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Faster Randomized Dynamical Decoupling
We present a randomized dynamical decoupling (DD) protocol that can substantially improve the performance of any given deterministic DD scheme for suppressing coherent noise by using no more than two additional pulses. Our construction is implemented by probabilistically applying sequences of pulses, which, when combined, effectively eliminate the error terms that scale linearly with the system-environment coupling strength. As a result, we show that a randomized protocol using a few pulses can outperform deterministic DD protocols that require considerably more pulses. Furthermore, we prove that the randomized protocol provides an improvement compared to deterministic DD sequences that aim to reduce the error in the system’s Hilbert space, such as Uhrig DD, which had been previously regarded to be optimal. To rigorously evaluate the performance, we introduce new analytical methods suitable for analyzing higher-order DD protocols that might be of independent interest. Here, we also present numerical simulations confirming the significant advantage of using randomized protocols compared to widely used deterministic protocols.
Analysis of Neural Networks as Random Dynamical Systems
In this report we present our findings and outcomes of the NNRDS (analysis of Neural Networks as Random Dynamical Systems) project. The work is largely motivated by the analogy of a large class of neural networks (NNs) with a discretized ordinary differential equation (ODE) schemes. Namely, residual NNs, or ResNets, can be viewed as a discretization of neural ODEs (NODEs) where the NN depth plays the role of the time evolution. We employ several legacy tools from ODE theory, such as stiffness, nonlocality, autonomicity, to enable regularization of ResNets thus improving their generalization capabilities. Furthermore, armed with NN analysis tools borrowed from the ODE theory, we are able to efficiently augment NN predictions with uncertainty overcoming wellknown dimensionality challenges and adding a degree of trust towards NN predictions. Finally, we have developed a Python library QUiNN (Quantification of Uncertainties in Neural Networks) that incorporates improved-architecture ResNets, besides classical feed-forward NNs, and contains wrappers to PyTorch NN models enabling several major classes of uncertainty quantification methods for NNs. Besides synthetic problems, we demonstrate the methods on datasets from climate modeling and materials science.
Max Launch Abort System (MLAS) Pad Abort Test Vehicle (PATV) II Attitude Control System (ACS) Integration and Pressurization Subsystem Dynamic Random Vibration Analysis
In order to mitigate catastrophic failures on future generation space vehicles, engineers at the National Aeronautics and Space Administration have begun to integrate a novel crew abort systems that could pull a crew module away in case of an emergency at the launch pad or during ascent. The Max Launch Abort System (MLAS) is a recent test vehicle that was designed as an alternative to the baseline Orion Launch Abort System (LAS) to demonstrate the performance of a "tower-less" LAS configuration under abort conditions. The MLAS II test vehicle will execute a propulsive coast stabilization maneuver during abort to control the vehicles trajectory and thrust. To accomplish this, the spacecraft will integrate an Attitude Control System (ACS) with eight hypergolic monomethyl hydrazine liquid propulsion engines that are capable of operating in a quick pulsing mode. Two main elements of the ACS include a propellant distribution subsystem and a pressurization subsystem to regulate the flow of pressurized gas to the propellant tanks and the engines. The CAD assembly of the Attitude Control System (ACS) was configured and integrated into the Launch Abort Vehicle (LAV) design. A dynamic random vibration analysis was conducted on the Main Propulsion System (MPS) helium pressurization panels to assess the response of the panel and its components under increased gravitational acceleration loads during flight. The results indicated that the panels fundamental and natural frequencies were farther from the maximum Acceleration Spectral Density (ASD) vibrations which were in the range of 150-300 Hz. These values will direct how the components will be packaged in the vehicle to reduce the effects high gravitational loads.
Reliability of degrading dynamic systems subject to dynamic random loads
Reliability was determined for two degrading dynamic systems subject to random load processes. Damage is caused by loss of components for Daniels systems and crack extension for plates with cracks. The analysis accounted for the coupling between response and current damage state of the system. It is based on mean crossing rates of conditional processes and properties of diffusion models. Simple systems are used to illustrate proposed methods for estimating reliability.
Data-Driven Closures and Assimilation for Stiff Multiscale Random Dynamics
Here, we introduce a data-driven and physics-informed framework for propagating uncertainty in stiff, multiscale random ordinary differential equations (RODEs) driven by correlated (colored) noise. Unlike systems subjected to Gaussian white noise, a deterministic equation for the joint probability density function (PDF) of RODE state variables does not exist in closed form. Moreover, such an equation would require as many phase-space variables as there are states in the RODE system. To alleviate this curse of dimensionality, we instead derive exact, albeit unclosed, reduced-order PDF (RoPDF) equations for low-dimensional observables/quantities of interest. The unclosed terms take the form of state-dependent conditional expectations, which are directly estimated from data at sparse observation times. However, for systems exhibiting stiff, multiscale dynamics, data sparsity introduces regression discrepancies that compound during RoPDF evolution. This is overcome by introducing a kinetic-like defect term to the RoPDF equation, which is learned by assimilating in sparse, low-fidelity RoPDF estimates. Two assimilation methods are considered, namely nudging and deep neural networks, which are successfully tested against Monte Carlo simulations.
Memory row recording for mitigating crosstalk in dynamic random access memory
A method includes adding a set of one or more victim rows to a first probabilistic filter and to a second probabilistic filter, in response to a memory access request, identifying a candidate victim row adjacent to a memory address specified by a memory access request, identifying the candidate victim row as a victim row in the set of victim rows based on performing a lookup of the candidate victim row in a selected filter, where the selected filter includes one of the first probabilistic filter and the second probabilistic filter, in response to identifying the candidate row as the victim row, enabling a row hammering countermeasure, clearing the first probabilistic filter in each of a first set of time periods, and clearing the second probabilistic filter in each of a second set of time periods interleaved with the first set of time periods.
Calculation of Dynamic Loads Due to Random Vibration Environments in Rocket Engine Systems
An important part of rocket engine design is the calculation of random dynamic loads resulting from internal engine "self-induced" sources. These loads are random in nature and can greatly influence the weight of many engine components. Several methodologies for calculating random loads are discussed and then compared to test results using a dynamic testbed consisting of a 60K thrust engine. The engine was tested in a free-free condition with known random force inputs from shakers attached to three locations near the main noise sources on the engine. Accelerations and strains were measured at several critical locations on the engines and then compared to the analytical results using two different random response methodologies.
Stability problems in randomly-excited dynamic systems.
Stability problems in randomly excited dynamic systems, discussing partial differential equations governing evolution of conditional probabilities and expectations
Dynamically controlled random lasing with colloidal titanium carbide MXene
Control of lasing properties through tailorable and dynamically tunable materials and reconfigurable compositions can augment the performance of random lasers for a wide range of applications. Here, a colloid of randomly dispersed weakly scattering single-layer titanium carbide (Ti 3 C 2 T x ) MXene flakes embedded within rhodamine 101 gain medium is experimentally shown to provide feedback for random lasing. Additionally, in contrast to previously reported random laser systems where the optical properties of scatterers are static, the relative permittivity of Ti 3 C 2 T x MXene flakes can be varied under optical pumping due to the saturable absorption properties. Numerical simulations indicate that the observed nonlinear response of Ti 3 C 2 T x MXene flakes enables dynamically tunable random lasing. Thus, pumping the Ti 3 C 2 T x MXene flakes with a second optical source decreases the gain threshold required to obtain random lasing. Also, using numerical simulations, it is shown that the control over the intensity of the second pump enables tuning the field distribution of the random lasing modes. Considering the diversity of the MXenes family, the proposed MXene colloidal metamaterial design opens up a new avenue to advanced control of lasing properties for photonic applications.
Memory-efficient nonsmooth dynamic optimization using adaptive randomized compression
Dynamic optimization problems arise in many applications including flow control, full waveform inversion, and medical imaging. These problems are plagued by significant computational challenges. One such challenge — and the focus of this work — is the memory limitation induced by the size of the underlying dynamical system. In particular, the entire dynamic trajectory is required for derivative computation and therefore must be stored or recomputed using, e.g., checkpointing. Although recent work demonstrated the use of adaptive randomized sketching to overcome the memory challenge, that work only applies to smooth unconstrained problems, prohibiting its use for nonsmooth regularized and constrained problems. The inclusion of nonsmooth regularizers and constraints is critical as they often arise in an attempt to preserve certain physical properties or to promote sparsity. To solve these problems, we introduce a trust-region algorithm for minimizing the sum of a smooth nonconvex function and a nonsmooth convex function that leverages randomized sketching to compress the dynamical system trajectories and adaptively adjust the sketch rank to satisfy a gradient inexactness condition. We prove convergence of this algorithm and demonstrate that it achieves substantial memory reduction on three discretized PDE-constrained optimization applications.
A Cascaded Random Access Quantum Memory
Dynamic random access memory is critical to classical computing but notably absent in experimental quantum computers. Here we realize an 8-bit cascaded random access quantum memory using superconducting circuits and cavities and showcase the ability to perform arbitrary gate operations on it. In addition to individual error channels such as photon loss, quantum memories can also experience decoherence from many-body self-interaction. We characterize the origin and contributions of many-body infidelity throughout the memory cycle. We find that individual modes can be accessed with $\lesssim 1.5\%$ infidelity per mode and that the entire memory can be accessed in arbitrary order with an error rate below the depolarization threshold of the surface code, paving the way for fault-tolerant quantum memories.
Understanding random-walk dynamical phase coexistence through waiting times
We study the appearance of first-order dynamical phase transitions (DPTs) as “intermittent” coexisting phases in the fluctuations of random walks on graphs. We show that the diverging timescale leading to critical behavior is the waiting time to jump from one phase to another. This timescale is crucial for observing the system's relaxation to stationarity and demonstrate ergodicity of the system at criticality. We illustrate these results through three analytical examples which provide insights into random walks exploring random graphs. Published by the American Physical Society 2024
Limiting performance characteristics of randomly disturbed dynamic systems, a survey
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The Steady State Behavior of Randomly Perturbed Dynamical Systems
The statistical behavior of nonlinear systems near stable.
Dynamic response and input identification of MDOF structures subjected to coupled random vector inputs
A method of random dynamic analysis is presented which is based on the classical approach applied to a discretized structure. The method assumes that the system identification is available in the form of natural modes and frequencies. These modes and frequencies can be found from either available solutions or approximately from finite element programs. A computer program has been developed to perform the computations required in the analysis. All computations are performed with transformed modal variables, which results in significant economy since the number of modal degrees of freedom is almost always less than the number of physical degrees of freedom. The program computes the response to force and base inputs which are statistically coupled. A method is also presented for predicting one of the inputs if the second input and the acceleration response at a point on the structure are known. Finally, results are presented for the random response of a rectangular plate subjected to a random pressure and a random base input. The inputs are considered individually and with various degrees of statistical coupling.
An approximate method for determining response of nonlinear dynamic systems to random disturbances
Approximation method for determining response of nonlinear dynamic systems to random disturbances
CoNNeCT Baseband Processor Module
A document describes the CoNNeCT Baseband Processor Module (BPM) based on an updated processor, memory technology, and field-programmable gate arrays (FPGAs). The BPM was developed from a requirement to provide sufficient computing power and memory storage to conduct experiments for a Software Defined Radio (SDR) to be implemented. The flight SDR uses the AT697 SPARC processor with on-chip data and instruction cache. The non-volatile memory has been increased from a 20-Mbit EEPROM (electrically erasable programmable read only memory) to a 4-Gbit Flash, managed by the RTAX2000 Housekeeper, allowing more programs and FPGA bit-files to be stored. The volatile memory has been increased from a 20-Mbit SRAM (static random access memory) to a 1.25-Gbit SDRAM (synchronous dynamic random access memory), providing additional memory space for more complex operating systems and programs to be executed on the SPARC. All memory is EDAC (error detection and correction) protected, while the SPARC processor implements fault protection via TMR (triple modular redundancy) architecture. Further capability over prior BPM designs includes the addition of a second FPGA to implement features beyond the resources of a single FPGA. Both FPGAs are implemented with Xilinx Virtex-II and are interconnected by a 96-bit bus to facilitate data exchange. Dedicated 1.25- Gbit SDRAMs are wired to each Xilinx FPGA to accommodate high rate data buffering for SDR applications as well as independent SpaceWire interfaces. The RTAX2000 manages scrub and configuration of each Xilinx.