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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Fed-DeepONet: Stochastic Gradient-Based Federated Training of Deep Operator Networks

The Deep Operator Network (DeepONet) framework is a different class of neural network architecture that one trains to learn nonlinear operators, i.e., mappings between infinite-dimensional spaces. Traditionally, DeepONets are trained using a centralized strategy that requires transferring the training data to a centralized location. Such a strategy, however, limits our ability to secure data privacy or use high-performance distributed/parallel computing platforms. To alleviate such limitations, in this paper, we study the federated training of DeepONets for the first time. That is, we develop a framework, which we refer to as Fed-DeepONet, that allows multiple clients to train DeepONets collaboratively under the coordination of a centralized server. To achieve Fed-DeepONets, we propose an efficient stochastic gradient-based algorithm that enables the distributed optimization of the DeepONet parameters by averaging first-order estimates of the DeepONet loss gradient. Then, to accelerate the training convergence of Fed-DeepONets, we propose a moment-enhanced (i.e., adaptive) stochastic gradient-based strategy. Finally, we verify the performance of Fed-DeepONet by learning, for different configurations of the number of clients and fractions of available clients, (i) the solution operator of a gravity pendulum and (ii) the dynamic response of a parametric library of pendulums.

Moya, Christian↗
DOE OSTI2022

Grassmannian Diffusion Maps--Based Dimension Reduction and Classification for High-Dimensional Data

This work introduces the Grassmannian diffusion maps (GDMaps), a novel nonlinear dimensionality reduction technique that defines the affinity between points through their representation as low-dimensional subspaces corresponding to points on the Grassmann manifold. Here, the method is designed for applications, such as image recognition and data-based classification of constrained high-dimensional data where each data point itself is a high-dimensional object (i.e., a large matrix) that can be compactly represented in a lower-dimensional subspace. The GDMaps is composed of two stages. The first is a pointwise linear dimensionality reduction wherein each high-dimensional object is mapped onto the Grassmann manifold representing the low-dimensional subspace on which it resides. The second stage is a multipoint nonlinear kernel-based dimension reduction using diffusion maps to identify the subspace structure of the points on the Grassmann manifold. To this end, an appropriate Grassmannian kernel is used to construct the transition matrix of a random walk on a graph connecting points on the Grassmann manifold. Spectral analysis of the transition matrix yields low-dimensional Grassmannian diffusion coordinates embedding the data into a low-dimensional reproducing kernel Hilbert space. Further, a novel data classification/recognition technique is developed based on the construction of an overcomplete dictionary of reduced dimension whose atoms are given by the Grassmannian diffusion coordinates. Three examples are considered. First, a "toy" example shows that the GDMaps can identify an appropriate parametrization of structured points on the unit sphere. The second example demonstrates the ability of the GDMaps to revealing the intrinsic subspace structure of high-dimensional random field data. In the last ex- ample, a face recognition problem is solved considering face images subject to varying illumination conditions, changes in face expressions, and occurrence of occlusions. The technique presented high recognition rates (i.e., 95% in the best case) using a fraction of the data required by conventional methods.

42 ENGINEERING↗
DOE OSTI2022

Learning high-dimensional parametric maps via reduced basis adaptive residual networks

We propose a scalable framework for the learning of high-dimensional parametric maps via adaptively constructed residual network (ResNet) maps between reduced bases of the inputs and outputs. When just few training data are available, it is beneficial to have a compact parametrization in order to ameliorate the ill-posedness of the neural network training problem. By linearly restricting high-dimensional maps to informed reduced bases of the inputs, one can compress high-dimensional maps in a constructive way that can be used to detect appropriate basis ranks, equipped with rigorous error estimates. A scalable neural network learning framework is thus to learn the nonlinear compressed reduced basis mapping. Unlike the reduced basis construction, however, neural network constructions are not guaranteed to reduce errors by adding representation power, making it difficult to achieve good practical performance. Inspired by recent approximation theory that connects ResNets to sequential minimizing flows, we present an adaptive ResNet construction algorithm. This algorithm allows for depth-wise enrichment of the neural network approximation, in a manner that can achieve good practical performance by first training a shallow network and then adapting. We prove universal approximation of the associated neural network class for $L^2_v$ functions on compact sets. Our overall framework allows for constructive means to detect appropriate breadth and depth, and related compact parametrizations of neural networks, significantly reducing the need for architectural hyperparameter tuning. Numerical experiments for parametric PDE problems and a 3D CFD wing design optimization parametric map demonstrate that the proposed methodology can achieve remarkably high accuracy for limited training data, and outperformed other neural network strategies we compared against.

42 ENGINEERING↗
DOE OSTI2025

Improved high-resolution mapping of phase-matching conditions in second-order nonlinear crystals via imaging

Large-aperture nonlinear crystals for frequency conversion and parametric amplification exhibit spatial variations in phase-matching conditions, which affect the performance of high-power laser systems. We demonstrate significant improvements in speed and resolution to a technique that spatially maps these phase-matching conditions using imaging of the beam resulting from detuned second-harmonic generation. The phase-matching conditions at the pyramidal sector boundary of partially deuterated potassium dihydrogen phosphate (DKDP) are mapped with sub-0.1-mm resolution. We examine the effect of further increases in scan rate on the precision of the technique and demonstrate a scan rate of 0.8 cm 2 per minute at the aforementioned resolution.

Wampler, R. [Univ. of Rochester, NY (United States↗
DOE OSTI2023

Influence of doping and thickness on domain avalanches in lead zirconate titanate thin films

In undoped lead zirconate titanate films of 1–2 μm thick, domain walls move in clusters with a correlation length of approximately 0.5–2 μm. Band excitation piezoresponse force microscopy mapping of the piezoelectric nonlinearity revealed that niobium (Nb) doping increases the average concentration or mobility of domain walls without changing the cluster area of correlated domain wall motion. In comparison, manganese (Mn) doping reduces the contribution of mobile domain walls to the dielectric and piezoelectric responses without changing the cluster area for correlated motion. In both Nb and Mn doped films, the cluster area increases and the cluster density drops as the film thickness increases from 250 to 1250 nm. This is evident in spatial maps generated from the analysis of irreversible to reversible ratios of the Rayleigh coefficients.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Inverse Design of Photonic Surfaces via High throughput Femtosecond Laser Processing and Tandem Neural Networks

Abstract This work demonstrates a method to design photonic surfaces by combining femtosecond laser processing with the inverse design capabilities of tandem neural networks that directly link laser fabrication parameters to their resulting textured substrate optical properties. High throughput fabrication and characterization platforms are developed that generate a dataset comprising 35280 unique microtextured surfaces on stainless steel with corresponding measured spectral emissivities. The trained model utilizes the nonlinear one‐to‐many mapping between spectral emissivity and laser parameters. Consequently, it generates predominantly novel designs, which reproduce the full range of spectral emissivities (average root‐mean‐squared‐error < 2.5%) using only a compact region of laser parameter space 25 times smaller than what is represented in the training data. Finally, the inverse design model is experimentally validated on a thermophotovoltaic emitter design application. By synergizing laser‐matter interactions with neural network capabilities, the approach offers insights into accelerating the discovery of photonic surfaces, advancing energy harvesting technologies.

36 MATERIALS SCIENCE↗
DOE OSTI2020

The extended auxiliary equation mapping method to determine novel exact solitary wave solutions of the nonlinear fractional PDEs

Abstract In this paper, some new nonlinear fractional partial differential equations (PDEs) have been considered.Three models are including the space-time fractional-order Boussinesq equation, space-time (2 + 1)-dimensional breaking soliton equations, and space-time fractional-order SRLW equation describe the behavior of these equations in the diverse applications. Meanwhile, the fractional derivatives in the sense of β -derivative are defined. Some fractional PDEs will convert to the considered ordinary differential equations by the help of transformation of β -derivative. These equations are analyzed utilizing an integration scheme, namely, the extended auxiliary equation mapping method. The different kinds of traveling wave solutions, solitary, topological, dark soliton, periodic, kink, and rational, fall out as a by-product of this scheme. Finally, the existence of the solutions for the constraint conditions is also shown. The outcome indicates that some fractional PDEs are used as a growing finding in the engineering sciences, mathematical physics, and so forth.

Engineering↗
DOE OSTI2026

Extremized nonlinear and linearized responses in soft metamaterials enabled by gradient-based design and grayscale digital light processing

In this study, we develop a gradient-based design approach that exploits grayscale digital light processing (DLP) 3D printing for extremizing the nonlinear and linearized response of soft metamaterials — materials that harness engineered geometric instabilities to undergo large and programmable changes in configuration. Grayscale DLP approaches modulate local mechanical properties at the pixel scale by tuning the light intensity within a single grayscale image, unlocking an exceptionally large design space. To effectively navigate this space, we develop smooth mappings between local light intensity values and global quantities of interest that characterize the behavior of soft metamaterials. Enabling these smooth mappings are robust and differentiable nonlinear finite element simulations powered by a trust region solver. A PDE-constrained optimization problem is then solved to invert these mappings and produce light intensity distributions that endow the printed part with varying stiffness and flexibility in distinctive regions. It is shown that optimizing the distribution of soft and stiff phases throughout a metamaterial structure results in markedly different buckling and self-contact configurations to drive extremized nonlinear compression and linearized vibration responses. Optimized light intensity distributions are translated to grayscale images and directly used to print soft metamaterial samples, showing remarkable agreement between the buckling and self-contact response in simulated and measured deformed configurations.

Additive manufacturing↗
DOE OSTI2022

Manifold Learning-Based Polynomial Chaos Expansions for High-Dimensional Surrogate Models

In this work we introduce a manifold learning-based method for uncertainty quantification (UQ) in systems describing complex spatiotemporal processes. Our first objective is to identify the embedding of a set of high-dimensional data representing quantities of interest of the computational or analytical model. For this purpose, we employ Grassmannian diffusion maps, a two-step nonlinear dimension reduction technique which allows us to reduce the dimensionality of the data and identify meaningful geometric descriptions in a parsimonious and inexpensive manner. Polynomial chaos expansion is then used to construct a mapping between the stochastic input parameters and the diffusion coordinates of the reduced space. An adaptive clustering technique is proposed to identify an optimal number of clusters of points in the latent space. The similarity of points allows us to construct a number of geometric harmonic emulators which are finally utilized as a set of inexpensive pretrained models to perform an inverse map of realizations of latent features to the ambient space and thus perform accurate out-of-sample predictions. Thus, the proposed method acts as an encoder-decoder system which is able to automatically handle very high-dimensional data while simultaneously operating successfully in the small-data regime. The method is demonstrated on two benchmark problems and on a system of advection-diffusion-reaction equations which model a first-order chemical reaction between two species. In all test cases, the proposed method is able to achieve highly accurate approximations which ultimately lead to the significant acceleration of UQ tasks.

42 ENGINEERING↗
DOE OSTI2026

MAPS: the MFEM Anisotropic Plasma Solver

Simulating magnetically confined fusion plasmas presents a uniquely challenging problem due to the nonlinear anisotropic heat conduction. We introduce the MAPS (MFEM Anisotropic Plasma Solver) tool, which uses a high-order finite element method to compute transport solutions on unstructured meshes. We show results for a set of three 2-D verification tests, two of which demonstrate the expected convergence properties for various mesh resolutions and polynomial degrees. We then discuss the convergence rate for the third test.

Barnett, Rhea [ORNL] (ORCID:0000000317527979)↗
DOE OSTI2024

Circularly Polarized Attosecond Pulses Enabled by an Azimuthal Phase and Polarization Grating

High-harmonic generation (HHG) is an extreme nonlinear optical process that can map the properties of an infrared driving laser beam onto short wavelength attosecond pulse trains. However, current techniques for generating circularly polarized high harmonics for probing magnetic materials and chiral systems have limitations: two-color collinear counter-rotating driving lasers result in a low cutoff photon energy, while single-color non-collinear counter-rotating schemes suffer from low conversion efficiency. In this work, we generate circularly polarized attosecond pulse trains by using a structured laser driver which has a rotating polarization and phase grating along the azimuthal coordinate. Furthermore, our experimental and numerical results demonstrate the production of left and right circularly polarized harmonics, which naturally separate upon propagation. Our approach uses a single laser color in a collinear geometry, that can be scaled for high efficiency. Simulations show this scheme can extend into the soft x-ray region when driven by mid-infrared driving lasers, while preserving the same high phase-matching cutoff photon energy as for linearly-polarized high harmonics.

attosecond science↗
DOE OSTI2022

Learning Distributed Geometric Koopman Operator for Sparse Networked Dynamical Systems

Koopman operator theory provides an alternative to study nonlinear networked dynamical systems by mapping the state space to an abstract higher dimensional space where the system evolution is linear. Recent works show the application of graph neural networks (GNNs) to learn state to object-centric embeddings and achieve centralized block-wise computation of Koopman operator (KO) under additional assumptions on the underlying agents properties and constraints on the KO structure. However, the computational complexity of learning the Koopman increases exponentially for networked systems where the number of possible system states grows in a combinatorial fashion with the number of nodes. The learning challenge is further amplified for sparse networks by two factors: 1) sample sparsity for learning the Koopman operator in the non-linear space, and 2) the divergence in the dynamics of individual nodes or from one subgraph to another. Our work aims to address these challenge by formulating the representation learning of networked dynamical systems into a multi-agent paradigm and learning the Koopman operator in a distributive manner. The computational as well as performance advantages of distributed Koopman is predominant for sparse networks whereas for fully connected networks, it is shown to coincide with the centralized one. The empirical study on rope system, network of oscillators and a synthetic power system show comparable and superior performance along with computational benefits with the state-of-the-art methods.

Mukherjee, Sayak↗
DOE OSTI2024

A Bayesian Multi-fidelity Neural Network to Predict Nonlinear Frequency Backbone Curves

The use of structural mechanics models during the design process often leads to the development of models of varying fidelity. Often low-fidelity models are efficient to simulate but lack accuracy, while the high-fidelity counterparts are accurate with less efficiency. Here, this paper presents a multi-fidelity surrogate modeling approach that combines the accuracy of a high-fidelity finite element model with the efficiency of a low-fidelity model to train an even faster surrogate model that parameterizes the design space of interest. The objective of these models is to predict the nonlinear frequency backbone curves of the Tribomechadynamics Research Challenge benchmark structure which exhibits simultaneous nonlinearities from frictional contact and geometric nonlinearity. The surrogate model consists of an ensemble of neural networks that learn the mapping between low and high-fidelity data through nonlinear transformations. Bayesian neural networks are used to assess the surrogate model's uncertainty. Once trained, the multi-fidelity neural network is used to perform sensitivity analysis to assess the influence of the design parameters on the predicted backbone curves. Additionally, Bayesian calibration is performed to update the input parameter distributions to correlate the model parameters to the collection of experimentally measured backbone curves.

42 ENGINEERING↗
DOE OSTI2025

Online regularization of Poincaré map of storage rings with Shannon entropy

A measurable chaos indicator is used as the online optimization objective in tuning a complicated nonlinear system—the National Synchrotron Light Source-II storage ring. Through analyzing the Shannon entropy in measured Poincaré maps, not only can the commonly used nonlinear characterizations be extracted, but more importantly, the chaos can be quantified and then used for an online regularization of these maps. The method itself is general and applicable to other tunable nonlinear systems as well. Published by the American Physical Society 2025

36 MATERIALS SCIENCE↗
DOE OSTI2021

Learning Optimal Power Flow Solutions using Linearized Models in Power Distribution Systems

Solving nonlinear optimal power flow (OPF) problem is computationally expensive, and poses scalability challenges for power distribution networks. An alternative to solving the original nonlinear OPF is the linear approximated OPF models. Although, these linear approximated OPF models are fast, the resulting solutions may result in significant optimality gap. Lately, the application of machine learning (ML) methods in successfully solving the nonlinear OPF has been reported. These methods learn and estimate the nonlinear control policies using a purely data-driven approach. In this paper, we propose an approach to complements the ML based approach to solving OPF using solutions from known linearized OPF model. Specifically, we use supervised learning to map the solutions of linear OPF to nonlinear control variables. Unlike, the traditional ML based methods for OPF that approximate the full distribution feeder model using function approximation, our approach uses a two-node approximation of radial networks. The proposed approach is validated using IEEE 123 bus test system for OPF solutions obtained using the nonlinear OPF models.

optimal power flow, power distribution systems, su↗
DOE OSTI2023

Trust-Enhancing Probabilistic Transfer Learning for Sparse and Noisy Data Environments

There is an increasing aspiration to utilize machine learning (ML) for various tasks of relevance to national security. ML models have thus far been mostly applied to tasks and domains that, while impactful, have sufficient volume of data. For predictive tasks of national security relevance, ML models of great capacity (ability to approximate nonlinear trends in input-output maps) are often needed to capture the complex underlying physics. However, scientific problems of relevance to national security are often accompanied by various sources of sparse and/or incomplete data, including experiments and simulations, across different regimes of operation, of varying degrees of fidelity, and include noise with different characteristics and/or intensity. State-of-the-art ML models, despite exhibiting superior performance on the task and domain they were trained on, may suffer detrimental loss in performance in such sparse data environments. This report summarizes the results of the Laboratory Directed Research and Development project entitled Trust-Enhancing Probabilistic Transfer Learning for Sparse and Noisy Data Environments. The objective of the project was to develop a new transfer learning (TL) framework that aims to adaptively blend the data across different sources in tackling one task of interest, resulting in enhanced trustworthiness of ML models for mission- and safety-critical systems. The proposed framework determines when it is worth applying TL and how much knowledge is to be transferred, despite uncontrollable uncertainties. The framework accomplishes this by leveraging concepts and techniques from the fields of Bayesian inverse modeling and uncertainty quantification, relying on strong mathematical foundations of probability and measure theories to devise new uncertainty-aware TL workflows.

97 MATHEMATICS AND COMPUTING↗