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DOE OSTI2025

Multi-head physics-informed neural networks for learning functional priors and uncertainty quantification

In numerous applications, the integration of prior knowledge and historical information is essential, particularly for tasks requiring the solution of ordinary or partial differential equations (ODEs/PDEs) in data-sparse or noisy environments. For instance, achieving accurate solutions to time-dependent PDEs with limited initial condition measurements necessitates an effective strategy for embedding prior knowledge. Hard-parameter sharing architectures in neural networks (NNs) have demonstrated success in both traditional and scientific machine learning domains, facilitating the learning of informative representations. Here, in this study, we introduce a novel, yet efficient, method to enhance physics-informed neural networks (PINNs) by incorporating a multi-head structure that enables the learning of functional priors from both empirical data and governing physical laws. This prior information can then be used to address data sparsity and high-level noise in solving ODE/PDE problems with uncertainty quantification (UQ). The approach, termed Multi-Head PINN (MH-PINN), consists of a shared body NN and multiple head NNs, each corresponding to an individual PINN instance. Our framework for functional prior learning is carried out in two stages: (1) training the MH-PINNs to develop a shared body NN alongside multiple head NNs, and (2) employing these trained head NNs to estimate a prior distribution through a normalizing flow-based density estimator. The learned functional prior can then be applied as a regularization mechanism in deterministic contexts or as an informative prior within a Bayesian inference framework, aiding in the resolution of subsequent ODE/PDE tasks. We evaluate the efficacy of MH-PINNs across five benchmark problems, including a high-dimensional parametric PDE, all characterized by data sparsity or substantial noise levels. Our findings reveal that MH-PINNs deliver accurate solutions and robust UQ, demonstrating adaptability across a range of complex and challenging scenarios.

Bayesian inference↗

DOE OSTI2024

Polynomial chaos expansions on principal geodesic Grassmannian submanifolds for surrogate modeling and uncertainty quantification

In this work we introduce a manifold learning-based surrogate modeling framework for uncertainty quantification in high-dimensional stochastic systems. Our first goal is to perform data mining on the available simulation data to identify a set of low-dimensional (latent) descriptors that efficiently parameterize the response of the high-dimensional computational model. To this end, we employ Principal Geodesic Analysis on the Grassmann manifold of the response to identify a set of disjoint principal geodesic submanifolds, of possibly different dimension, that captures the variation in the data. Since operations on the Grassmann require the data to be concentrated, we propose an adaptive algorithm based on Riemannian K-means and the minimization of the sample Fréchet variance on the Grassmann manifold to identify “local” principal geodesic submanifolds that represent different system behavior across the parameter space. Polynomial chaos expansion is then used to construct a mapping between the random input parameters and the projection of the response on these local principal geodesic submanifolds. Here, the method is demonstrated on four test cases, a toy-example that involves points on a hypersphere, a Lotka-Volterra dynamical system, a continuous-flow stirred-tank chemical reactor system, and a two-dimensional Rayleigh-Bénard convection problem.

42 ENGINEERING↗

DOE OSTI2024

A high-throughput and data-driven computational framework for novel quantum materials

Two-dimensional layered materials, such as transition metal dichalcogenides (TMDs), possess an intrinsic van der Waals gap at the layer interface, allowing for remarkable tunability of the optoelectronic features via external intercalation of foreign guests such as atoms, ions, or molecules. Herein, we introduce a high-throughput, data-driven computational framework for the design of novel quantum materials derived from intercalating planar conjugated organic molecules into bilayer transition metal dichalcogenides and dioxides. By combining first-principles methods, material informatics, and machine learning, we characterize the energetic and mechanical stability of this new class of materials and identify the fifty (50) most stable hybrid materials from a vast configurational space comprising ∼105 materials, employing intercalation energy as the screening criterion.

Kastuar, Srihari M. (ORCID:0000000279001561)↗

NASA NTRS2013

Semi-Supervised Eigenbasis Novelty Detection

Recent discoveries in high-time-resolution radio astronomy data have focused attention on a new class of events. Fast transients are rare pulses of radio frequency energy lasting from microseconds to seconds that might be produced by a variety of exotic astrophysical phenomena. For example, X-ray bursts, neutron stars, and active galactic nuclei are all possible sources of short-duration, transient radio signals. It is difficult to anticipate where such signals might appear, and they are most commonly discovered through analysis of high-time- resolution data that had been collected for other purposes. Transients are often faint and difficult to detect, so improved detection algorithms can directly benefit the science yield of all such commensal monitoring. A new detection algorithm learns a low-dimensional linear manifold for describing the normal data. High reconstruction error indicates a novel signal that does not match the patterns of normal data. One unsupervised portion of the manifold model adapts its representation in response to recent data. A second supervised portion of the model is made of a basis trained in advance using labeled examples of RFI; this prevents false positives due to these events. For a linear model, an orthonormalization operation is used to combine these bases prior to the anomaly detection decision. Another novel aspect of the approach lies in combining basis vectors learned in an unsupervised, online fashion from the data stream with supervised basis vectors learned in advance from known examples of false alarms. Adaptive, data-driven detection is achieved that is also informed by existing domain knowledge about signals that may be statistically anomalous, but are not interesting and should therefore be ignored. The method was evaluated using data from the Parkes Multibeam Survey. This data set was originally collected to search for pulsars, which are astronomical sources that emit radio pulses at regular periods. However, several non-pulsar anomalies have recently been discovered in this dataset, making it a compelling test case. By explicitly filtering known false alarm patterns, the approach yields significantly better performance than current transient detection methods.

Wagstaff, Kiri L.↗

NASA NTRS2008

Variations of Strahl Properties with Fast and Slow Solar Wind

The interplanetary solar wind electron velocity distribution function generally shows three different populations. Two of the components, the core and halo, have been the most intensively analyzed and modeled populations using different theoretical models. The third component, the strahl, is usually seen at higher energies, is confined in pitch-angle, is highly field-aligned and skew. This population has been more difficult to identify and to model in the solar wind. In this work we make use of the high angular, energy and time resolution and three-dimensional data of the Cluster/PEACE electron spectrometer to identify and analyze this component in the ambient solar wind during high and slow speed solar wind. The moment density and fluid velocity have been computed by a semi-numerical integration method. The variations of solar wind density and drift velocity with the general build solar wind speed could provide some insight into the source, origin, and evolution of the strahl.

Figueroa-Vinas, Adolfo↗

DOE OSTI2025

Low‐dimensional manifold learning for uncertainty quantification in complex multi‐scale stochastic systems

Broadly speaking, the goals of the project are to develop techniques to use manifold learning to develop reduced‐order and surrogate models for "hyper‐reduction" of very high‐dimensional complex multi‐scale systems. This is being achieved by employing a newly proposed form of manifold projection and learning that leverages recent advancements in computational geometry and data‐driven modeling. In particular, we are applying a manifold projection technique to project the solutions of very high‐dimensional systems onto the so‐called Grassmannmanifold, a Reimannian manifold comprised of orthonormal matrices. We then apply data‐driven machine learning techniques to classify the solutions on the manifold (e.g. clustering techniques) according to their proximity on the manifold and leverage a further nonlinear dimension reduction to organize the structured data on the manifold. Finally, we are developing novel techniques that enable us to directly interpolate the hyper‐reduced data such that we can predict the solution of the complex, high‐ dimensional system without need to call the full expensive computational model. Given their adherence to the underlying structure of the solution of the physical system, it is expected that these approximate solutions will be sufficiently constrained so as to (approximately) adhere to physical principles.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2003

Method and Apparatus for Virtual Interactive Medical Imaging by Multiple Remotely-Located Users

A virtual interactive imaging system allows the displaying of high-resolution, three-dimensional images of medical data to a user and allows the user to manipulate the images, including rotation of images in any of various axes. The system includes a mesh component that generates a mesh to represent a surface of an anatomical object, based on a set of data of the object, such as from a CT or MRI scan or the like. The mesh is generated so as to avoid tears, or holes, in the mesh, providing very high-quality representations of topographical features of the object, particularly at high- resolution. The system further includes a virtual surgical cutting tool that enables the user to simulate the removal of a piece or layer of a displayed object, such as a piece of skin or bone, view the interior of the object, manipulate the removed piece, and reattach the removed piece if desired. The system further includes a virtual collaborative clinic component, which allows the users of multiple, remotely-located computer systems to collaboratively and simultaneously view and manipulate the high-resolution, three-dimensional images of the object in real-time.

Ross, Muriel D.↗

DOE OSTI2024

Online randomized interpolative decomposition with a posteriori error estimator for temporal PDE data reduction

Traditional low-rank approximation is a powerful tool for compressing large data matrices that arise in simulations of partial differential equations (PDEs), but suffers from high computational cost and requires several passes over the PDE data. The compressed data may also lack interpretability thus making it difficult to identify feature patterns from the original data. Here, to address these issues, we present an online randomized algorithm to compute the interpolative decomposition (ID) of large-scale data matrices in situ. Compared to previous randomized IDs that used the QR decomposition to determine the column basis, we adopt a streaming ridge leverage score-based column subset selection algorithm that dynamically selects proper basis columns from the data and thus avoids an extra pass over the data to compute the coefficient matrix of the ID. In particular, we adopt a single-pass error estimator based on the non-adaptive Hutch++ algorithm to provide real-time error approximation for determining the best coefficients. As a result, our approach only needs a single pass over the original data and thus is suitable for large and high-dimensional matrices stored outside of core memory or generated in PDE simulations. A strategy to improve the accuracy of the reconstructed data gradient, when desired, within the ID framework is also presented. We provide numerical experiments on turbulent channel flow and ignition simulations, and on the NSTX Gas Puff Image dataset, comparing our algorithm with the offline ID algorithm to demonstrate its utility in real-world applications.

Column subset selection↗

DOE OSTI2026

Generative models on phase space

Deep generative models such as diffusion and flow matching are powerful machine learning tools capable of learning and sampling from high-dimensional distributions. They are particularly useful when the training data appears to be concentrated on a submanifold of the data embedding space. For high-energy physics data, consisting of collections of relativistic energy-momentum 4-vectors, this submanifold can enforce extremely strong physically-motivated priors, such as energy and momentum conservation. If these constraints are learned only approximately, rather than exactly, this can inhibit the interpretability and reliability of such generative models. To remedy this deficiency, we introduce generative models which are, by construction, confined at every step of their sampling trajectory to the manifold of massless N-particle Lorentz-invariant phase space in the center-of-momentum frame. In the case of diffusion models, the "pure noise" forward process endpoint corresponds to the uniform distribution on phase space, which provides a clear starting point from which to identify how correlations among the particles emerge during the reverse (de-noising) process. We demonstrate that our models are able to learn both few-particle and many-particle distributions with various singularity structures, paving the way for future interpretability studies using generative models trained on simulated jet data.

Bogorad, Zachary [Fermilab]↗

DOE OSTI2024

High‐speed 4‐dimensional scanning transmission electron microscopy using compressive sensing techniques

Abstract Here we show that compressive sensing allows 4‐dimensional (4‐D) STEM data to be obtained and accurately reconstructed with both high‐speed and reduced electron fluence. The methodology needed to achieve these results compared to conventional 4‐D approaches requires only that a random subset of probe locations is acquired from the typical regular scanning grid, which immediately generates both higher speed and the lower fluence experimentally. We also consider downsampling of the detector, showing that oversampling is inherent within convergent beam electron diffraction (CBED) patterns and that detector downsampling does not reduce precision but allows faster experimental data acquisition. Analysis of an experimental atomic resolution yttrium silicide dataset shows that it is possible to recover over 25 dB peak signal‐to‐noise ratio in the recovered phase using 0.3% of the total data. Lay abstract : Four‐dimensional scanning transmission electron microscopy (4‐D STEM) is a powerful technique for characterizing complex nanoscale structures. In this method, a convergent beam electron diffraction pattern (CBED) is acquired at each probe location during the scan of the sample. This means that a 2‐dimensional signal is acquired at each 2‐D probe location, equating to a 4‐D dataset. Despite the recent development of fast direct electron detectors, some capable of 100kHz frame rates, the limiting factor for 4‐D STEM is acquisition times in the majority of cases, where cameras will typically operate on the order of 2kHz. This means that a raster scan containing 256^2 probe locations can take on the order of 30s, approximately 100‐1000 times longer than a conventional STEM imaging technique using monolithic radial detectors. As a result, 4‐D STEM acquisitions can be subject to adverse effects such as drift, beam damage, and sample contamination. Recent advances in computational imaging techniques for STEM have allowed for faster acquisition speeds by way of acquiring only a random subset of probe locations from the field of view. By doing this, the acquisition time is significantly reduced, in some cases by a factor of 10‐100 times. The acquired data is then processed to fill‐in or inpaint the missing data, taking advantage of the inherently low‐complex signals which can be linearly combined to recover the information. In this work, similar methods are demonstrated for the acquisition of 4‐D STEM data, where only a random subset of CBED patterns are acquired over the raster scan. We simulate the compressive sensing acquisition method for 4‐D STEM and present our findings for a variety of analysis techniques such as ptychography and differential phase contrast. Our results show that acquisition times can be significantly reduced on the order of 100‐300 times, therefore improving existing frame rates, as well as further reducing the electron fluence beyond just using a faster camera.

Robinson, Alex W.↗

NASA NTRS1947

Investigation of Axial-flow Fan and Compressor Rotors Designed for Three-dimensional Flow

An investigation has been conducted to determine whether three-dimensional flows may be utilized in axial-flow fan and compressor rotors so that the spanwise load distribution may be varied to obtain high pressure rise. Two rotors, one with approximately uniform and one with solid-body downstream tangential-velocity distributions, were designed and tested at the design blade angle. Radial surveys of total pressure, static pressure, and flow angle were made upstream and downstream of the test rotors through a quantity-coefficient range. Tests of the solid-body rotor were also conducted at a large value of tip clearance. The results indicated that the three-dimensional flows may be utilized with high efficiency and that the three-dimensional theory used in conjunction with two-dimensional cascade data is sufficiently accurate for design purposes. The tests also showed that the tip-clearance losses of rotors highly loaded at the tips are not excessive. The existing three-dimensional theory in simplified for and an illustrative rotor design are presented in appendixes.

Kahane, A↗

NASA NTRS1994

Three-dimensional magnetic bubble memory system

A compact memory uses magnetic bubble technology for providing data storage. A three-dimensional arrangement, in the form of stacks of magnetic bubble layers, is used to achieve high volumetric storage density. Output tracks are used within each layer to allow data to be accessed uniquely and unambiguously. Storage can be achieved using either current access or field access magnetic bubble technology. Optical sensing via the Faraday effect is used to detect data. Optical sensing facilitates the accessing of data from within the three-dimensional package and lends itself to parallel operation for supporting high data rates and vector and parallel processing.

Stadler, Henry L.↗

DOE OSTI2025

Machine Learning to Select Experiments Driven by Fundamental Science and Applications for Targeted Nuclear Data Improvement

This work describes a blueprint for a process that accelerates progress in science by quantitatively answering the following question: What is the optimal combination of fundamental-science and application-driven experiments to maximally reduce pertinent data uncertainties? Answering this question entails solving a high-dimensional and complex optimization problem that is best solved with advanced statistic techniques often classified as machine learning. We apply this process within the framework of nuclear data with the aim to select an experiment combination that will reduce uncertainties in 239 Pu nuclear data for neutron energies between 1 and 600 keV. In this field, fundamental-physics driven data, called differential, look at one nuclear physics observable at a time. They are contrasted to application-driven, integral, data where one or few resulting values inform a broad set of nuclear data across several nuclides and energies. The candidates for integral experiments are criticality measurements that were refined by a genetic algorithm to be maximally sensitive to 239 Pu fission cross sections in the desired energy range. Twenty-three candidate differential experiments were investigated and span multiple nuclear physics observables (e.g., total, capture cross sections) for isotopes appearing in the integral experiments. The optimal combination among these candidate experiments was investigated via generalized least squares fitting, augmented with Gaussian processes to ameliorate statistical irregularities in data, and the D-optimality criterion. The latter evaluates for each pair of candidates the joint reduction in uncertainties of all 12200 nuclear data appearing in the integral experiments compared to the knowledge we have from 168 past experiments, theory, and nuclear data. We chose as differential measurements those that investigate 63 Cu and 239 Pu total cross sections, based on D-optimality rank and feasibility constraints. Two integral (criticality) experiments were selected: An experiment with Al 2 ⁢O 3 and graphite interleaved with Pu and a thick Cu reflector explores 1–30 keV, while we target the 30–600 keV range with an experiment that swaps boron in place of graphite with a different geometry.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS1986

Application of laser-velocimetry to the study of the flow around a two-dimensional airfoil

The experimental techniques employed by NASA researchers to obtain a high volume throughput of data in a study of high-lift multielement airfoils using a laser velocimeter (LV) are detailed. The two-dimensional LV system recorded mean velocity, turbulence intensities, Re shear stresses, skewness and kurtosis of the flow. A computer-controlled positioning mount for the LV allowed automated surveys of the flows with a 0.001 in. positioning accuracy. The flow was seeded with oil droplets and additional refinement of the wind tunnel controls permitted rapid speedup at selected areas of the flowfield over specific regions of the airfoil. Surface pressure taps furnished data for selecting regions for more detailed investigation. The data processing capabilities processed 30-40 samples every 10 min in an automated mode. Profiles of the data were computed automatically to furnish graphical displays on demand. Numerous samples of the data displays generated are provided.

Braden, J. A.↗

NASA NTRS1987

Chordwise pressure measurements on a blade of Mod-2 Wind Turbine

Pressure measurements covering a range of wind velocities were made at one span location on a blade of the Mod-2 Wind Turbine. The data show the existence of higher pressure coefficients than would be expected from wind tunnel data. These high pressure coefficients may be the result of three-dimensional flow over the blade that delays flow separations. Data is presented showing the repetitiveness and abrupt changes in the pressure distribution that occurs as the blade rotates. Calculated values of suction and flap coefficients are also presented.

Nyland, T. W.↗

DOE OSTI2026

Neural Posterior Estimation for Scalable and Accurate Inverse Parameter Inference in Li-Ion Batteries

Diagnosing the internal state of Li-ion batteries is critical for battery research, operation of real-world systems, and prognostic evaluation of remaining lifetime. By using physics-based models to perform probabilistic parameter estimation via Bayesian calibration, diagnostics can account for the uncertainty due to model fitness, data noise, and the observability of any given parameter. However, Bayesian calibration in Li-ion batteries using electrochemical data is computationally intensive even when using a fast surrogate in place of physics-based models, requiring many thousands of model evaluations. A fully amortized alternative is neural posterior estimation (NPE). NPE shifts the computational burden from the parameter estimation step to data generation and model training, reducing the parameter estimation time from minutes to milliseconds, enabling real-time applications. The present work shows that NPE can infer parameters equally or more accurately than Bayesian calibration, even if it leads to higher voltage reconstruction errors. We also demonstrate that the higher computational costs for data generation are tractable even in high-dimensional cases (ranging from 6 to 27 estimated parameters). The NPE method also offers several interpretability advantages over Bayesian calibration, such as local parameter sensitivity to specific regions of the voltage curve. The NPE method is demonstrated using an experimental fast charge dataset, with parameter estimates validated against measurements of loss of lithium inventory and loss of active material. The implementation is made available in a companion repository (https://github.com/NatLabRockies/BatFIT).

25 ENERGY STORAGE↗

NASA NTRS1996

Fast 3D Net Expeditions: Tools for Effective Scientific Collaboration on the World Wide Web

Two new technologies, the FASTexpedition and Remote FAST, have been developed that provide remote, 3D (three dimensional), high resolution, dynamic, interactive viewing of scientific data. The FASTexpedition permits one to access scientific data from the World Wide Web, take guided expeditions through the data, and continue with self controlled expeditions through the data. Remote FAST permits collaborators at remote sites to simultaneously view an analysis of scientific data being controlled by one of the collaborators. Control can be transferred between sites. These technologies are now being used for remote collaboration in joint university, industry, and NASA projects. Also, NASA Ames Research Center has initiated a project to make scientific data and guided expeditions through the data available as FASTexpeditions on the World Wide Web for educational purposes. Previously, remote visualization of dynamic data was done using video format (transmitting pixel information) such as video conferencing or MPEG (Motion Picture Expert Group) movies on the Internet. The concept for this new technology is to send the raw data (e.g., grids, vectors, and scalars) along with viewing scripts over the Internet and have the pixels generated by a visualization tool running on the viewers local workstation. The visualization tool that is currently used is FAST (Flow Analysis Software Toolkit). The advantages of this new technology over using video format are: (1) The visual is much higher in resolution (1280x1024 pixels with 24 bits of color) than typical video format transmitted over the network. (2) The form of the visualization can be controlled interactively (because the viewer is interactively controlling the visualization tool running on his workstation). (3) A rich variety of guided expeditions through the data can be included easily. (4) A capability is provided for other sites to see a visual analysis of one site as the analysis is interactively performed. Control of the analysis can be passed from site to site. (5) The scenes can be viewed in 3D using stereo vision. (6) The network bandwidth for the visualization using this new technology is much smaller than when using video format. (The measured peak bandwidth used was 1 Kbit/sec whereas the measured bandwidth for a small video picture was 500 Kbits/sec.) This talk will illustrate the use of these new technologies and present a proposal for using these technologies to improve science education.

Watson, Val↗

NASA NTRS1995

Vertical bloch line memory

A new read gate design for the vertical Bloch line (VBL) memory is disclosed which offers larger operating margin than the existing read gate designs. In the existing read gate designs, a current is applied to all the stripes. The stripes that contain a VBL pair are chopped, while the stripes that do not contain a VBL pair are not chopped. The information is then detected by inspecting the presence or absence of the bubble. The margin of the chopping current amplitude is very small, and sometimes non-existent. A new method of reading Vertical Bloch Line memory is also disclosed. Instead of using the wall chirality to separate the two binary states, the spatial deflection of the stripe head is used. Also disclosed herein is a compact memory which uses vertical Bloch line (VBL) memory technology for providing data storage. A three-dimensional arrangement in the form of stacks of VBL memory layers is used to achieve high volumetric storage density. High data transfer rate is achieved by operating all the layers in parallel. Using Hall effect sensing, and optical sensing via the Faraday effect to access the data from within the three-dimensional packages, an even higher data transfer rate can be achieved due to parallel operation within each layer.

Katti, Romney R.↗