenitatis basins are obtained, and high‐density bodies are found at the depths 10–60 km, likely indicating a significant uplift of the high‐density mantle beneath the two mascon basins.

Two-Stage Method for Diagonal Recurrent Neural Network Identification of a High-Power Continuous Microwave Heating System

This paper proposes a diagonal recurrent neural network (DRNN) based identification scheme to handle the complexity and nonlinearity of high-power continuous microwave heating system (HPCMHS). The new DRNN design involves a two-stage training process that couples an efficient forward model selection technique with gradient-based optimization. In the first stage, an impact recurrent network structure is obtained by a fast recursive algorithm in a stepwise forward procedure. To ensure stability, update rules are further developed using Lyapunov stability criterion to tune parameters of reduced size model at the second stage. The proposed approach is tested with an experimental regression problem and a practical HPCMHS identification, and the results are compared with four typical network models. The results show that the new design demonstrates improved accuracy and model compactness with reduced computational complexity over the existing methods.

Euclid preparation: II. The EuclidEmulator – a tool to compute the cosmology dependence of the nonlinear matter power spectrum

We present a new power spectrum emulator named EuclidEmulator that estimates the nonlinear correction to the linear dark matter power spectrum. It is based on a spectral decomposition method called polynomial chaos expansion. All steps in the construction of the emulator have been tested and optimized: the large high-resolution N-body simulations carried out with PKDGRAV3 were validated using a simulation from the Euclid Flagship campaign and demonstrated to have converged up to wavenumbers $k\approx 5\,h\,{\rm Mpc}^{-1}$ for redshifts $z\leq 5$. The emulator is constructed using the uncertainty quantification software UQLab and it has been optimized first by creating mock emulators based on Takahashi's HALOFIT. We show that it is possible to successfully predict the performance of the final emulator in this way prior to performing any N-body simulations. We provide a C-code to calculate the nonlinear correction at a relative accuracy of $\sim0.3\%$ with respect to N-body simulations within 50 ms. The absolute accuracy of the final nonlinear power spectrum is comparable to one obtained with N-body simulations, i.e. $\sim 1\%$ for $k\lesssim 1\,h\,{\rm Mpc}^{-1}$ and $z\lesssim 3.5$. This enables efficient forward modeling in the nonlinear regime allowing for maximum likelihood estimation of cosmological parameters. EuclidEmulator has been compared to HALOFIT and CosmicEmu, an alternative emulator based on the Mira-Titan Universe, and shown to be more accurate than these other approaches. This work paves a new way for optimal construction of future emulators that also consider other cosmological observables, use higher resolution input simulations and investigate higher dimensional cosmological parameter spaces.

Contribution to the modeling and the mechanical characterization of the subsoil in the LSBB environment

The present research work aims at better characterizing the specific underground environment of the LSBB (Low Noise Inter-Disciplinary Underground Science and Technology, Rustrel, France) using mechanical wave propagation information. The LSBB experimental environment is characterized by a system of cylindrical galleries, some of them presenting a concrete layer. In the global project, three steps are considered : firstly the construction of an efficient forward mechanical wave propagation model to calculate the displacement vector and stress tensor components; secondly a sensitivity analysis to extract the pertinent parameters in the configurations and models under study (viscoelastic or poroviscoelastic media with potential anisotropy); and lastly an inversion strategy to recover some of the pertinent parameters. In this proposal, the first step, under progress, is described. The work carried out is in the continuity of the work presented by Yi et al. (2016) [1] who studied the harmonic response of a cylindrical elastic tunnel, impacted by a plane compressional wave, embedded in an infinite elastic ground. The interface between the rock mass and the linen is an imperfect contact modeled with two spring parameters, Achenbach and Zhu (1989) [2]. We choose a semi-analytical approach to calculate the two-dimensional displacement and stress fields in order to get a fast tool, from the numerical point of view. The main steps of the theoretical approach are : use of the Helmholtz decomposition, solving the wave equation based on the separation method and the expansion in Bessel function series in the harmonic domain. The harmonic results are validated by comparison with Yi et al. (2016) [1] and new ones are presented. Moreover, the transient regime case obtained with the use of a Fourier transform on the time variable, is under progress.

Modeling Three‐Dimensional Wave Propagation in Anelastic Models With Surface Topography by the Optimal Strong Stability Preserving Runge‐Kutta Method

AbstractAccurate and efficient forward modeling methods are important for simulation of seismic wave propagation in 3D realistic Earth models and crucial for high‐resolution full waveform inversion. In the presence of attenuation, wavefield simulation could be inaccurate or unstable over time if not well treated, indicating the importance of the implementation of a strong stability preserving time discretization scheme. In this study, to solve the anelastic wave equation, we choose the optimal strong stability preserving Runge‐Kutta (SSPRK) method for the temporal discretization and apply the fourth‐order MacCormack scheme for the spatial discretization. We approximate the rheological behaviors of the Earth by using the generalized Maxwell body model and use an optimization procedure to calculate the anelastic coefficients determined by the Q(ω) law. This optimization constrains positivity of the anelastic coefficients and ensures the decay of total energy with time, resulting in a stable viscoelastic system even in the presence of strong attenuation. Moreover, we perform theoretical and numerical analyses of the SSPRK method, including the stability criteria and the numerical dispersion. Compared with the traditional fourth‐order Runge‐Kutta method, the SSPRK has a larger stability condition number and can better suppress numerical dispersion. We use the complex‐frequency‐shifted perfectly matched layer for the absorbing boundary conditions based on the auxiliary difference equation and employ the traction image method for the free‐surface boundary condition on curvilinear grids representing the surface topography. Finally, we perform several numerical experiments to demonstrate the accuracy of our anelastic modeling in the presence of surface topography.

Analysis of GPR Wave Propagation Using CUDA‐Implemented Conformal Symplectic Partitioned Runge‐Kutta Method

Accurate forward modeling is of great significance for improving the accuracy and speed of inversion. For forward modeling of large sizes and fine structures, numerical accuracy and computational efficiency are not high, due to the stability conditions and the dense grid number. In this paper, the symplectic partitioned Runge‐Kutta (SPRK) method, surface conformal technique, and graphics processor unit (GPU) acceleration technique are combined to establish a precise and efficient numerical model of electromagnetic wave propagation in complex geoelectric structures, with the goal of realizing a refined and efficient calculation of the electromagnetic response of an arbitrarily shaped underground target. The results show that the accuracy and efficiency of ground‐penetrating radar (GPR) forward modeling are greatly improved when using our algorithm. This provides a theoretical basis for accurately interpreting GPR detection data and accurate and efficient forward modeling for the next step of inversion imaging.

Impaired forward model updating in young adults with Tourette syndrome.

Current theories of motor control emphasize how the brain may use internal models of the body to ensure accurate planning and control of movements. One such internal model-a forward model-is thought to generate an estimate of the next motor state and/or the sensory consequences of an upcoming movement, thereby allowing movement errors to be monitored. In addition, forward models may provide a means by which to determine a sense of agency, i.e. the (conscious) sense of authorship and control over our actions. Tourette syndrome is a developmental neurological condition characterized by the occurrence of motor and phonic tics. The involuntary (or voluntary) nature of tics has been the subject of considerable debate, and it was recently argued that the presence of tics in Tourette syndrome could result in a blurring of any subjective boundary between voluntary and involuntary movements. In particular, it was proposed that the level of sensorimotor noise that accompanies tics may be particularly high in Tourette syndrome, and this may contribute to less efficient forward models used to determine agency. We investigated whether the internal monitoring of movements is impaired in individuals with Tourette syndrome, relative to a matched group of typically developing individuals, using a task that involved executing double-step aiming movements using a hand-held robot manipulandum. Participants were required on each trial to execute two movements in turn, each directed to a remembered target location without visual feedback. Importantly, we assumed that to perform accurately on the second (return) movement it would be necessary to update any forward model to take into account errors made during the first (outward) movement. Here we demonstrate that while the Tourette syndrome group were equally accurate, and no more variable, than the matched control group in executing aiming movements to the first (outward) target location, they were significantly less accurate, and exhibited greater movement variability, than controls when executing the second (return) movement. Furthermore, we show that for the return movement only, movement accuracy and movement variability were significantly predicted by the Tourette syndrome group's clinical severity scores. We interpret these findings as consistent with the view that individuals with Tourette syndrome may experience a reduction in the precision of the forward model estimates thought necessary for the accurate planning and control of movements.

Leap-Frog Continuous–Discontinuous Galerkin Time Domain Method for Nanoarchitectures With the Drude Model

A continuous–discontinuous Gakerkin time domain method (CDGTD) with vector basis functions is proposed to analyze the wideband response of plasmonic structures with the Drude dispersive model. Compared to the conventional time domain approaches, such as FDTD and PSTD, the unstructured mesh can provide a better geometrical approximation of curved surfaces and fine features. An EB scheme Riemann solver is employed to calculate the flux between adjacent subdomains. The relationship between the electric field and the polarization currents is modeled by a first order auxiliary differential equation (ADE). A leap-frog scheme is proposed to update Maxwell's equations, the ADEs of the Drude medium and the perfectly matched layer (PML) in an efficient manner. This new approach is validated by virtue of simulating the ultra-wideband behavior of a gold nanoloop antenna with and without a substrate as well as the reflectivity of a dual-band infrared absorber. Its advantage in computational cost is demonstrated via comparison to a commercial software package. In this light, the CDGTD method represents a more efficient forward modeling tool, which has been successfully employed here to perform a parametric study of a dual-band infrared absorber.

Computational design and automated fabrication of kirchhoff-plateau surfaces

We propose a computational tool for designing Kirchhoff-Plateau Surfaces---planar rod networks embedded in pre-stretched fabric that deploy into complex, three-dimensional shapes. While Kirchhoff-Plateau Surfaces offer an intriguing and expressive design space, navigating this space is made difficult by the highly nonlinear nature of the underlying mechanical problem. In order to tackle this challenge, we propose a user-guided but computer-assisted approach that combines an efficient forward simulation model with a dedicated optimization algorithm in order to implement a powerful set of design tools. We demonstrate our method by designing a diverse set of complex-shaped Kirchhoff-Plateau Surfaces, each validated through physically-fabricated prototypes.

Fully Nonlinear ${SP}_{3}$ Approximation Based Fluorescence Optical Tomography.

In fluorescence optical tomography, many works in the literature focus on the linear reconstruction problem to obtain the fluorescent yield or the linearized reconstruction problem to obtain the absorption coefficient. The nonlinear reconstruction problem, to reconstruct the fluorophore absorption coefficient, is of interest in imaging studies as it presents the possibility of better reconstructions owing to a more appropriate model. Accurate and computationally efficient forward models are also critical in the reconstruction process. The approximation to the radiative transfer equation (RTE) is gaining importance for tomographic reconstructions owing to its computational advantages over the full RTE while being more accurate and applicable than the commonly used diffusion approximation. This paper presents Gauss-Newton-based fully nonlinear reconstruction for the approximated fluorescence optical tomography problem with respect to shape as well as the conventional finite-element method-based representations. The contribution of this paper is the Frechet derivative calculations for this problem and demonstration of reconstructions in both representations. For the shape reconstructions, radial-basis-function represented level-set-based shape representations are used. We present reconstructions for tumor-mimicking test objects in scattering and absorption dominant settings, respectively, for moderately noisy data sets in order to demonstrate the viability of the formulation. Comparisons are presented between the nonlinear and linearized reconstruction schemes in an element wise setting to illustrate the benefits of using the former especially for absorption dominant media.

Noninvasive Personalization of a Cardiac Electrophysiology Model From Body Surface Potential Mapping.

We use noninvasive data (body surface potential mapping, BSPM) to personalize the main parameters of a cardiac electrophysiological (EP) model for predicting the response to different pacing conditions. First, an efficient forward model is proposed, coupling the Mitchell-Schaeffer transmembrane potential model with a current dipole formulation. Then, we estimate the main parameters of the cardiac model: activation onset location and tissue conductivity. A large patient-specific database of simulated BSPM is generated, from which specific features are extracted to train a machine learning algorithm. The activation onset location is computed from a Kernel Ridge Regression and a second regression calibrates the global ventricular conductivity. The evaluation of the results is done both on a benchmark dataset of a patient with premature ventricular contraction (PVC) and on five nonischaemic implanted cardiac resynchonization therapy (CRT) patients with a total of 21 different pacing conditions. Good personalization results were found in terms of the activation onset location for the PVC (mean distance error, MDE = 20.3mm), for the pacing sites (MDE = 21.7 mm) and for the CRT patients (MDE = 24.6 mm). We tested the predictive power of the personalized model for biventricular pacing and showed that we could predict the new electrical activity patterns with a good accuracy in terms of BSPM signals. We have personalized the cardiac EP model and predicted new patient-specific pacing conditions. This is an encouraging first step towards a noninvasive preoperative prediction of the response to different pacing conditions to assist clinicians for CRT patient selection and therapy planning.