Understanding Musical Sound with Forward Models and Physical Models

Multiple paired forward and inverse models for motor control

Resistivity methods are commonly used in mineral exploration to map lithology, structure, sulphides and alteration. In the Athabasca Basin, resistivity methods are used to detect alteration associated with uranium. At the Midwest deposit, there is an alteration zone in the Athabasca sandstones that is above a uraniferous conductive graphitic fault in the basement and below a conductive lake at surface. Previous geophysical work in this area has yielded resistivity sections that we feel are ambiguous in the area where the alteration is expected. Resolve® and TEMPEST sections yield an indistinct alteration zone, while two-dimensional (2D) inversions of the ground resistivity data show an equivocal smeared conductive feature in the expected location between the conductive graphite and the conductive lake. Forward modelling alone cannot identify features in the pseudosections that are clearly associated with alteration, as the section is dominated by the feature associated with the near-surface conductive lake; inverse modelling alone produces sections that are smeared and equivocal. We advocate an approach that uses a combination of forward and inverse modelling. We generate a forward model from a synthetic geoelectric section; this forward data is then inverse modelled and compared with the inverse model generated from the field data using the same inversion parameters. The synthetic geoelectric section is then adjusted until the synthetic inverse model closely matches the field inverse model. We found that this modelling process required a conductive alteration zone in the sandstone above the graphite, as removing the alteration zone from the sandstone created an inverse section very dissimilar to the inverse section derived from the field data. We therefore conclude that the resistivity method is able to identify conductive alteration at Midwest even though it is below a conductive lake and above a conductive graphitic fault. We also concluded that resistivity inversions suggest a conductive paleoweathering surface on the top of the basement rocks at the basin/basement unconformity.

Transdermal drug delivery systems are a key technology to administer drugs with a high first-pass effect in a non-invasive and controlled way. Physics-based modeling and simulation are on their way to become a cornerstone in the engineering of these healthcare devices since it provides a unique complementarity to experimental data and additional insights. Simulations enable to virtually probe the drug transport inside the skin at each point in time and space. However, the tedious experimental or numerical determination of material properties currently forms a bottleneck in the modeling workflow. We show that multiparameter inverse modeling to determine the drug diffusion and partition coefficients is a fast and reliable alternative. We demonstrate this strategy for transdermal delivery of fentanyl. We found that inverse modeling reduced the normalized root mean square deviation of the measured drug uptake flux from 26 to 9%, when compared to the experimental measurement of all skin properties. We found that this improved agreement with experiments was only possible if the diffusion in the reservoir holding the drug was smaller than the experimentally measured diffusion coefficients suggested. For indirect inverse modeling, which systematically explores the entire parametric space, 30,000 simulations were required. By relying on direct inverse modeling, we reduced the number of simulations to be performed to only 300, so a factor 100 difference. The modeling approach’s added value is that it can be calibrated once in-silico for all model parameters simultaneously by solely relying on a single measurement of the drug uptake flux evolution over time. We showed that this calibrated model could accurately be used to simulate transdermal patches with other drug doses. We showed that inverse modeling is a fast way to build up an accurate mechanistic model for drug delivery. This strategy opens the door to clinically ready therapy that is tailored to patients.

The problem of computing a human arm posture that will take the hand to a desired hand position given by vision is called an inverse kinematics problem. To solve this problem, the human nervous system has a system for solving the inverse kinematics problem computing the proper joint angles from the desired hand position.Although the direct inverse modeling method is popular for the acquisition of an inverse kinematics model, a sufficient inverse model cannot be obtained for such systems with many‐to‐one input‐output correspondence as a human arm system.This paper, proposes a new model of a human inverse kinematics solver which uses the learned inverse model of the linearized model of the human arm. This inverse model transforms the hand position error to the update vector of the joint angles. The solver inverse kinematics problems by using the hand position error feedback. The performance of the solver is shown using numerical simulations.

To enhance the performance for high-speed tracking control of a piezoelectric tube actuator (PTA), an improved direct inverse rate-dependent PI model is obtained in this paper, and then adopted to design a practical feedforward controller achieving high-speed tracking control for a high-frequency trajectory with strong robustness. Specifically, based on the Prandtl-Ishlinskii (PI) model, an improved direct rate-dependent inverse model is set up for the PTA, with a polynomial function module introduced to eliminate the influence caused by the structure nonlinearity. Then, considering the features of the PTA structure, some preprocessing procedure is proposed to handle the collected experimental data, with the results utilized to identify all the unknown parameters over a wide bandwidth. Based on the obtained model, a practical feedforward controller, which presents the advantages of high-speed response, simple structure and convenient implementation, is then designed to enable the PTA to track high-frequency trajectories with satisfactory precision. Some experimental results are provided, which clearly demonstrate the high precision of the constructed/identified model, and the satisfactory performance of the proposed practical feedforward tracking control law.

This work is concerned with the modeling of elastic wave scattering by solid or fluid-filled objects embedded in an inhomogeneous elastic background. The medium is probed by a monochromatic force and the scattered field is computed (forward problem) or observed (inverse problem) at some known receiver locations. Based on vector integral equations for elastic scattering, a general framework is developed, independent of both the problem geometry and the transmitter-receiver characteristics. This framework encompasses both forward and inverse modeling. In the forward model, a Born approximation for an inhomogeneous background is applied to obtain a closed form expression for the scattered field. In the inverse model, this approximation is also invoked to linearize for the multiparameter characteristic of the object. Finally, an iterative inversion scheme alternating forward and inverse modeling is proposed to improve the resolution and accuracy of the reconstruction algorithm.

Inverse tracing of fire source in a single room based on CFD simulation and deep learning

Abstract. With the rapid development of multispectral imaging technique, it is desired that the spectral color can be accurately reproduced using desktop color printers. However, due to the specific spectral gamuts determined by printer inks, it is almost impossible to exactly replicate the reflectance spectra in other media. In addition, as ink densities can not be individually controlled, desktop printers can only be regarded as red-green-blue devices, making physical models unfeasible. We propose a locally adaptive method, which consists of both forward and inverse models, for desktop printer characterization. In the forward model, we establish the adaptive transform between control values and reflectance spectrum on individual cellular subsets by using weighted polynomial regression. In the inverse model, we first determine the candidate space of the control values based on global inverse regression and then compute the optimal control values by minimizing the color difference between the actual spectrum and the predicted spectrum via forward transform. Experimental results show that the proposed method can reproduce colors accurately for different media under multiple illuminants.

The sensory-motor coordination system in humans is able to adjust for the presence of noise and delay in sensory feedback, and for changes in the body and the environment that alter the relationship between motor commands and their sensory consequences. This adjustment is achieved by employing anticipatory mechanisms based on the concept of internal models. Specifically, forward models receive a copy of the outgoing motor commands and generate a prediction of the expected sensory consequences. This output may be used to: i. adjust fingertip forces to object properties in anticipation of the upcoming force requirements, ii. increase the velocity of the smooth eye movement while pursuing a moving target, iii. make necessary adjustments to maintain body posture and equilibrium in anticipation of need, iv. trigger corrective responses when detecting a mismatch between predicted and actual sensory input, involving the corresponding update of the relevant internal model. Several behavioural studies have shown that the sensory-motor system acquires and maintains forward models of different systems (i.e., arm dynamics, grip force, eye velocity, external objects and tools dynamics, and postural stability within the body and between the body and the support surface), and it has been widely hypothesized that the cerebellum is the location of those internal models, and that the theory of cerebellar learning might come into play to allow the models to be adjusted. Even though the major evidence of the role of the cerebellum comes from imaging studies, recent electrophysiological research has analyzed recordings from cerebellar neurons in trying to identify patterns of neural discharge that might represent the output of diverse internal models. As reviewed within this chapter, although not in an exhaustive manner, several independent efforts in the robotics field have been inspired on human anticipatory mechanisms based on internal models to provide efficient and adaptive robot control. Each one of those efforts addresses predictive behaviour within the context of one specific motor system; e.g, visuo-motor coordination to determine the implications of a spatial arrangement of obstacles, or to place a spoon during a feeding task, object manipulation

The study of greenhouse gas (GHG) fluxes in terrestrial ecosystems is becoming increasingly important as the observed rise in global temperature and increased frequency of extreme weather events are attributed by the majority of climate experts to increased atmospheric GHG concentrations. Adequate and comprehensive knowledge of surface GHG fluxes is important for obtaining reliable information on CO2 and other GHG fluxes at regional and global scales, as well as for preparing reports on national GHG emissions and removals. The need to obtain accurate estimates of GHG fluxes at regional and global scales has led to the development of innovative mathematical models of varying complexity. These models can be divided into forward and inverse models. Forward algorithms provide the ability to estimate GHG fluxes when sufficient information on the structure of GHG sources and sinks is available. Inverse algorithms allow the retrieval of surface fluxes using remote sensing data. The most promising way to study high resolution fluxes over areas with complex topography and mosaic vegetation patterns is the use of unmanned aerial vehicles (UAVs).In our study, we proposed and tested a forward and inverse model for estimating GHG fluxes over an inhomogeneous underlying surface. The forward model is based on the RANS hydrodynamic model to calculate the wind velocity and turbulence coefficient, and the solution of the advection-diffusion equation to find a three-dimensional distribution of GHG concentrations. The GHG fluxes at the specified height above the ground surface are then calculated using the obtained concentration distribution and turbulence coefficient. The inverse algorithm is based on minimizing a cost functional, defined as the root mean square deviation of the modeled concentration field from the measured data. Concentration measurements at multiple (at least two) levels can be performed using UAV-based gas analyzers.Three experimental sites selected for our modeling study differ in geographic location, topography, and vegetation heterogeneity. These sites are: i) swampy and forested areas of the "Mukhrino" carbon supersite (Khanty-Mansiysk Autonomous Okrug, Russia, 60°53'20" N, 68°42'10" E), ii) the Roshni-Chu mountain forest site, which is part of the "Way Carbon" supersite (Chechen Republic, Russia, 43°2'59" N, 45°25'32" E), iii) the mixed forest experimental site "Lyali" (Komi Republic, Russia, 62°16'28" N, 50°39'54" E). For our numerical experiments we used measured data on surface topography, LAI, soil respiration, air temperature, prevailing wind direction, vertical canopy CO2 concentration profile and CO2 fluxes measured by eddy covariance technique.The model results show a rather good agreement with the measured data and could help to interpret the experimentally observed dependence of CO2 fluxes on wind direction in areas with an inhomogeneous underlying surface.

The thermochronometric systems discussed in this volume broadly share three features: parent isotopes, daughter products, and one or more time-dependent, temperature-sensitive processes by which daughter products are altered or lost. If these processes can be measured in the laboratory, and their behavior confidently extrapolated to geological time scales, it becomes possible to construct a forward model of the system that predicts how a given instance of it will evolve assuming a particular starting arrangement and subsequent time-temperature history. Once a forward model has been created and verified, it then becomes possible to apply it in the inverse sense: given a measured ending condition and an assumed starting one, find the intervening time-temperature history. In general, because of information loss, limited precision of measurements, and lack of system uniqueness, more than one history is consistent with a given ending condition. As a result, an inverse model solution usually consists of a set of thermal histories that are consistent with the measured data, as judged by some statistical criterion. This chapter will concentrate on two low-temperature thermochronometers: fission-track (primarily for apatite) and (U-Th)/He. All of the calculations described here are implemented in a computer program called “HeFTy,” which is available with this volume (see Ehlers et al. 2005). A theme that will be touched upon throughout this chapter is that forward and inverse models are only as good as the data and assumptions behind them. Although this principle of course holds for all scientific investigations, it is often obscured when such details are packaged in user-friendly software that produces publication-ready graphics. Fission tracks form continuously over time at a rate dependent solely upon the concentration of uranium present. Earlier-formed fission tracks tend to be shorter than later-formed tracks, as they will have had more time to anneal, and may have experienced …

This study presents an automated circuit design approach using neural networks to optimize the dynamic range (DR) of active filters, illustrated through the design of a 7th-order Chebyshev low-pass filter. Traditional design methods rely heavily on designer expertise, often resulting in time-intensive and energy-consuming processes. Two techniques are proposed: inverse modeling and forward modeling. In inverse modeling, artificial neural networks (ANNs) predict circuit parameters to meet specific performance goals. A randomly selected subset, comprising 0.05% of the 1,953,125 possible circuit configurations, was used to train and validate the model, providing an accurate representation of the entire dataset without requiring full-scale data analysis. In forward modeling, the same subset was used to train the network, which was then used to predict DR values for the remaining dataset. This approach enabled the identification of circuit parameters that resulted in optimal DR values. The results confirm the effectiveness of these techniques, with both inverse modeling and forward modeling outperforming the standard circuit design. At 160 kHz, a critical frequency for the operation of the designed filter, inverse modeling achieved a DR of 140.267 dB and forward modeling reached 136.965 dB, compared to 132.748 dB for the standard circuit designed using the traditional approach. These findings demonstrate that ANN-based methods can significantly enhance design accuracy, reduce time requirements, and improve energy efficiency in analog circuit optimization.

This article investigates the inverse hysteresis model for the hysteresis compensation. A direct inverse(DI) model based on the new inverse operators is proposed to model the inversion of hysteresis and compensate for the hysteresis effect. The extended application of the DI model for rate-dependent hysteresis in the reluctance actuator is presented as well. Some simulations and experiments are executed to validate the proposed DI hysteresis model. Results show that DI has high accuracy in fitting the inverse hysteresis loops, and can alleviate hysteresis nonlinearity significantly as a feedforward compensator for both the rate-independent and rate-dependent hysteresis.

This work presents an application of the forward and inverse predictive modeling methodology of Cacuci and Ionescu-Bujor (2010) in the inverse mode to determine, within a tight a priori specified convergence criterion and overall accuracy, an unknown time-dependent boundary condition (specifically, the time-dependent inlet acid concentration) for a dissolver model case study by using measurements of the state function (specifically, the time-dependent acid concentration) at a specified location (specifically, in the dissolver’s compartment farthest from the inlet). The unknown time-dependent boundary condition is described by 635 unknown discrete scalar parameters. This forward and inverse predictive modeling methodology uses the maximum entropy principle to construct an optimal approximation of the unknown a priori distribution by using the a priori known mean values and uncertainties characterizing the model parameters, along with the computed and experimentally measured model responses and their covariances. This a priori distribution is subsequently combined using Bayes’ theorem with the likelihood provided by the computational model. The first-order response sensitivities serve as weighting functions in this objective combination of computational and experimental information.The use of the maximum entropy principle enables the forward and inverse predictive modeling of Cacuci and Ionescu-Bujor (2010) to construct an intrinsic regularizing metric for solving any inverse problem. In the present dissolver case study, the unknown time-dependent boundary condition is predicted by the methodology within an a priori selected convergence criterion, without user intervention and/or introduction of arbitrary regularization parameters, as the currently popular procedures need to do. This predictive modeling methodology yields optimally calibrated values for all model parameters, with reduced predicted uncertainties, as well as optimal (best-estimate) predicted values for the model responses (in this case study, the time-dependent acid concentrations in the dissolver’s compartments), also with reduced predicted uncertainties. Notably, even though the experimental data pertain solely to the compartment farthest from the inlet (where the data were measured), the application of this predictive modeling methodology actually improves the predicted values and reduces their predicted uncertainties not only in the compartment in which the data were actually measured but also throughout the entire dissolver, including the compartment farthest from the measurements (i.e., at the inlet). This is because this forward and inverse predictive modeling methodology combines and transmits information simultaneously over the entire phase-space, comprising all time steps and spatial locations.These results underscore the importance of this work in presenting the objective resolution (i.e., resolution in the absence of user-defined subjective adjustment of arbitrary regularization parameters) of a time-dependent inverse case study of potential importance to diversion activities associated with proliferation and international safeguards. The results obtained in this work establish confidence in the dissolver model’s accuracy for simulating the acid concentrations required to dissolve used nuclear fuel. In turn, these results will be used to generate source terms for key reprocessing facility components downstream and to support material accountability for nuclear safeguards.

Photodiode-based machine learning for optimization of laser powder bed fusion parameters in complex geometries