Learning the dynamical response of nonlinear non-autonomous dynamical systems with deep operator neural networks
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Recently, deep learning surrogates and neural operators have shown promise in solving partial differential equations (PDEs). However, they often require a large amount of training data and are limited to bounded domains. In this work, we present a novel physics-informed neural operator method to solve parameterized boundary value problems without labeled data. By reformulating the PDEs into boundary integral equations (BIEs), we can train the operator network solely on the boundary of the domain. This approach reduces the number of required sample points from $O(N^d)$ to $O(N^{d-1}$), where $d$ is the domain’s dimension, leading to a significant acceleration of the training process. Additionally, our method can handle unbounded problems, which are unattainable for existing physics-informed neural networks (PINNs) and neural operators. Finally, our numerical experiments show the effectiveness of parameterized complex geometries and unbounded problems.
Objective: Improve the resiliency of power systems with optimization-based methods that leverage advanced microgrid technologies to reduce system recovery times after extreme event induced outages. Outcome: First-of-kind, high-fidelity physics-based optimization method for modeling networked microgrids which includes key engineering constraints associated with system recovery after extreme events.
Chronology of actions taken by ground control facilities following Apollo 13 flight emergency
Unattended station operation was implemented that permitted full operational control from the network operations center (NOCC). Sensors were installed in the mechanical subsystem to monitor critical functions and to permit automated premission checkout of the subsystem, automated reaction to component failure, and identification of failed components under control of the antenna pointing computer. This monitoring installation is a prototype for monitoring equipment to be installed throughout the DSN.
The ORBCOMM system is designed to provide low-cost, two-way data communications for mobile and remote users. The communications system is ideally configured for low data rate applications where communicating devices are geographically dispersed and two-way communications through terrestrial means is cumbersome and not cost effective. The remote terminals use VHF frequencies which allow for the use of very small, low-cost terminals. ORBCOMM has entered into joint development agreements with several large manufacturers of both consumer and industrial electronics to design and build the remote terminals. Based on prototype work, the estimated retail cost of these units will range from $50 to $400 depending on the complexity of the design. Starting in the fall of 1993, ORBCOMM will begin service with a demonstration network consisting of two operating satellites. By the end of 1994, a full operating network of 26 satellites, four Gateway Earth Stations, and a Network Control Center will be in place. The full constellation will provide full coverage of the entire world with greater than 94 percent communications availability for the continental U.S. This paper describes the ORBCOMM system, the technology used in its implementation, and its applications.
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Ground control of space station robotics systems, unmanned space platform servicing, earth-based control of lunar and planetary rover missions, and planetary balloon missions.
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The use of neural operators in a digital twin model of an offshore floating structure holds the potential for a significant shift in the prediction of structural responses and health monitoring, offering valuable real-time control insights. In this work, we investigate the effectiveness of three neural operators, namely the deep operator network (DeepONet), the Fourier neural operator (FNO), and the Wavelet neural operator (WNO), to accurately capture the responses of a floating structure under six different sea state codes (3 − 8) based on the wave characteristics described by the World Meteorological Organization (WMO). To further enhance the accuracy of the vanilla architecture of the neural operators, novel extensions, such as wavelet-DeepONet and self-adaptive WNO, are proposed in this paper. The results demonstrate that these high-precision neural operators can deliver structural responses more efficiently, up to two orders of magnitude faster than a dynamic analysis using conventional numerical solvers. Additionally, compared to gated recurrent units (GRUs), a commonly used recurrent neural network for time-series estimation, neural operators are both more accurate and efficient, especially in situations with limited data availability. Taken together, our study shows that FNO outperforms all other operators for approximating the mapping of one input functional space to the output space as well as for responses that have small bandwidth of the frequency spectrum. Conversely, DeepONet, with historical states, proves most accurate in learning the mapping of multiple input functions to the output space and capturing responses within a broad frequency spectrum.
The increasing demands for electricity and the increase in extreme weather conditions are putting unprecedented pressure on our electric grids. Often, this pressure leads to electrical component failures, which might ignite wildfires. This work develops a novel model to balance the reliability of power network operations and the risk of wildfire ignition by opti- mizing the operational schedule of power transmission networks considering time-varying risk measures that include exogenous and operational factors. Energy storage systems are considered to deliver power during peak wildfire hours and enable temporal load shifting. The problem is formulated as a mixed-integer linear program that maximizes a weighted sum of the served power demand and the reduction in grid-induced wildfire risk. The results demonstrate the ability of the model to significantly reduce wildfire risk without considerable load shedding.
The growing demands for electricity and the increase in extreme weather conditions are putting unprecedented pressure on our electrical grids. Oftentimes, this pressure leads to electrical components failures which might ignite wildfires. This work develops a novel model to balance the reliability of power networks operations and risks of wildfires ignition by optimizing the operational schedule of power transmission networks considering time-varying risk measures that consider exogenous and operational factors. Energy storage systems are considered to deliver power during peak wildfire hours and enable temporal load shifting. The problem is formulated as a mixed-integer linear program that maximizes a weighted sum of the served power demand and the reduction in grid-induced wildfires risk. The results demonstrate the ability of the model to reduce wildfires risks significantly without considerable load shedding.
LunaNet is planned to be the network of networks operated by a set of cooperating organizations to provide interoperable Communications, networking, Position, Navigation, and Timing (CPNT) services to users on and around the Moon based on a framework of mutually agreed-upon standards, protocols, frequency bands and interface requirements. LunaNet follows a service-oriented architecture that is agnostic about the types of organizations that provide services, e.g., government, industry, or academia. LunaNet is open, scalable, resilient, secure, and extensible. To achieve these goals, LunaNet Service Providers (LNSP) must coordinate with each other to define and develop the architecture, to plan initial and evolved capabilities, and to operate their networks. One of the central LunaNet tenets is the use of shared spectrum. For example, the Lunar Augmented Navigation Service (LANS) acts like a Global Navigation Satellite System (GNSS) such as the US Global Positioning System (GPS) or European Galileo but the LNSPs’ contributions to LunaNet must use the same frequency band (2483.5 MHz-2500.0 MHz) and transmit the same waveform synchronized by highly accurate clocks so that Users ‘see’ one virtual network and use the same multilateration algorithm to determine their positions. This necessitates a high degree of spectrum coordination. NASA’s Lunar and Human Spaceflight Spectrum Management Team has been actively supporting development of the LunaNet Interoperability Specification (LNIS), soliciting inputs from spectrum policy and planning experts across NASA, ESA and JAXA. Cislunar spectrum use considerations have been studied and adjudicated within the Space Frequency Coordination Group (SFCG) and inform the ongoing discussion of a lunar communication and navigation architecture within the existing radio regulatory framework of the International Telecommunication Union, leading to the 2027 World Radiocommunication Conference (WRC-27). The frequency plan contained in the publicly released draft of the LunaNet Interoperability Specification reflects the initial phase of exploration (roughly to 2030) defining an optimal set of radio frequencies in appropriately allocated services consistent with WRC-23 decisions for use by known or planned CPNT applications, while striving to maximize coexistence and compatibility amongst cislunar systems and other systems within the near-Earth regime (< 2 million km from Earth). Important considerations include: protection of extremely sensitive receive-only radio astronomy systems on the lunar far side, known as the Shielded Zone of the Moon (SZM); compatibility between Direct with Earth (DWE) communications links and links needed to support relay satellites in lunar orbit with their customer systems on orbit or on the lunar surface; compatibility between multiple lunar surface communications systems and capabilities over varied and challenging terrain and distances; as well as ensuring compatibility and interoperability between navigation systems which either leverage Earth-based or in-situ lunar systems. In addition, the lunar CPNT architecture is envisioned to be the basis – with adjustments – of the future Mars CPNT architecture as we expand into the solar system using Interplanetary Networking (IPN). The second phase of lunar spectrum definition will address planned international capabilities for the next decade that will require action at WRC-27 and beyond. This paper will discuss each of these considerations in more depth and how the current LunaNet frequency plan addresses them.
The Deep operator network (DeepONet) is a powerful yet simple neural operator architecture that utilizes two deep neural networks to learn mappings between infinite-dimensional function spaces. This architecture is highly flexible, allowing the evaluation of the solution field at any location within the desired domain. However, it imposes a strict constraint on the input space, requiring all input functions to be discretized at the same locations; this limits its practical applications. Here, in this work, we introduce a general framework for operator learning from input–output data with arbitrary number and locations of sensors. This begins by introducing a resolution-independent DeepONet (RI-DeepONet), enabling it to handle input functions that are arbitrarily, but sufficiently finely, discretized. To this end, we propose two dictionary learning algorithms to adaptively learn a set of appropriate continuous basis functions, parameterized as implicit neural representations (INRs), from correlated signals defined on arbitrary point cloud data. These basis functions are then used to project arbitrary input function data as a point cloud onto an embedding space (i.e., a vector space of finite dimensions) with dimensionality equal to the dictionary size, which can be directly used by DeepONet without any architectural changes. In particular, we utilize sinusoidal representation networks (SIRENs) as trainable INR basis functions. The introduced dictionary learning algorithms are then used in a similar way to learn an appropriate dictionary of basis functions for the output function data, which defines a new neural operator architecture referred to as the R esolution I ndependent N eural O perator (RINO). In the RINO, the operator learning task simplifies to learning a mapping from the coefficients of input basis functions to the coefficients of output basis functions. We demonstrate the robustness and applicability of RINO in handling arbitrarily (but sufficiently richly) sampled input and output functions during both training and inference through several numerical examples.