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All sourcesNASA NTRSDOE OSTI
NASA NTRS2002

Digital Distortion Caused by Traveling- Wave-Tube Amplifiers Simulated

Future NASA missions demand increased data rates in satellite communications for near real-time transmission of large volumes of remote data. Increased data rates necessitate higher order digital modulation schemes and larger system bandwidth, which place stricter requirements on the allowable distortion caused by the high-power amplifier, or the traveling-wave-tube amplifier (TWTA). In particular, intersymbol interference caused by the TWTA becomes a major consideration for accurate data detection at the receiver. Experimentally investigating the effects of the physical TWTA on intersymbol interference would be prohibitively expensive, as it would require manufacturing numerous amplifiers in addition to acquiring the required digital hardware. Thus, an accurate computational model is essential to predict the effects of the TWTA on system-level performance when a communication system is being designed with adequate digital integrity for high data rates. A fully three-dimensional, time-dependent, TWT interaction model has been developed using the electromagnetic particle-in-cell code MAFIA (Solution of Maxwell's equations by the Finite-Integration-Algorithm). It comprehensively takes into account the effects of frequency-dependent AM (amplitude modulation)/AM and AM/PM (phase modulation) conversion, gain and phase ripple due to reflections, drive-induced oscillations, harmonic generation, intermodulation products, and backward waves. This physics-based TWT model can be used to give a direct description of the effects of the nonlinear TWT on the operational signal as a function of the physical device. Users can define arbitrary excitation functions so that higher order modulated digital signals can be used as input and that computations can directly correlate intersymbol interference with TWT parameters. Standard practice involves using communication-system-level software packages, such as SPW, to predict if adequate signal detection will be achieved. These models use a nonlinear, black-box model to represent the TWTA. The models vary in complexity, but most make several assumptions regarding the operation of the high-power amplifier. When the MAFIA TWT interaction model was used, these assumptions were found to be in significant error. In addition, digital signal performance, including intersymbol interference, was compared using direct data input into the MAFIA model and using the system-level analysis tool SPW for several higher order modulation schemes. Results show significant differences in predicted degradation between SPW and MAFIA simulations, demonstrating the significance of the TWTA approximations made in the SPW model on digital signal performance. For example, a comparison of the SPW and MAFIA output constellation diagrams for a 16-ary quadrature amplitude modulation (16-QAM) signal (data shown only for second and fourth quadrants) is shown. The upper-bound degradation was calculated from the corresponding eye diagrams. In comparison to SPW simulations, the MAFIA data resulted in a 3.6-dB larger degradation.

Kory, Carol L.↗
NASA NTRS1999

The Analysis and Design of Low Boom Configurations Using CFD and Numerical Optimization Techniques

The use of computational fluid dynamics (CFD) for the analysis of sonic booms generated by aircraft has been shown to increase the accuracy and reliability of predictions. CFD takes into account important three-dimensional and nonlinear effects that are generally neglected by modified linear theory (MLT) methods. Up to the present time, CFD methods have been primarily used for analysis or prediction. Some investigators have used CFD to impact the design of low boom configurations using trial and error methods. One investigator developed a hybrid design method using a combination of Modified Linear Theory (e.g. F-functions) and CFD to provide equivalent area due to lift driven by a numerical optimizer to redesign or modify an existing configuration to achieve a shaped sonic boom signature. A three-dimensional design methodology has not yet been developed that completely uses nonlinear methods or CFD. Constrained numerical optimization techniques have existed for some time. Many of these methods use gradients to search for the minimum of a specified objective function subject to a variety of design variable bounds, linear and nonlinear constraints. Gradient based design optimization methods require the determination of the objective function gradients with respect to each of the design variables. These optimization methods are efficient and work well if the gradients can be obtained analytically. If analytical gradients are not available, the objective gradients or derivatives with respect to the design variables must be obtained numerically. To obtain numerical gradients, say, for 10 design variables, might require anywhere from 10 to 20 objective function evaluations. Typically, 5-10 global iterations of the optimizer are required to minimize the objective function. In terms of using CFD as a design optimization tool, the numerical evaluation of gradients can require anywhere from 100 to 200 CFD computations per design for only 10 design variables. If one CFD computation requires an hour of computational time on a Cray computer, one can see that the use of constrained numerical optimization quickly becomes impractical.Hence, in order to practically couple a numerical design optimization technique with a CFD method, the CFD method must be extremely efficient with running times on the order of only minutes. The CFD Euler code developed under NASA sponsorship and referred to as MIM3D-SB for the most part fulfills these efficiency requirements. Analysis of wing- body configurations can be computed in a matter of a few minutes. The present study will concentrate on the feasibility of the use of this CFD code in conjunction with a numerical design optimization technique for the sonic boom reduction of candidate HSCT configurations. A preliminary supersonic aircraft design system has been established that utilizes the numerical design optimization code NPSOL developed at Stanford University coupled with the supersonic NUM3D-SB CFD code. Many questions still need to be answered in regard to using CFD and numerical optimizers as design tools. There are difficulties related to both the CFD codes and the numerical optimizers. Numerical optimizers can converge to a local minima rather than a global minima. This behavior is largely a function of the initial guess in the design space. The optimizer also is searching for a minimum of the function in terms of its derivative without any regard to the actual function value. Numerically (i.e. CFD) determined gradients can also generate spurious numerical local minima. In addition, for the sonic boom problem, grid fineness will also determine the accuracy of the final design solution. Design optimization methods work well on problems defined by continuous objective functions. The sonic boom signature design problem is not necessarily defined by a continuous objective function. The signature can have a variety of shapes; i.e. from N-wave to multiple shocks. The far-field or ground signature may not transition continuously from one shape to another and hence, may exhibit discontinuous behavior. This is also a source of difficulty in using design optimization methods.In the following sections, several low boom and one reference aircraft configuration will be analyzed to predict their sonic boom signature characteristics. Modifications to some of these designs will also be presented to demonstrate the feasibility of using CFD as a design tool and to demonstrate the feasibility of designing shaped sonic boom signatures. Design modifications to some configurations will be presented to demonstrate the feasibility of achieving shaped signatures with reduced levels and not necessarily to represent realistic or aerodynamically efficient design modifications. Fuselage volume or camber are used as design variables in order to have a minimal effect on the primary wing aerodynamics. The paper will also seek to demonstrate whether a hybrid or ramped signature is feasible to achieve. For the low-boom configurations, the CFD predicted signatures will be compared qualitatively to their MLT design signatures.

Siclari, Michael J.↗
DOE OSTI2025

Time-Varying Output Delay Compensation-A Model-Free Approach and its Application on Cooperative On-Ramp Merging

This paper presents a model-free approach to compensate for time-varying output delay in networked control systems. The proposed architecture combines a model-free observer and the Smith predictor. The model-free observer estimates the current state while handling modeling errors and uncertainties of the system. The Smith predictor moves the effect of time delay outside the control closed-loop using the estimated delayed output and the actual output of the plant. The proposed method is applied to a cooperative on-ramp merging problem. First, an ultra-local model predictive control is implemented to provide a computationally efficient online speed planner agnostic to the vehicle dynamics. After that, a model-free observer is designed to estimate the current state. Finally, the proposed architecture is tested against a time-varying output delay with an upper bound of 200 milliseconds. The results demonstrate the effectiveness of the proposed method with improved tracking of intervehicle distance.

Waleed khan, Muhammad [The University of Texas at ↗
DOE OSTI2022

Neural Network-Based Electric Vehicle Range Prediction for Smart Charging Optimization

Range prediction is a standard feature in most modern road vehicles, allowing drivers to make informed decisions about when to refuel. Most vehicles make range predictions through data- or model-driven means, monitoring the average fuel consumption rate or using a tuned vehicle model to predict fuel consumption. The uncertainty of future driving conditions makes the range prediction problem challenging, particularly for less pervasive battery electric vehicles (BEV). Most contemporary machine learning-based methods attempt to forecast the battery SOC discharge profile to predict vehicle range. In this work, we propose a novel approach using two recurrent neural networks (RNNs) to predict the remaining range of BEVs and the minimum charge required to safely complete a trip. Each RNN has two outputs that can be used for statistical analysis to account for uncertainties; the first loss function leads to mean and variance estimation (MVE), while the second results in bounded interval estimation (BIE). These outputs of the proposed RNNs are then used to predict the probability of a vehicle completing a given trip without charging, or if charging is needed, the remaining range and minimum charging required to finish the trip with high probability. Training data was generated using a low-order physics model to estimate vehicle energy consumption from historical drive cycle data collected from medium-duty last-mile delivery vehicles. Here, the proposed method demonstrated high accuracy in the presence of day-to-day route variability, with the root-mean-square error (RMSE) below 6% for both RNN models.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
NASA NTRS1989

Alternative majority-voting methods for real-time computing systems

Two techniques that provide a compromise between the high time overhead in maintaining synchronous voting and the difficulty of combining results in asynchronous voting are proposed. These techniques are specifically suited for real-time applications with a single-source/single-sink structure that need instantaneous error masking. They provide a compromise between a tightly synchronized system in which the synchronization overhead can be quite high, and an asynchronous system which lacks suitable algorithms for combining the output data. Both quorum-majority voting (QMV) and compare-majority voting (CMV) are most applicable to distributed real-time systems with single-source/single-sink tasks. All real-time systems eventually have to resolve their outputs into a single action at some stage. The development of the advanced information processing system (AIPS) and other similar systems serve to emphasize the importance of these techniques. Time bounds suggest that it is possible to reduce the overhead for quorum-majority voting to below that for synchronous voting. All the bounds assume that the computation phase is nonpreemptive and that there is no multitasking.

Shin, Kang G.↗
NASA NTRS1993

On-board closed-loop congestion control for satellite based packet switching networks

NASA LeRC is currently investigating a satellite architecture that incorporates on-board packet switching capability. Because of the statistical nature of packet switching, arrival traffic may fluctuate and thus it is necessary to integrate congestion control mechanism as part of the on-board processing unit. This study focuses on the closed-loop reactive control. We investigate the impact of the long propagation delay on the performance and propose a scheme to overcome the problem. The scheme uses a global feedback signal to regulate the packet arrival rate of ground stations. In this scheme, the satellite continuously broadcasts the status of its output buffer and the ground stations respond by selectively discarding packets or by tagging the excessive packets as low-priority. The two schemes are evaluated by theoretical queuing analysis and simulation. The former is used to analyze the simplified model and to determine the basic trends and bounds, and the later is used to assess the performance of a more realistic system and to evaluate the effectiveness of more sophisticated control schemes. The results show that the long propagation delay makes the closed-loop congestion control less responsive. The broadcasted information can only be used to extract statistical information. The discarding scheme needs carefully-chosen status information and reduction function, and normally requires a significant amount of ground discarding to reduce the on-board packet loss probability. The tagging scheme is more effective since it tolerates more uncertainties and allows a larger margin of error in status information. It can protect the high-priority packets from excessive loss and fully utilize the downlink bandwidth at the same time.

Chu, Pong P.↗
NASA NTRS2010

Collective Intelligence and Three Aspects of Planning in Organizations: A NASA Example

For many complex sociotechnical systems, planning seems to require explicit coordination; certainly, in executing a plan the activities of different actors must be tightly coupled. However, distributing the needed planning information can be very burdensome and error prone, because different groups need different collections of information, updated or kept current on different time cycles. Further, the information needed to form successful plans is often highly distributed, and while feedback about the success of prior plans may exist, it may not be available to those in a position of using this to improve plans or to detect and resolve other problems in the system (Weick, 1995). Tools to support various aspects of planning have been developed, and can provide a huge benefit to the individuals working on that aspect. To be tractable, most solutions address a quite bounded slice of work, isolating it from the larger context. Prospective planning takes place over multiple, nested cycles of decision making. This builds a plan that specifies activities of different granularity. "Subplans" may specify multiple parallel activities by different groups and individuals, as well as sequential, nested actions by a single actor. Planning produces valuable, sharable, external, representations: in addition to prospective use, plans support retrospective assessment and also action in the present. Viewing planning in a larger context - both temporal and organizational -- enables noticing what one does not know and generating more systemic and effective solutions. Viewing a problem as one of collective intelligence invites thinking about the larger organizational context. Many approaches to supporting collective intelligence do not support execution of highly contingent actions, distributed across many players, and hence provide incomplete support for planning. However, CI technology maybe helpful in managing the processes of gathering information for decision making in planning and of distributing plan information to various actors, needed on various time cycles.

Billman, Dorrit↗
NASA NTRS2019

Uncertainty in Soil Moisture Retrievals: an Ensemble Approach Using SMOS L-Band Microwave Data

The uncertainty of soil moisture (SM) retrievals from satellite brightness temperature (TB) observations depends primarily on the choice of radiative transfer model (RTM) parameters, prior SM information and TB inputs. This paper studies the sensitivity of several (quasi-)operational and experimental SM retrieval products from the Soil Moisture Ocean Salinity (SMOS) mission to these choices at 11 reference sites, located in 7 watersheds across the United States (US). Different literature-based RTM parameter sets cause large biases between retrievals. Whereas typical RTM parameter sets are calibrated for SM retrievals, it is shown that a parameter set carefully optimized for TB forward modeling can also be used for retrieving SM. It is also shown that the inclusion of dynamic prior SM estimates in a Bayesian retrieval scheme can strongly improve SM retrievals, regardless of the choice of RTM parameters, and that the use of multi-angular and multi-polarization TB does not necessarily lead to superior retrievals compared to retrievals based on TB data at a single incidence angle and polarization. The second part of this paper evaluates ensemble uncertainty metrics for SM retrievals obtained by propagating a wide range of RTM parameters through the RTM. As expected for bounded variables, the spread in the ensemble SM retrievals is smallest for wet and dry SM values and highest for intermediate SM values. After removal of the strong long-term mean bias associated with the RTM parameter values for individual ensemble members, the remaining anomaly ensemble SM spread of 0.037 cu m/cu m approximates the actual time series unbiased root-mean-square-difference of 0.042 cu m/cu m between ensemble mean retrievals and in situ reference data across the reference sites. However, the temporal variability in the anomaly ensemble spread reveals higher-order biases in the retrieval error, which should be accounted for when characterizing retrieval error.

Jan Quets↗
DOE OSTI2021

Distributed State Estimation Over Time-Varying Graphs: Exploiting the Age-of-Information

Here, we study the problem of designing a distributed observer for an LTI system over a time-varying communication graph. The limited existing work on this topic imposes various restrictions either on the observation model or on the sequence of communication graphs. In contrast, we propose a single-time-scale distributed observer that works under mild assumptions. Specifically, our communication model only requires strong-connectivity to be preserved over non-overlapping, contiguous intervals that are even allowed to grow unbounded over time. We show that under suitable conditions that bound the growth of such intervals, joint observability is sufficient to track the state of any discrete-time LTI system exponentially fast, at any desired rate. We also develop a variant of our algorithm that is provably robust to worst-case adversarial attacks, provided the sequence of graphs is sufficiently connected over time. The key to our approach is the notion of a "freshness-index" that keeps track of the age-of-information being diffused across the network. Such indices enable nodes to reject stale estimates of the state, and, in turn, contribute to stability of the error dynamics.

42 ENGINEERING↗
DOE OSTI2020

A Novel Modeling Framework for Computationally Efficient and Accurate Real-Time Ensemble Flood Forecasting With Uncertainty Quantification

A novel modeling framework that simultaneously improves accuracy, predictability, and computational efficiency is presented. It embraces the benefits of three modeling techniques integrated together for the first time: surrogate modeling, parameter inference, and data assimilation. The use of polynomial chaos expansion (PCE) surrogates significantly decreases computational time. Parameter inference allows for model faster convergence, reduced uncertainty, and superior accuracy of simulated results. Ensemble Kalman filters assimilate errors that occur during forecasting. To examine the applicability and effectiveness of the integrated framework, we developed 18 approaches according to how surrogate models are constructed, what type of parameter distributions are used as model inputs, and whether model parameters are updated during the data assimilation procedure. We conclude that (1) PCE must be built over various forcing and flow conditions, and in contrast to previous studies, it does not need to be rebuilt at each time step; (2) model parameter specification that relies on constrained, posterior information of parameters (so-called Selected specification) can significantly improve forecasting performance and reduce uncertainty bounds compared to Random specification using prior information of parameters; and (3) no substantial differences in results exist between single and dual ensemble Kalman filters, but the latter better simulates flood peaks. The use of PCE effectively compensates for the computational load added by the parameter inference and data assimilation (up to ~80 times faster). Therefore, the presented approach contributes to a shift in modeling paradigm arguing that complex, high-fidelity hydrologic and hydraulic models should be increasingly adopted for real-time and ensemble flood forecasting.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

An energy-modified quantum defect method for the analysis of Rydberg spectra: Application to 2-butyne

The high resolution Rydberg absorption spectrum of 2-butyne C 4 H 6 recorded previously at the SOLEIL synchrotron facility has been interpreted using multichannel quantum defect theory (MQDT). The calculations are based on the continuum scattering calculations of Xu et al., J. Chem. Phys. 136, 154303 (2012) and of Jacovella et al., J. Phys. Chem. A 119, 12339 (2015) pertaining to the dipole-allowed excited state symmetries in absorption from the ground state. In contrast to the traditional approach of calculating low-lying electronic states first and then attempting to extend the calculations to ever higher energy, here the analysis proceeds through the extension of these detailed calculations of the electronic continuum scattering down into the discrete region of the spectrum. The continuum reaction matrices and dipole transition moments are adapted to the discrete Rydberg region via the use of an energy-modified formulation of MQDT theory and associated energy dependences of the quantum defects. The analysis reproduces more than 40 Rydberg states from n ≈ 10 down to the 3 d and 4 s levels with an rms error of better than 20 cm −1 . Further, these belong to five Rydberg series with three different molecular symmetries. While the approach predicts many additional series, most of these are calculated and observed to carry only little oscillator strength. The analysis shows that the Rydberg spectrum is dominated by the excitation of an e″ symmetry electron of fδ and gπ type, in line with what previous studies of the above-threshold shape resonance of 2-butyne have shown. The present study is intended to serve as an example showing how first principles continuum calculations may be useful for the interpretation of highly bound discrete states in a range that poses problems for the standard ab initio techniques. The quantitative treatment of the dipole absorption cross sections is deferred to a future paper.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Spike-Free Adaptive Sliding Mode Control: Application to Permanent Magnet Synchronous Motors

A new methodology for adaptive sliding mode control (ASMC) has been widely used to improve the control performance in various systems. This method exhibits several advantages, including low sliding mode control (SMC) chattering, no knowledge of the system disturbance bound, and no overestimation of the control gain. Despite its advantages, this method can be hampered by the spike phenomenon, slow control gain convergence, and difficulty in achieving optimal performance under varying disturbances. Consequently, this article proposes a spike-free ASMC method with a disturbance observer (DOB) to address these problems. Previous ASMC methods have been analyzed via simulations to verify the aforementioned problems. Here, this analysis highlights the need for disturbance compensation and improvements in the SMC gain adaptation law. Therefore, a DOB is designed to mitigate the spike phenomenon by compensating for disturbances. Subsequently, an SMC gain adaptation law based on disturbance error estimation is designed to eliminate the spike phenomenon completely. The proposed adaptation law makes the SMC gain to converge to a slightly higher value than the disturbance estimation error. Consequently, the proposed method not only eliminates the spike phenomenon, but also ensures optimal performance under varying disturbances. The performance of the proposed method is experimen tally validated through a comparative study.

42 ENGINEERING↗
NASA NTRS2012

Asymmetric Uncertainty Expression for High Gradient Aerodynamics

When the physics of the flow around an aircraft changes very abruptly either in time or space (e.g., flow separation/reattachment, boundary layer transition, unsteadiness, shocks, etc), the measurements that are performed in a simulated environment like a wind tunnel test or a computational simulation will most likely incorrectly predict the exact location of where (or when) the change in physics happens. There are many reasons for this, includ- ing the error introduced by simulating a real system at a smaller scale and at non-ideal conditions, or the error due to turbulence models in a computational simulation. The un- certainty analysis principles that have been developed and are being implemented today do not fully account for uncertainty in the knowledge of the location of abrupt physics changes or sharp gradients, leading to a potentially underestimated uncertainty in those areas. To address this problem, a new asymmetric aerodynamic uncertainty expression containing an extra term to account for a phase-uncertainty, the magnitude of which is emphasized in the high-gradient aerodynamic regions is proposed in this paper. Additionally, based on previous work, a method for dispersing aerodynamic data within asymmetric uncer- tainty bounds in a more realistic way has been developed for use within Monte Carlo-type analyses.

Pinier, Jeremy T↗
NASA NTRS1992

Error Analysis of Combined Optical-Flow and Stereo Passive Ranging

The motion of an imaging sensor causes each imaged point of the seem to describe a time trajectory on the image plane. The trajectories of all imaged points are reminiscent of a flow (eg, of liquid) which is the source of the term "optical flow". Optical-flow ranging is a method by which the stream of two-dimensional images obtained from a forward-looking forward-moving passive sensor is used to compute range to points in the field of view. Another well-known ranging method consists of triangulation based on stereo images obtained from at least two stationary sensors. In this paper we analyze the potential accuracies of a combined optical flow and stereo passive-ranging system in the context of helicopter nap-of-the-earth obstacle avoidance. The Cramer-Rao lower bound (CRLB) is developed for the combined system under the assumption of a random angular misalignment common to both cameras of a stereo pair. It is shown that the range accuracy degradations caused by misalignment is negligible for a combined optical-flow and stereo system as compared with a monocular optical-flow system.

Barniv, Yair↗
NASA NTRS2006

Conflict Detection Using Variable Four-Dimensional Uncertainty Bounds to Control Missed Alerts

Decision-support tools for maintaining pairwise aircraft separation rely on conflict detection to alert the operator when the predicted trajectories of aircraft will result in a loss of separation. But aircraft frequently do not follow their predicted trajectories exactly. This can cause missed alerts and the failure of strategic separation procedures. We present a technique for modeling a bounded region of uncertainty around a four-dimensional predicted trajectory and an algorithm for detecting conflicts between trajectories modeled in this way that avoids missed alerts as long as the aircraft remain within the specified regions of uncertainty. In addition, we present an algorithm for detecting the intrusion of a trajectory modeled in this way into an area hazard modeled as a polygonal region. The size of the region of uncertainty can vary along the trajectory continually and independently in the along-path, cross-track, and vertical dimensions, providing an opportunity to reduce the likelihood of false alerts while protecting against typical prediction errors. The algorithm has been implemented in the Autonomous Operations Planner, a NASA Langley prototype decision support tool for airborne self-separation.

Karr, David A.↗
NASA NTRS1994

Determining structure in molecular clouds

We descibe an automatic, objective routine for analyzing the clumpy structure in a spectral line position-position-velocity data cube. The algorithm works by first contouring the data at a multiple of the rms noise of the observations, then searches for peaks of emission which locate the clumps, and then follows them down to lower intensities. No a proiri clump profile is assumed. By creating simulated data, we test the performance of the algorithm and show that a contour map most accurately depicts internal structure at a contouring interval equal to twice the rms noise of the map. Blending of clump emission leads to small errors in mass and size determinations and in severe cases can result in a number of clumps being misidentified as a single unit, flattening the measured clump mass spectrum. The algorithm is applied to two real data sets as an example of its use. The Rosette molecular cloud is a 'typical' star-forming cloud, but in the Maddalena molecular cloud high-mass star formation is completely absent. Comparison of the two clump lists generated by the algorithm show that on a one-to-one basis the clumps in the star-forming cloud have higher peak temperatures, higher average densities, and are more gravitationally bound than in the non-star-forming cloud. Collective properties of the clumps, such as temperature-size-line-width-mass relations appear very similar, however. Contrary to the initial results reported in a previous paper (Williams & Blitz 1993), we find that the current, more thoroughly tes ted analysis finds no significant difference in the clump mass spectrum of the two clouds.

Williams, Jonathan P.↗
NASA NTRS2002

On the validity of the double integrator approximation in deep space formation flying

Free-flying models are commonly used f o r path planning and open loop control design (i. e., guidance design) and translational feedback control design (i. e., control design) for deep space precision formation flying. The free flying model, essentially a double integrator, results from discarding small terms in the relative spacecraft equations of motion. While the magnitude of these discarded terms may be small, one must show that their dynamic effects are small as compared to the precision performance requirements. We do so by deriving a theoretical method for bounding the difference between the solution of a nonlinear truth model of the relative translational spacecraft dynamics and a Simplified linear time-invariant model. Presently, the method incorporates feedforward and static output feedback control. The method is applied to a Terrestrial Planet Finder- based example. Using only feedforward control (guidance) the free-flying model and a Hill- Clohessy- Wiltshire Equations-based model are shown to be accurate to 1 c m for up to 4 and 30 hours, respectively. Also shown is that the simplest free-flying model may not be sufficient for low-gain feedback control design-closed-loop tracking errors can be as large as 8 meters.

formation flying free flying model double integrat↗
DOE OSTI2025

Efficient Training of Deep Neural Operator Networks via Randomized Sampling

Neural operators (NOs) employ deep neural networks to learn the mappings between infinitedimensional function spaces. Deep operator network (DeepONet), a popular NO architecture, has demonstrated success in the real-time prediction of complex dynamics across various scientific and engineering applications. In this work, we introduce a random sampling technique to be adopted during the training of DeepONet, aimed at improving the generalization ability of the model, while significantly reducing the computational time. The proposed approach targets the trunk network of the DeepONet model that outputs the basis functions corresponding to the spatiotemporal locations of the bounded domain on which the physical system is defined. While constructing the loss function, DeepONet training traditionally considers a uniform grid of spatiotemporal points at which all the output functions are evaluated for each iteration. This approach leads to a larger batch size, resulting in poor generalization and increased memory demands, due to the limitations of the stochastic gradient descent (SGD) optimizer. The proposed random sampling over the inputs of the trunk net mitigates these challenges, improving generalization and reducing the memory requirements during training, resulting in significant computational gains. We validate our hypothesis through three benchmark examples, demonstrating substantial reductions in training time while achieving comparable or lower overall test errors relative to the traditional training approach. Our results indicate that incorporating randomization in the trunk network inputs during training enhances the efficiency and robustness of DeepONet, offering a promising avenue for improving the framework’s performance in modeling complex physical systems.

Karumuri, Sharmila [Department of Civil & Systems ↗