Tensor Network Space-Time Spectral Collocation Method for Solving the Nonlinear Convection Diffusion Equation
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97 MATHEMATICS AND COMPUTING↗
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Space-Time Neural Networks
Concept of space-time neural network affords distributed temporal memory enabling such network to model complicated dynamical systems mathematically and to recognize temporally varying spatial patterns. Digital filters replace synaptic-connection weights of conventional back-error-propagation neural network.
Villarreal, James A.↗
A space-time neural network
Introduced here is a novel technique which adds the dimension of time to the well known back propagation neural network algorithm. Cited here are several reasons why the inclusion of automated spatial and temporal associations are crucial to effective systems modeling. An overview of other works which also model spatiotemporal dynamics is furnished. A detailed description is given of the processes necessary to implement the space-time network algorithm. Several demonstrations that illustrate the capabilities and performance of this new architecture are given.
Villarreal, James A.↗
Application of space-time neural networks to detect tether skiprope phenomenon in space operations
The feasibility of operating tethered payloads in earth orbit will be studied during a space shuttle flight scheduled for 1992. Tethered systems may exhibit a circular transverse oscillation or skiprope phenomenon due to interaction between the earth's magnetic field and current pulsing through the tether. Effective damping of this skiprope motion depends on rapid and accurate detection of its magnitude and phase. Satellite attitude motion has characteristic oscillations as well as many other perturbations and therefore the relationship between skiprope parameters and attitude time history is very complex and nonlinear. A space-time neural network (STNN) for filtering satellite rate gyro data is proposed for rapid detection and prediction of skiprope magnitude and phase. A validated orbital operations simulator and STNN software will be used for training and testing of this skiprope detection system. The advantages of STNNs are discussed and STNN configurations and preliminary results are presented.
Lea, Robert N.↗
Learning characteristics of a space-time neural network as a tether skiprope observer
The Software Technology Laboratory at the Johnson Space Center is testing a Space Time Neural Network (STNN) for observing tether oscillations present during retrieval of a tethered satellite. Proper identification of tether oscillations, known as 'skiprope' motion, is vital to safe retrieval of the tethered satellite. Our studies indicate that STNN has certain learning characteristics that must be understood properly to utilize this type of neural network for the tethered satellite problem. We present our findings on the learning characteristics including a learning rate versus momentum performance table.
Lea, Robert N.↗
Learning characteristics of a space-time neural network as a tether skiprope observer
The Software Technology Laboratory at JSC is testing a Space Time Neural Network (STNN) for observing tether oscillations present during retrieval of a tethered satellite. Proper identification of tether oscillations, known as 'skiprope' motion, is vital to safe retrieval of the tethered satellite. Our studies indicate that STNN has certain learning characteristics that must be understood properly to utilize this type of neural network for the tethered satellite problem. We present our findings on the learning characteristics including a learning rate versus momentum performance table.
Lea, Robert N.↗
Neural network for processing both spatial and temporal data with time based back-propagation
Neural networks are computing systems modeled after the paradigm of the biological brain. For years, researchers using various forms of neural networks have attempted to model the brain's information processing and decision-making capabilities. Neural network algorithms have impressively demonstrated the capability of modeling spatial information. On the other hand, the application of parallel distributed models to the processing of temporal data has been severely restricted. The invention introduces a novel technique which adds the dimension of time to the well known back-propagation neural network algorithm. In the space-time neural network disclosed herein, the synaptic weights between two artificial neurons (processing elements) are replaced with an adaptable-adjustable filter. Instead of a single synaptic weight, the invention provides a plurality of weights representing not only association, but also temporal dependencies. In this case, the synaptic weights are the coefficients to the adaptable digital filters. Novelty is believed to lie in the disclosure of a processing element and a network of the processing elements which are capable of processing temporal as well as spacial data.
Villarreal, James A.↗
Space-Time Finite Element Tensor Network Approach for the Time-Dependent Convection–Diffusion–Reaction Equation with Variable Coefficients
In this paper, we present a new space-time Galerkin-like method, where we treat the discretization of spatial and temporal domains simultaneously. This method utilizes a mixed formulation of the tensor-train (TT) and quantized tensor-train (QTT) (please see Section Tensor-Train Decomposition), designed for the finite element discretization (Q1-FEM) of the time-dependent convection–diffusion–reaction (CDR) equation. We reformulate the assembly process of the finite element discretized CDR to enhance its compatibility with tensor operations and introduce a low-rank tensor structure for the finite element operators. Recognizing the banded structure inherent in the finite element framework’s discrete operators, we further exploit the QTT format of the CDR to achieve greater speed and compression. Additionally, we present a comprehensive approach for integrating variable coefficients of CDR into the global discrete operators within the TT/QTT framework. The effectiveness of the proposed method, in terms of memory efficiency and computational complexity, is demonstrated through a series of numerical experiments, including a semi-linear example.
convection–diffusion–reaction equation↗
ECLEIRS: Exact conservation law embedded identification of reduced states for parameterized nonlinear conservation laws from sparse and noisy data
Multi-query applications such as parameter estimation, uncertainty quantification and design optimization for parameterized partial differential equation (PDE) systems are expensive. While reduced/latent state dynamics approaches for parameterized PDEs offer a viable alternative, these approaches rely on high-quality data and struggle with highly sparse spatiotemporal noisy measurements typically obtained from experiments. Furthermore, there is no guarantee that these models satisfy governing physical conservation laws. In this article, we propose a reduced state dynamics approach, referred to as ECLEIRS, that embeds exact conservation in the solution and flux representation by utilizing a space-time divergence-free neural network formulation. We compare ECLEIRS with other reduced state dynamics approaches, those that do not enforce any physical constraints and those with physics-informed loss functions, for three shock-propagation problems: 1-D advection, 1-D Burgers and 2-D Euler equations. In conclusion, the numerical experiments conducted in this study demonstrate that ECLEIRS provides the most accurate prediction of dynamics for unseen parameters even in the presence of highly sparse and noisy data.
97 MATHEMATICS AND COMPUTING↗
Overlapping qubits from non-isometric maps and de Sitter tensor networks
The emergence of a local effective theory from a more fundamental theory of quantum gravity with seemingly fewer degrees of freedom is a major puzzle of theoretical physics. A recent approach to this problem is to consider general features of the Hilbert space maps relating these theories. In this work, we construct approximately local observables, or overlapping qubits, from such non-isometric maps. We show that local processes in effective theories can be spoofed with a quantum system with fewer degrees of freedom, with deviations from actual locality identifiable as features of quantum gravity. For a concrete example, we construct two tensor network models of de Sitter space-time, demonstrating how exponential expansion and local physics can be spoofed for a long period before breaking down. Our results highlight the connection between overlapping qubits, Hilbert space dimension verification, degree-of-freedom counting in black holes, holography, and approximate locality in quantum gravity.
Quantum information↗
The impact of conventional surface data upon VAS regression retrievals in the lower troposphere
Surface temperature and dewpoint reports are added to the infrared radiances from the VISSR Atmospheric Sounder (VAS) in order to improve the retrieval of temperature and moisture profiles in the lower troposphere. The conventional (airways) surface data are combined with the twelve VAS channels as additional predictors in a ridge regression retrieval scheme, with the aim of using all available data to make high resolution space-time interpolations of the radiosonde network. For one day of VAS observations, retrievals using only VAS radiances are compared with retrievals using VAS radiances plus surface data. Temperature retrieval accuracy evaluated at coincident radiosonde sites shows a significant impact within the boundary layer. Dewpoint retrieval accuracy shows a broader improvement within the lowest tropospheric layers. The most dramatic impact of surface data is observed in the improved relative spatial and temporal continuity of low-level fields retrieved over the Midwestern United States.
Lee, T. H.↗
The impact of conventional surface data upon VAS regression retrievals in the lower troposphere
Surface temperature and dewpoint reports are added to the infrared radiances from the VISSR Atmospheric Sounder (VAS) in order to improve the retrieval of temperature and moisture profiles in the lower troposphere. The conventional (airways) surface data are combined with the twelve VAS channels as additional predictors in a ridge regression retrieval scheme, with the aim of using all available data to make high resolution space-time interpolations of the radiosonde network. For one day of VAS observations, retrievals using only VAS radiances are compared with retrievals using VAS radiances plus surface data. Temperature retrieval accuracy evaluated at coincident radiosonde sites shows a significant impact within the boundary layer. Dewpoint retrieval accuracy shows a broader improvement within the lowest tropospheric layers. The most dramatic impact of surface data is observed in the improved relative spatial and temporal continuity of low-level fields retrieved over the Midwestern United States. Previously announced in STAR as N83-27522
Lee, T.-H.↗
Quantum dynamics of cosmological particle production: interacting quantum field theories with matrix product states
Understanding real-time dynamics of interacting quantum fields in curved space-time remains a major theoretical challenge. We employ tensor network methods to study such dynamics using interacting scalar and gauge theories in 1+1 spacetime dimensions, subject to a quench modeling a homogeneously expanding gravitational background. The models considered are the scalar λϕ 4 theory and the Schwinger model, i.e. a Dirac fermion coupled to a U(1) gauge field which is equivalent via bosonization to a scalar field with a cosine self-interaction. In the free scalar limit, both theories reproduce known analytical results, providing a nontrivial numerical validation of bosonization in curved spacetime for the Schwinger model. Our central finding is that self-interactions lead to a suppression of gravitational particle production compared to the free-field case, as evidenced by two-point functions and the spectra of produced particles. We further examine the behavior of entanglement generation and find that interactions suppress entanglement growth in the λϕ 4 theory, while in the Schwinger model, the interplay between suppressed particle production and enhanced inter-particle correlations leads to more complex entanglement behavior. Our results pave the way for further explorations of nonperturbative quantum real-time dynamics of interacting scalar and gauge theories in arbitrary gravitational backgrounds.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Recurrent convolutional neural networks for modeling nonadiabatic dynamics of quantum-classical systems
Recurrent neural networks (RNNs) have recently been extensively applied to model the time evolution in fluid dynamics, weather predictions, and even chaotic systems due to their ability to capture temporal dependencies and sequential patterns in data. Here we present an RNN model based on convolutional neural networks for modeling the nonlinear nonadiabatic dynamics of hybrid quantum-classical systems. The dynamical evolution of the hybrid systems is governed by equations of motion for classical degrees of freedom and von Neumann equation for electrons. The Physics-Aware Recurrent Convolution (PARC) neural network structure incorporates a differentiator-integrator architecture that inductively models the spatiotemporal dynamics of generic physical systems. Here, we apply our RNN approach to learn the space-time evolution of a one-dimensional semiclassical Holstein model after an interaction quench. For shallow quenches (small changes in electron-lattice coupling), the deterministic dynamics can be accurately captured using a single-CNN-based recurrent network. In contrast, deep quenches induce chaotic evolution, making long-term trajectory prediction significantly more challenging. Nonetheless, we demonstrate that the PARC-CNN architecture can effectively learn the statistical climate of the Holstein model under deep-quench conditions.
Holstein model↗
Analysis of selective chopper radiometer data
Data from SCR-B on Nimbus 5 have been processed to yield global, orbital temperatures at 10, 5, 2, 1, and 0.4 mb for the period January 1977 through April 1978 under the current task. In addition gridded values at 10 deg latitude by 20 deg longitude were prepared by space-time interpolation for the period January 1975 through April 1978. Temperature retrieval was based on regression of radiances against Meteorological Rocket Network data, with regressions recomputed at approximately six-month intervals. This data now completes a consistent time series from April 1970 to April 1978 for all available radiance data from SCR A and SCR B on Nimbus 4 and 5. The processing details for the current period are discussed, but is also applicable to the previous data periods. The accuracy of the temperature retrievals for each 6-month period for the entire eight years is given in the Appendices.
Roe, J.↗
Fault-tolerant optical interconnects for neutral-atom arrays
We analyze the use of photonic links to enable large-scale fault-tolerant connectivity of locally error-corrected modules based on neutral atom arrays. Our approach makes use of recent theoretical results showing the robustness of surface codes to boundary noise and combines recent experimental advances in atom-array quantum computing with logical qubits with optical quantum networking techniques. We find the conditions for fault tolerance can be achieved with local two-qubit Rydberg gate and nonlocal Bell-pair errors below 1% and 10%, respectively, without requiring distillation or space-time overheads. Realizing the interconnects with a lens, a single optical cavity, or an array of cavities enables—with sufficient multiplexing—a Bell-pair generation rate in the 1–50 MHz range. When directly interfacing logical qubits, this rate translates to error-correction cycles in the 25–2000 kHz range, satisfying all requirements for fault tolerance and in the upper range fast enough for 100 kHz logical clock cycles. Published by the American Physical Society 2025
Sinclair, Josiah (ORCID:0000000215238295)↗
A raingage, radar and satellite simulation study of the estimation of convective rainfall by area-time integrals
Correlations between area-averaged rainrates and the areal fraction of rainrates exceeding a preset threshold, F(T), are examined using data from a network of 22 raingages located within 120 km of the NOAA/Tropical Ocean-Global Atmosphere (TOGA) C-band meteorological radar at Darwin, Australia. The results show that the area averages of convective rainfall are highly correlated with the fraction F(T). To simulate the use of the relationship between area-averaged rainrates and F(T) to obtain space-time averaged rainrates from a satellite sensor, observations from the NOAA/TOGA radar observations are used to estimate F(T) using a reflectivity threshold. The use of area-time integral methods for inferring area-averaged rainrates from satellites is examined, noting the possible use of the methodology for the Tropical Rainfall Measuring Mission.
Short, David A.↗
AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 34th and AIAA/ASME Adaptive Structures Forum, La Jolla, CA, Apr. 19-22, 1993, Technical Papers. Pts. 1-6
Topics addressed include the prediction of helicopter component loads using neural networks, spacecraft on-orbit coupled loads analysis, hypersonic flutter of a curved shallow panel with aerodynamic heating, thermal-acoustic fatigue of ceramic matrix composite materials, transition elements based on transfinite interpolation, damage progression in stiffened composite panels, a direct treatment of min-max dynamic response optimization problems, and sources of helicopter rotor hub inplane shears. Also discussed are dynamics of a layered elastic system, confidence bounds on structural reliability, mixed triangular space-time finite elements, advanced transparency development for USAF aircraft, a low-velocity impact on a graphite/PEEK, an automated mode-tracking strategy, transonic flutter suppression by a passive flap, a nonlinear response of composite panels to random excitation, an optimal placement of elastic supports on a simply supported plate, a probabilistic assessment of composite structures, a model for mode I failure of laminated composites, a residual flexibility approach to multibody dynamics,and multilayer piezoelectric actuators.
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