Modeling turbulent and self-gravitating fluids with Fourier neural operators
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Keith Poletti↗
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Clifford Neural Operators on Atmospheric Data Influenced Partial Differential Equations
Mathematical representations of the atmosphere are key to forecasting and research tasks across Earth science. Numerically solving the underlying partial differential equations(PDEs) of the atmosphere, however, can be difficult and computationally expensive with numerous trade-offs between computing efficiency and accuracy. Utilizing neural net-works to learn approximations of the PDE solutions from the data can help us model complex phenomena more efficiently than traditional numerical schemes. Here, we have applied Clifford algebra-based neural operators for predicting atmospheric variables. Clifford Fourier neural operators are used with two different backbone architectures, ResNet and UNet, on custom data of U10, V10 and surface pressure as well as U500, V500 and Z500. Clifford Fourier neural operators, coupled with ResNet and UNet architectures, are applied to a key reanalysis dataset. Model performance is initially strong, but we observe increasing errors, resulting in the model becoming highly unstable.
Sujit Roy↗
Estimation of Stability and Control Derivatives of an F-15
A technique for real-time estimation of stability and control derivatives (derivatives of moment coefficients with respect to control-surface deflection angles) was used to support a flight demonstration of a concept of an indirect-adaptive intelligent flight control system (IFCS). Traditionally, parameter identification, including estimation of stability and control derivatives, is done post-flight. However, for the indirect-adaptive IFCS concept, parameter identification is required during flight so that the system can modify control laws for a damaged aircraft. The flight demonstration was carried out on a highly modified F-15 airplane (see Figure 1). The main objective was to estimate the stability and control derivatives of the airplane in nearly real time. A secondary goal was to develop a system to automatically assess the quality of the results, so as to be able to tell a learning neural network which data to use. Parameter estimation was performed by use of Fourier-transform regression (FTR) a technique developed at NASA Langley Research Center. FTR is an equation- error technique that operates in the frequency domain. Data are put into the frequency domain by use of a recursive Fourier transform for a discrete frequency set. This calculation simplifies many subsequent calculations, removes biases, and automatically filters out data beyond the chosen frequency range. FTR as applied here was tailored to work with pilot inputs, which produce correlated surface positions that prevent accurate parameter estimates, by replacing half the derivatives with predicted values. FTR was also set up to work only on a recent window of data, to accommodate changes in flight condition. A system of confidence measures was developed to identify quality-parameter estimates that a learning neural network could use. This system judged the estimates primarily on the basis of their estimated variances and of the level of aircraft response. The resulting FTR system was implemented in the Simulink software system and auto-coded in the C programming language for use on the Airborne Research Test System (ARTS II) computer installed in the F-15 airplane. The Simulink model was also used in a control room that utilizes the Ring Buffered Network Bus hardware and software, making it possible to evaluate test points during flights. In-flight parameter estimation was done for piloted and automated maneuvers, primarily at three test conditions. Figure 2 shows results for pitching moment due to symmetric stabilator actuations for a series of three pitch doublet maneuvers (in a doublet maneuver, a command to change attitude in a given direction by a given amount is followed immediately by a command to change attitude in the opposite direction by the same amount). A time window of 5 seconds was used. The portions of the curves shown in red are those that passed the confidence tests. The technique showed good convergence for most derivatives for both kinds of maneuvers - typically within a few seconds. The confidence tests were marginally successful, and it would be necessary to refine them for use in an IFCS.
Smith, Mark↗
Analysis of Salinity Intrusion in the San Francisco Bay-Delta using a GA- Optimized Neural Net, and Application of the Model to Prediction in the Elkhorn Slough Habitat
The San Francisco Bay Delta is a large hydrodynamic complex that incorporates the Sacramento and San Joaquin Estuaries, the Burman Marsh, and the San Francisco Bay proper. Competition exists for the use of this extensive water system both from the fisheries industry, the agricultural industry, and from the marine and estuarine animal species within the Delta. As tidal fluctuations occur, more saline water pushes upstream allowing fish to migrate beyond the Burman Marsh for breeding and habitat occupation. However, the agriculture industry does not want extensive salinity intrusion to impact water quality for human and plant consumption. The balance is regulated by pumping stations located alone the estuaries and reservoirs whereby flushing of fresh water keeps the saline intrusion at bay. The pumping schedule is driven by data collected at various locations within the Bay Delta and by numerical models that predict the salinity intrusion as part of a larger model of the system. The Interagency Ecological Program (IEP) for the San Francisco Bay/Sacramento-San Joaquin Estuary collects, monitors, and archives the data, and the Department of Water Resources provides a numerical model simulation (DSM2) from which predictions are made that drive the pumping schedule. A problem with this procedure is that the numerical simulation takes roughly 16 hours to complete a C:~ prediction. We have created a neural net, optimized with a genetic algorithm, that takes as input the archived data from multiple stations and predicts stage, salinity, and flow at the Carquinez Straits (at the downstream end of the Burman Marsh). This model seems to be robust in its predictions and operates much faster than the current numerical DSM2 model. Because the system is strongly tidal driven, we used both Principal Component Analysis and Fast Fourier Transforms to discover dominant features within the IEP data. We then filtered out the dominant tidal forcing to discover non-primary tidal effects, and used this to enhance the neural network by mapping input-output relationships in a more efficient manner. Furthermore, the neural network implicitly incorporates both the hydrodynamic and water quality models into a single predictive system. Although our model has not yet been enhanced to demonstrate improve pumping schedules, it has the possibility to support better decision-making procedures that may then be implemented by State agencies if desired. Our intention is now to use this model in the smaller Elkhorn Slough complex near Monterey Bay where no such hydrodynamic model currently exists. At the Elkhorn Slough, we are fusing the neural net model of tidally-driven flow with in situ flow data and airborne and satellite remote sensation data. These further constrain the behavior of the model in predicting the longer-term health and future of this vital estuary.
Thompson, David E.↗
Multi-Stage System for Automatic Target Recognition
A multi-stage automated target recognition (ATR) system has been designed to perform computer vision tasks with adequate proficiency in mimicking human vision. The system is able to detect, identify, and track targets of interest. Potential regions of interest (ROIs) are first identified by the detection stage using an Optimum Trade-off Maximum Average Correlation Height (OT-MACH) filter combined with a wavelet transform. False positives are then eliminated by the verification stage using feature extraction methods in conjunction with neural networks. Feature extraction transforms the ROIs using filtering and binning algorithms to create feature vectors. A feedforward back-propagation neural network (NN) is then trained to classify each feature vector and to remove false positives. The system parameter optimizations process has been developed to adapt to various targets and datasets. The objective was to design an efficient computer vision system that can learn to detect multiple targets in large images with unknown backgrounds. Because the target size is small relative to the image size in this problem, there are many regions of the image that could potentially contain the target. A cursory analysis of every region can be computationally efficient, but may yield too many false positives. On the other hand, a detailed analysis of every region can yield better results, but may be computationally inefficient. The multi-stage ATR system was designed to achieve an optimal balance between accuracy and computational efficiency by incorporating both models. The detection stage first identifies potential ROIs where the target may be present by performing a fast Fourier domain OT-MACH filter-based correlation. Because threshold for this stage is chosen with the goal of detecting all true positives, a number of false positives are also detected as ROIs. The verification stage then transforms the regions of interest into feature space, and eliminates false positives using an artificial neural network classifier. The multi-stage system allows tuning the detection sensitivity and the identification specificity individually in each stage. It is easier to achieve optimized ATR operation based on its specific goal. The test results show that the system was successful in substantially reducing the false positive rate when tested on a sonar and video image datasets.
Chao, Tien-Hsin↗
Passive IFF: Autonomous Nonintrusive Rapid Identification of Friendly Assets
A proposed optoelectronic instrument would identify targets rapidly, without need to radiate an interrogating signal, apply identifying marks to the targets, or equip the targets with transponders. The instrument was conceived as an identification, friend or foe (IFF) system in a battlefield setting, where it would be part of a targeting system for weapons, by providing rapid identification for aimed weapons to help in deciding whether and when to trigger them. The instrument could also be adapted to law-enforcement and industrial applications in which it is necessary to rapidly identify objects in view. The instrument would comprise mainly an optical correlator and a neural processor (see figure). The inherent parallel-processing speed and capability of the optical correlator would be exploited to obtain rapid identification of a set of probable targets within a scene of interest and to define regions within the scene for the neural processor to analyze. The neural processor would then concentrate on each region selected by the optical correlator in an effort to identify the target. Depending on whether or not a target was recognized by comparison of its image data with data in an internal database on which the neural processor was trained, the processor would generate an identifying signal (typically, friend or foe ). The time taken for this identification process would be less than the time needed by a human or robotic gunner to acquire a view of, and aim at, a target. An optical correlator that has been under development for several years and that has been demonstrated to be capable of tracking a cruise missile might be considered a prototype of the optical correlator in the proposed IFF instrument. This optical correlator features a 512-by-512-pixel input image frame and operates at an input frame rate of 60 Hz. It includes a spatial light modulator (SLM) for video-to-optical image conversion, a pair of precise lenses to effect Fourier transforms, a filter SLM for digital-to-optical correlation-filter data conversion, and a charge-coupled device (CCD) for detection of correlation peaks. In operation, the input scene grabbed by a video sensor is streamed into the input SLM. Precomputed correlation-filter data files representative of known targets are then downloaded and sequenced into the filter SLM at a rate of 1,000 Hz. When there occurs a match between the input target data and one of the known-target data files, the CCD detects a correlation peak at the location of the target. Distortion- invariant correlation filters from a bank of such filters are then sequenced through the optical correlator for each input frame. The net result is the rapid preliminary recognition of one or a few targets.
Moynihan, Philip↗
Sensing Super-Position: Human Sensing Beyond the Visual Spectrum
The coming decade of fast, cheap and miniaturized electronics and sensory devices opens new pathways for the development of sophisticated equipment to overcome limitations of the human senses. This paper addresses the technical feasibility of augmenting human vision through Sensing Super-position by mixing natural Human sensing. The current implementation of the device translates visual and other passive or active sensory instruments into sounds, which become relevant when the visual resolution is insufficient for very difficult and particular sensing tasks. A successful Sensing Super-position meets many human and pilot vehicle system requirements. The system can be further developed into cheap, portable, and low power taking into account the limited capabilities of the human user as well as the typical characteristics of his dynamic environment. The system operates in real time, giving the desired information for the particular augmented sensing tasks. The Sensing Super-position device increases the image resolution perception and is obtained via an auditory representation as well as the visual representation. Auditory mapping is performed to distribute an image in time. The three-dimensional spatial brightness and multi-spectral maps of a sensed image are processed using real-time image processing techniques (e.g. histogram normalization) and transformed into a two-dimensional map of an audio signal as a function of frequency and time. This paper details the approach of developing Sensing Super-position systems as a way to augment the human vision system by exploiting the capabilities of Lie human hearing system as an additional neural input. The human hearing system is capable of learning to process and interpret extremely complicated and rapidly changing auditory patterns. The known capabilities of the human hearing system to learn and understand complicated auditory patterns provided the basic motivation for developing an image-to-sound mapping system. The human brain is superior to most existing computer systems in rapidly extracting relevant information from blurred, noisy, and redundant images. From a theoretical viewpoint, this means that the available bandwidth is not exploited in an optimal way. While image-processing techniques can manipulate, condense and focus the information (e.g., Fourier Transforms), keeping the mapping as direct and simple as possible might also reduce the risk of accidentally filtering out important clues. After all, especially a perfect non-redundant sound representation is prone to loss of relevant information in the non-perfect human hearing system. Also, a complicated non-redundant image-to-sound mapping may well be far more difficult to learn and comprehend than a straightforward mapping, while the mapping system would increase in complexity and cost. This work will demonstrate some basic information processing for optimal information capture for headmounted systems.
Maluf, David A.↗