Reduced Basis Approximations of Parameterized Dynamic PDEs via Neural Networks
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Here, parametrized quantum circuits can be used as quantum neural networks and have the potential to outperform their classical counterparts when trained for addressing learning problems. To date, much of the results on their performance on practical problems are heuristic in nature. In particular, the convergence rate for the training of quantum neural networks is not fully understood. Here, we analyze the dynamics of gradient descent for the training error of a class of variational quantum machine learning models. We define wide quantum neural networks as parametrized quantum circuits in the limit of a large number of qubits and variational parameters. Then, we find a simple analytic formula that captures the average behavior of their loss function and discuss the consequences of our findings. For example, for random quantum circuits, we predict and characterize an exponential decay of the residual training error as a function of the parameters of the system. Finally, we validate our analytic results with numerical experiments.
The dynamic stability of formation geometry is vital to the design of large scale multiagent systems. In this paper, we probe into the structure of the formation system matrix using the Laplacian of a digraph to develop several fundamental theoretical results on the stability of formation geometry. Our key-results include the integration of the graph Laplacian into linear and weak-nonlinear relative dynamics, the development of several new coordinate transformations that expose the influence of the graph Laplacian matrix on the control laws of the agents, and the use of direct adaptive control as stability restoring devices. We also develop two fundamental results that provide upper bounds for stable formation evolution under nonlinear perturbations of agent dynamics. Finally, we use an illustrative example to demonstrate our theoretical findings.
Fluctuations of synaptic weights, among many other physical, biological, and ecological quantities, are driven by coincident events of two “parent” processes. Here we propose a multiplicative shot-noise model that can capture the behaviors of a broad range of such natural phenomena, and analytically derive an approximation that accurately predicts its statistics. We apply our results to study the effects of a multiplicative synaptic plasticity rule that was recently extracted from measurements in physiological conditions. Using mean-field theory analysis and network simulations, we investigate how this rule shapes the connectivity and dynamics of recurrent spiking neural networks. The multiplicative plasticity rule is shown to support efficient learning of input stimuli, and it gives a stable, unimodal synaptic-weight distribution with a large fraction of strong synapses. The strong synapses remain stable over long times but do not “run away.” Our results suggest that the multiplicative shot-noise offers a new route to understand the tradeoff between flexibility and stability in neural circuits and other dynamic networks.
Wireless sensor networks (WSN) based on the IEEE 802.15.4 Personal Area Network (PAN) standard are finding increasing use in the home automation and emerging smart energy markets. The network and application layers, based on the ZigBee 2007 Standard, provide a convenient framework for component-based software that supports customer solutions from multiple vendors. WSNs provide the inherent fault tolerance required for aerospace applications. The Discovery and Systems Health Group at NASA Ames Research Center has been developing WSN technology for use aboard aircraft and spacecraft for System Health Monitoring of structures and life support systems using funding from the NASA Engineering and Safety Center and Exploration Technology Development and Demonstration Program. This technology provides key advantages for low-power, low-cost ancillary sensing systems particularly across pressure interfaces and in areas where it is difficult to run wires. Intelligence for sensor networks could be defined as the capability of forming dynamic sensor networks, allowing high-level application software to identify and address any sensor that joined the network without the use of any centralized database defining the sensors characteristics. The IEEE 1451 Standard defines methods for the management of intelligent sensor systems and the IEEE 1451.4 section defines Transducer Electronic Datasheets (TEDS), which contain key information regarding the sensor characteristics such as name, description, serial number, calibration information and user information such as location within a vehicle. By locating the TEDS information on the wireless sensor itself and enabling access to this information base from the application software, the application can identify the sensor unambiguously and interpret and present the sensor data stream without reference to any other information. The application software is able to read the status of each sensor module, responding in real-time to changes of PAN configuration, providing the appropriate response for maintaining overall sensor system function, even when sensor modules fail or the WSN is reconfigured. The session will present the architecture and technical feasibility of creating fault-tolerant WSNs for aerospace applications based on our application of the technology to a Structural Health Monitoring testbed. The interim results of WSN development and testing including our software architecture for intelligent sensor management will be discussed in the context of the specific tradeoffs required for effective use. Initial certification measurement techniques and test results gauging WSN susceptibility to Radio Frequency interference are introduced as key challenges for technology adoption. A candidate Developmental and Flight Instrumentation implementation using intelligent sensor networks for wind tunnel and flight tests is developed as a guide to understanding key aspects of the aerospace vehicle design, test and operations life cycle.
In large and complex systems, operational decision-making requires a systematic analysis with a vast amount of data from both process parameters and component status monitoring. In this paper, we present an integrated artificial reasoning approach for system state transition models that can help operational decision-making with explainable and traceable reasoning. The integrated artificial reasoning framework is a physics-based approach of defining the system structure in a Bayesian network, so we leveraged it in a Markov decision process (MDP) for finding optimal operational solutions. In our proposed framework, the MDP is implemented on a dynamic Bayesian network (DBN), which represents causalities in a system. The multilevel flow modeling was utilized in order to extract these causalities in a more efficient and objective manner. Since multilevel flow modeling is based on the fundamental energy and mass conservation laws, the target system is decomposed into several mass, energy, and information structures, which serve as the basis for a DBN. The MDP consists of the processes of finding a solution for the Bellman equation, which can be derived from the conditional probability equations of the constructed DBN. System operators can capture stochastic system dynamics as multiple subsystem state transitions based on their physical relations and uncertainties coming from the component degradation process or random failures. We analyzed a simplified example system to illustrate finding an optimal operational policy with this approach.
Herein we propose a multi-resolution convolutional autoencoder (MrCAE) architecture that integrates and leverages three highly successful mathematical architectures: (i) multigrid methods, (ii) convolutional autoencoders and (iii) transfer learning. The method provides an adaptive, hierarchical architecture that capitalizes on a progressive training approach for multiscale spatio-temporal data. This framework allows for inputs across multiple scales: starting from a compact (small number of weights) network architecture and low-resolution data, our network progressively deepens and widens itself in a principled manner to encode new information in the higher resolution data based on its current performance of reconstruction. Basic transfer learning techniques are applied to ensure information learned from previous training steps can be rapidly transferred to the larger network. As a result, the network can dynamically capture different scaled features at different depths of the network. The performance gains of this adaptive multiscale architecture are illustrated through a sequence of numerical experiments on synthetic examples and real-world spatial-temporal data.
A series of catalyst-free, room temperature dynamic bonds derived from a reversible thia-Michael reaction are utilized to access mechanically robust dynamic covalent network films. The equilibrium of the thiol addition to benzalcyanoacetate-based Michael-acceptors can be directly tuned by controlling the electron-donating/withdrawing nature of the Michael-acceptor. By modulating the composition of different Michael-acceptors in a dynamic covalent network, a wide range of mechanical properties and thermal responses can be realized. Additionally, the reported systems phase-separate in a process, coined dynamic reaction-induced phase separation (DRIPS), that yields reconfigurable phase morphologies and reprogrammable shape-memory behaviour as highlighted by the heat-induced folding of a predetermined structure.
This paper presents a latent-space dynamic neural network (LSDNN) model for the multi-step-ahead prediction and fault detection of a geothermal power plant’s operation. The model was trained to learn the dynamics of the power generation process from multivariate time-series data and the effects of exogenous variables, such as control adjustment and ambient temperature. In the LSDNN model, an encoder–decoder architecture was designed to capture cross-correlation among different measured variables. In addition, a latent space dynamic structure was proposed to propagate the dynamics in the latent space to enable prediction. The prediction power of the LSDNN was utilized for monitoring a geothermal power plant and detecting abnormal events. The model was integrated with principal component analysis (PCA)-based process monitoring techniques to develop a fault-detection procedure. The performance of the proposed LSDNN model and fault detection approach was demonstrated using field data collected from a geothermal power plant.
This paper presents a discussion of the applicability of neural networks in the identification and control of dynamic systems. Emphasis is placed on the understanding of how the neural networks handle linear systems and how the new approach is related to conventional system identification and control methods. Extensions of the approach to nonlinear systems are then made. The paper explains the fundamental concepts of neural networks in their simplest terms. Among the topics discussed are feed forward and recurrent networks in relation to the standard state-space and observer models, linear and nonlinear auto-regressive models, linear, predictors, one-step ahead control, and model reference adaptive control for linear and nonlinear systems. Numerical examples are presented to illustrate the application of these important concepts.
A new neural network architecture is proposed based upon effects of non-Lipschitzian dynamics. The network is fully connected, but these connections are active only during vanishingly short time periods. The advantages of this architecture are discussed.