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Results for “Deep operator networks”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Self-adaptive weights based on balanced residual decay rate for physics-informed neural networks and deep operator networks

Physics-informed deep learning has emerged as a promising alternative for solving partial differential equations. However, for complex problems, training these networks can still be challenging, often resulting in unsatisfactory accuracy and efficiency. In this work, we demonstrate that the failure of plain physics-informed neural networks arises from the significant discrepancy in the convergence rate of residuals at different training points, where the slowest convergence rate dominates the overall solution convergence. Based on these observations, we propose a pointwise adaptive weighting method that balances the residual decay rate across different training points. The performance of our proposed adaptive weighting method is compared with current state-of-the-art adaptive weighting methods on benchmark problems for both physics-informed neural networks and physics-informed deep operator networks. In conclusion, through extensive numerical results we demonstrate that our proposed approach of balanced residual decay rates offers several advantages, including bounded weights, high prediction accuracy, fast convergence rate, low training uncertainty, low computational cost, and ease of hyperparameter tuning.

Balanced convergence rate↗
DOE OSTI2025

Stacked networks improve physics-informed training: Applications to neural networks and deep operator networks

Physics-informed neural networks and operator networks have shown promise for effectively solving equations modeling physical systems. However, these networks can happen to be difficult or impossible to train accurately. Here, we present a novel multifidelity framework for stacking physics-informed neural networks and operator networks that facilitates training. We successively build a chain of networks, where the output at one step can act as a low-fidelity input for training a longer chain, gradually increasing the expressivity of the learnt model. The equations imposed at each step of the iterative process can be the same or different (akin to simulated annealing). The iterative (stacking) nature of the proposed method allows us to learn progressively features of a solution which could have been hard to learn directly. Through benchmark problems including a nonlinear pendulum, the wave equation, and the viscous Burgers equation, we show how stacking can be used to improve the accuracy and reduce the required size of physics-informed neural networks and operator networks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Neural Scaling Laws of Deep ReLU and Deep Operator Network: A Theoretical Study

Neural scaling laws play a pivotal role in the performance of deep neural networks and have been observed in a wide range of tasks. However, a complete theoretical framework for understanding these scaling laws remains underdeveloped. In this paper, we explore the neural scaling laws for deep operator networks, which involve learning mappings between function spaces, with a focus on the Chen and Chen style architecture. These approaches, which include the popular Deep Operator Network (DeepONet), approximate the output functions using a linear combination of learnable basis functions and coefficients that depend on the input functions. We establish a theoretical framework to quantify the neural scaling laws by analyzing its approximation and generalization errors. We articulate the relationship between the approximation and generalization errors of deep operator networks and key factors such as network model size and training data size. Moreover, we address cases where input functions exhibit low-dimensional structures, allowing us to derive tighter error bounds. These results also hold for deep ReLU networks and other similar structures. Our results offer a partial explanation of the neural scaling laws in operator learning and provide a theoretical foundation for their applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Surrogate Modeling of Landau Damping with Deep Operator Networks

Kinetic simulations excel at capturing microscale plasma physics phenomena with high accuracy, but their computational demands make them impractical for modeling large-scale space and astrophysical systems. In this context, we build a surrogate model, using Deep Operator Networks (DeepONets), based upon the Vlasov–Poisson simulation data to model the dynamical evolution of plasmas, focusing on the Landau damping process—a fundamental kinetic phenomenon in space and astrophysical plasmas. The trained DeepONets are able to capture the evolution of electric field energy in both linear and nonlinear regimes under various conditions. Extensive validation highlights DeepONets’ robust performance in reproducing complex plasma behaviors with high accuracy, paving the way for large-scale modeling of space and astrophysical plasmas.

plasma astrophysics↗
DOE OSTI2025

Efficient Training of Deep Neural Operator Networks via Randomized Sampling

Neural operators (NOs) employ deep neural networks to learn the mappings between infinitedimensional function spaces. Deep operator network (DeepONet), a popular NO architecture, has demonstrated success in the real-time prediction of complex dynamics across various scientific and engineering applications. In this work, we introduce a random sampling technique to be adopted during the training of DeepONet, aimed at improving the generalization ability of the model, while significantly reducing the computational time. The proposed approach targets the trunk network of the DeepONet model that outputs the basis functions corresponding to the spatiotemporal locations of the bounded domain on which the physical system is defined. While constructing the loss function, DeepONet training traditionally considers a uniform grid of spatiotemporal points at which all the output functions are evaluated for each iteration. This approach leads to a larger batch size, resulting in poor generalization and increased memory demands, due to the limitations of the stochastic gradient descent (SGD) optimizer. The proposed random sampling over the inputs of the trunk net mitigates these challenges, improving generalization and reducing the memory requirements during training, resulting in significant computational gains. We validate our hypothesis through three benchmark examples, demonstrating substantial reductions in training time while achieving comparable or lower overall test errors relative to the traditional training approach. Our results indicate that incorporating randomization in the trunk network inputs during training enhances the efficiency and robustness of DeepONet, offering a promising avenue for improving the framework’s performance in modeling complex physical systems.

Karumuri, Sharmila [Department of Civil & Systems ↗
NASA NTRS1982

NASA Deep Space Network Operations Scheduling

The functioning of the Deep Space Network Operations Scheduling, Jet Propulsion Laboratory, CA is reviewed. The primary objectives of the Operations Scheduling are: to schedule the worldwide global allocation of ground communications, tracking facilities, and equipment; and to provide deep space telecommunications for command, tracking, telemetry, and control in support of flight mission operations and tests. Elements of the earth set are Deep Space Stations (DSS) which provide the telecommunications link between the earth and spacecraft; NASA Communications Network; Network Data Processing Area; Network Operations Control Area which provides operational direction to the DSS; Mission Control and Computing systems; and Mission Support areas which provide flight control of the spacecraft. Elements of the space set include mission priorities and requirements which determine the spacecraft queue for allocating network resources. Scheduling is discussed in terms of long-range (3 years), mid-range (8 weeks), and short-range (2 weeks).

Enari, D. M.↗
NASA NTRS1982

NASA Deep Space Network operations organization

The organization of the NASA Deep Space Network (DSN), a network of tracking station control and data handling facilities, is briefly reviewed. It has been designed, constructed, maintained, and operated by the Jet Propulsion Laboratory at California Institute of Technology in support of NASA lunar and interplanetary flight programs. Some important technological and organizational advances made by DSN since the early development of spacecraft tracking in the 1950s are considered.

Chafin, R. L.↗
NASA NTRS1982

NASA Deep Space Network operating control

The primary function of the Deep Space Network (DSN) is to provide effective and reliable tracking and data acquisition for planetary and interplanetary space flight missions. This involves providing data to flight project mission operations, accepting commands from mission operations and transmitting the commands to stations and spacecraft, and providing a record of telemetry and command data to mission operations. Also included are network performance monitoring, the generation of predictions for antenna pointing and signal acquisition, network scheduling, and network validation tests. Descriptions are given of the three facilities and six systems of the DSN. Also described are interfaces, automation and standardized procedures, and discrepancy reporting. It is pointed out that the greatest challenge facing the DSN is the implementation of NASA's Network Consolidation Program, which is scheduled to be completed in 1986. The objectives of this program are enumerated.

Weisman, W. D.↗
NASA NTRS2002

Statistical porcess control in Deep Space Network operation

This report describes how the Deep Space Mission System (DSMS) Operations Program Office at the Jet Propulsion Laboratory's (EL) uses Statistical Process Control (SPC) to monitor performance and evaluate initiatives for improving processes on the National Aeronautics and Space Administration's (NASA) Deep Space Network (DSN).

Deep Space Network operations statistical process ↗
NASA NTRS1982

NASA deep space network operations planning and preparation

The responsibilities and structural organization of the Operations Planning Group of NASA Deep Space Network (DSN) Operations are outlined. The Operations Planning group establishes an early interface with a user's planning organization to educate the user on DSN capabilities and limitations for deep space tracking support. A team of one or two individuals works through all phases of the spacecraft launch and also provides planning and preparation for specific events such as planetary encounters. Coordinating interface is also provided for nonflight projects such as radio astronomy and VLBI experiments. The group is divided into a Long Range Support Planning element and a Near Term Operations Coordination element.

Jensen, W. N.↗
NASA NTRSDate not supplied

DeepONet-Assisted Optimization of Surface Topography for Transition Delay in A Mach 4.5 Boundary Layer

We use deep learning, an ensemble variationaltechnique (EnVar), and direct numerical simulations(DNS) to design an optimal topography for a two-dimensional roughness element that delays the on-set of laminar-turbulent transition in a Mach 4.5 flat-plate boundary layer. Deep operator networks (Deep-ONets), which have the known ability to learn com-plex nonlinear operators within dynamical systems,are used for machine learning. For the baseline config-uration of a smooth flat plate, the second-mode wavesat the DNS inflow cause a quick nonlinear breakdownof the high-speed boundary layer within the computa-tional domain. Results reported in the present studyvalidate the ability of DeepONets to model the tran-sition delay via a given topography of the roughnesselement. The computing cost to optimize the rough-ness element for minimal skin-friction drag is substan-tially lowered by the DeepONets-based reduced-ordermodel. In comparison to the baseline method of EnVaroptimization based on DNS alone, the DeepONets-based EnVar optimizer is able to delay transition pastthe outflow boundary of the computational domainwhile utilizing almost 5–6 times fewer DNS.

Machine Learning↗
NASA NTRS1995

Reengineering Deep Space Network Operations

Eight additional antennas are being added to NASA's Deep Space Network (DSN) at the same time that the budget is being decreased. Therefore, the DSN is reengineering its processes to operate more efficiently.

reengineering↗
NASA NTRS1993

Toward an embedded training tool for Deep Space Network operations

There are three issues to consider when building an embedded training system for a task domain involving the operation of complex equipment: (1) how skill is acquired in the task domain; (2) how the training system should be designed to assist in the acquisition of the skill, and more specifically, how an intelligent tutor could aid in learning; and (3) whether it is feasible to incorporate the resulting training system into the operational environment. This paper describes how these issues have been addressed in a prototype training system that was developed for operations in NASA's Deep Space Network (DSN). The first two issues were addressed by building an executable cognitive model of problem solving and skill acquisition of the task domain and then using the model to design an intelligent tutor. The cognitive model was developed in Soar for the DSN's Link Monitor and Control (LMC) system; it led to several insights about learning in the task domain that were used to design an intelligent tutor called REACT that implements a method called 'impasse-driven tutoring'. REACT is one component of the LMC training system, which also includes a communications link simulator and a graphical user interface. A pilot study of the LMC training system indicates that REACT shows promise as an effective way for helping operators to quickly acquire expert skills.

Hill, Randall W., Jr.↗
NASA NTRS1993

Toward an Embedded Training Tool for Deep Space Network Operations

There are three issues to consider when building an embedded training system for a task domain involving the operation of complex equipment: (1) how skill is acquired in the task domain; (2) how the training system should be designed to assist in the acquisition of the skill, and more specifically, how an intelligent tutor could aid in learning; and (3) whether it is feasible to incorporate the resulting training system into the operational environment. This paper describes how these issues have been addressed in a prototype training system that was developed for operations in NASA's Deep Space Network (DSN). The first two issues were addressed by building an executable cognitive model of problem solving and skill acquisition of the task domain and then using the model to design an intelligent tutor.

Johnson, W. Lewis↗
DOE OSTI2025

A resolution independent neural operator

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.

Deep operator network (DeepONet)↗
DOE OSTI2025

Neural operators for stochastic modeling of nonlinear structural system response to natural hazards

Traditionally, neural networks have been employed to learn the mapping between finite-dimensional Euclidean spaces. However, recent research has opened up new horizons, focusing on the utilization of deep neural networks to learn operators capable of mapping infinite-dimensional function spaces. Here, in this work, we employ two state-of-the-art neural operators, the deep operator network (DeepONet) and the Fourier neural operator (FNO) for the prediction of the nonlinear time history response of structural systems exposed to natural hazards, such as earthquakes and windstorms. Specifically, we propose two architectures, a self-adaptive FNO and a fast Fourier transform-based DeepONet (DeepFNOnet), where we employ a FNO beyond the DeepONet to learn the discrepancy between the ground truth and the solution predicted by the DeepONet. To demonstrate the efficiency and applicability of the architectures, two problems are considered. In the first, we use the proposed model to predict the seismic nonlinear dynamic response of a six-story shear building subject to stochastic ground motions. In the second problem, we employ the operators to predict the wind-induced nonlinear dynamic response of a high-rise building while explicitly accounting for the stochastic nature of the wind excitation. In both cases, the trained metamodels achieve high accuracy while being orders of magnitude faster than their corresponding high-fidelity models.

DeepONet↗