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.

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

The ability to formulate explicit mathematical models of motor systems has played a central role in recent progress in motor control research. As a result of these modeling efforts and in particular the incorporation of concepts drawn from control systems theory, ideas about motor control have changed substantially. There is growing emphasis on motor learning and particularly on predictive or anticipatory aspects of control that are related to the neural representation of dynamics. Two ideas have become increasingly prominent in mathematical modeling of motor function--forward internal models and inverse dynamics. The notion of forward internal models which has drawn from work in adaptive control arises from the recognition that the nervous system takes account of dynamics in motion planning. Inverse dynamics, a complementary way of adjusting control signals to deal with dynamics, has proved a simple means to establish the joint torques necessary to produce desired movements. In this paper, we review the force control formulation in which inverse dynamics and forward internal models play a central role. We present evidence in its favor and describe its limitations. We note that inverse dynamics and forward models are potential solutions to general problems in motor control--how the nervous system establishes a mapping between desired movements and associated control signals, and how control signals are adjusted in the context of motor learning, dynamics and loads. However, we find little empirical evidence that specifically supports the inverse dynamics or forward internal model proposals per se. We further conclude that the central idea of the force control hypothesis--that control levels operate through the central specification of forces--is flawed. This is specifically evident in the context of attempts to incorporate physiologically realistic muscle and reflex mechanisms into the force control model. In particular, the formulation offers no means to shift between postures without triggering resistance due to postural stabilizing mechanisms.

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.

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

This research report describes an approach to parameter estimation for physical models of sound-generating systems using distal teachers and forward models (Jordan & Rumelhart, 1992; Jordan, 1990). The general problem is to find an inverse model of a sound-generating system that transforms sounds to action parameters; these parameters constitute a model-based description of the sound. We first show that a two-layer feedforward model is capable of performing inverse mappings for a simple physical model of a violin string. We refer to this learning strategy as direct inverse modeling; it requires an explicit teacher and it is only suitable for convex regions of the parameter space. A model of two strings was implemented that had non-convex regions in its parameter space. We show how the direct modeling strategy failed at the task of learning the inverse model in this case and that forward models can be used, in conjunction with distal teachers, to bias the learning of an inverse model so that non-convex regions are mapped to single-point solutions in the parameter space. Our results show that forward models are appropriate for learning to map sounds to parametric representations.

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 …

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.

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.

To construct an appropriate motor command from signals that provide a representation of desired action, the nervous system must take into account the dynamic characteristics of the motor plant to be controlled. In the oculomotor system, signals specifying desired eye velocity are thought to be transformed into motor commands by an inverse dynamic model of the eye plant that is shared for all types of eye movements and implemented by a weighted combination of eye velocity and position signals. Neurons in the prepositus hypoglossi and adjacent medial vestibular nuclei (PH-BT neurons) were traditionally thought to encode the "eye position" component of this inverse model. However, not only are PH-BT responses inconsistent with this theoretical role, but compensatory eye movement responses to translation do not show evidence for processing by a common inverse dynamic model. Prompted by these discrepancies between theoretical notions and experimental observations, we reevaluated these concepts using multiple-frequency rotational and translational head movements. Compatible with the notion of a common inverse model, we show that PH-BT responses are unique among all premotor cell types in bearing a consistent relationship to the motor output during eye movements driven by different sensory stimuli. However, because their responses are dynamically identical to those of motoneurons, PH-BT neurons do not simply represent an internal component of the inverse model, but rather its output. They encode and distribute an estimate of the motor command, a signal critical for accurate motor execution and learning.

Structural details of the crust determined from P -wave velocity models can be improved with S -wave velocity models, and S -wave velocities are needed for model-based predictions of strong ground motion in southern California. We picked P - and S -wave travel times for refracted phases from explosive-source shots of the Los Angeles Region Seismic Experiment, Phase II (LARSE II); we developed refraction velocity models from these picks using two different inversion algorithms. For each inversion technique, we calculated ratios of P - to S -wave velocities ( V P / V S ) where there is coincident P - and S -wave ray coverage. We compare the two V P inverse velocity models to each other and to results from forward modeling, and we compare the V S inverse models. The V S and V P / V S models differ in structural details from the V P models. In particular, dipping, tabular zones of low V S , or high V P / V S , appear to define two fault zones in the central Transverse Ranges that could be parts of a positive flower structure to the San Andreas fault. These two zones are marginally resolved, but their presence in two independent models lends them some credibility. A plot of V S versus V P differs from recently published plots that are based on direct laboratory or down-hole sonic measurements. The difference in plots is most prominent in the range of V P =3 to 5 km/s (or V S ∼1.25 to 2.9 km/s), where our refraction V S is lower by a few tenths of a kilometer per second from V S based on direct measurements. Our new V S - V P curve may be useful for modeling the lower limit of V S from a V P model in calculating strong motions from scenario earthquakes.

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

The potentiality of Signals of Opportunity (SoOp) over land can be investigated by advanced forward and inverse modeling and simulation tools to provide viable measurements for Earth science data products over land. This research investigates various inversion techniques that can leverage SoOp sources for land-based Earth science measurements by applying them to simulated soil moisture profiles over bare- and vegetated- soils. Forward modeling is accomplished using Mississippi State University’s Signals of Opportunity Coherent Bistatic Scattering Model (SCoBi), a new, open-source electromagnetic scattering model that can determine coherent received signals at a receiving antenna through application of Maxwell’s equations at discrete scattering soil layer boundaries in conjunction with the distorted Born approximation to describe vegetation propagation and scattering. The results of the forward model are used in various inverse methods to investigate the potentiality of using multiple SoOp sources for Soil Moisture Profile (SMP) retrieval. Multiple SMPs are analyzed by SCoBi to determine the sensitivity of soil moisture variation to SoOp transmitter characteristics such as polarization and elevation angle. Simultaneously, SoOp measurements conducted at Purdue University’s Agronomy Center for Research and Education (ACRE) are used to determine the impact that changes in both physical SMPs and vegetation canopies have on the scattered SoOp. The characteristics of the scattering surfaces, vegetation, and SMPs at the ACRE facility are modeled within SCoBi to observe patterns and relationships captured in reflectivity measurements that are caused by vegetation growth periods as well as rain and drought effects manifested by changing SMPs.