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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Multilevel Parareal Algorithm with Averaging for Oscillatory Problems

The present study is an extension of the work done by Peddle, Haut, and Wingate and Haut and Wingate, where a two-level Parareal method with mapping and averaging is examined. The method proposed in this paper is a multilevel Parareal method with arbitrarily many levels, which is not restricted to the two-level case. We give an asymptotic error estimate which reduces to the two-level estimate for the case when only two levels are considered. Introducing more than two levels has important consequences for the averaging procedure, as we choose separate averaging windows for each of the different levels, which is an additional new feature of the present study. The different averaging windows make the proposed method especially appropriate for nonlinear multiscale problems, because we can introduce a level for each intrinsic scale of the problem and adapt the averaging procedure such that we reproduce the behavior of the model on the particular scale resolved by the level. The method is applied to nonlinear differential equations. The nonlinearities can generate a range of frequencies in the problem. The computational cost of the new method is investigated and studied on several examples.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

CAFE AU LAIT: Compute-Aware Federated Augmented Low-Rank AI Training

Federated finetuning is crucial for unlocking the knowledge embedded in pretrained Large Language Models (LLMs) when data are geographically distributed across clients. Unlike finetuning with data from a single institution, federated finetuning allows collaboration across multiple institutions, enabling the utilization of diverse and decentralized datasets while preserving data privacy. Given the high computing costs of LLM training and the emphasis on energy efficiency in Federated Learning (FL), Low-Rank Adaptation (LoRA) has emerged as a widely adopted algorithm due to its significantly reduced number of trainable parameters. However, this assumes that all data silos have the necessary computing resources to compute local updates of LLMs. Nevertheless, in practice, the computing resources across clients are highly heterogeneous: while some may have access to hundreds of GPUs, others might have limited or no GPU access. Recently, federated finetuning using synthetic data has been proposed, allowing clients to participate in a collaborative training run without training LLMs locally. However, our experimental results reveal a performance gap between models trained using synthetic data and those trained using local updates. Motivated by the observed heterogeneity in computing resources and the performance gap, we propose a novel two-stage algorithm that leverages the storage and computing capabilities of a strong server. In the first stage, under the coordination of the strong server, clients with limited computing resources collaborate to generate synthetic data, which is transferred to and stored on the strong server. In the second stage, the strong server uses this synthetic data on behalf of the resource-constrained clients to perform federated LoRA finetuning alongside clients with sufficient computing resources. This approach ensures that all clients can participate in the finetuning process. Experimental results demonstrate that incorporating local updates from even a small fraction of clients improves performance compared to using synthetic data for all clients. Furthermore, we incorporate the Gaussian mechanism in both stages to guarantee client-level differential privacy.

Wang, Jiayi [ORNL]↗
NASA NTRS1997

Constrained Multipoint Aerodynamic Shape Optimization Using an Adjoint Formulation and Parallel Computers

An aerodynamic shape optimization method that treats the design of complex aircraft configurations subject to high fidelity computational fluid dynamics (CFD), geometric constraints and multiple design points is described. The design process will be greatly accelerated through the use of both control theory and distributed memory computer architectures. Control theory is employed to derive the adjoint differential equations whose solution allows for the evaluation of design gradient information at a fraction of the computational cost required by previous design methods. The resulting problem is implemented on parallel distributed memory architectures using a domain decomposition approach, an optimized communication schedule, and the MPI (Message Passing Interface) standard for portability and efficiency. The final result achieves very rapid aerodynamic design based on a higher order CFD method. In order to facilitate the integration of these high fidelity CFD approaches into future multi-disciplinary optimization (NW) applications, new methods must be developed which are capable of simultaneously addressing complex geometries, multiple objective functions, and geometric design constraints. In our earlier studies, we coupled the adjoint based design formulations with unconstrained optimization algorithms and showed that the approach was effective for the aerodynamic design of airfoils, wings, wing-bodies, and complex aircraft configurations. In many of the results presented in these earlier works, geometric constraints were satisfied either by a projection into feasible space or by posing the design space parameterization such that it automatically satisfied constraints. Furthermore, with the exception of reference 9 where the second author initially explored the use of multipoint design in conjunction with adjoint formulations, our earlier works have focused on single point design efforts. Here we demonstrate that the same methodology may be extended to treat complete configuration designs subject to multiple design points and geometric constraints. Examples are presented for both transonic and supersonic configurations ranging from wing alone designs to complex configuration designs involving wing, fuselage, nacelles and pylons.

Reuther, James↗
DOE OSTI2026

Accelerating Bilevel Optimization With Hierarchical Many-Threaded Parallel Differential Evolution

Bilevel optimization is encountered in many relevant real-world applications. The main feature of this type of problem is that an upper-level optimization problem is constrained by a nested lower-level optimization problem. Because of this nested structure, bilevel problems (BLPs) are usually computationally expensive to solve. Differential evolution (DE) has demonstrated promising results in solving BLPs of relatively small scales. As the problem scale increases, the decision space becomes intrinsically larger, requiring a growing number of function evaluations for the method to work properly. In this context, heavy parallelization and high-performance computing techniques are indispensable to enable the resolution of more complex and challenging optimization problems. Hence, we propose a hierarchical many-threaded parallel DE approach for BLPs, where both levels are parallelized. The computational experiments demonstrate that the parallel implementation achieved runtime speeds ranging from 44 to 2559 times faster than the sequential version on a well-known scalable SMD benchmark test problem when executed on an NVIDIA A100 GPU. The findings indicate that the algorithm’s convergence is strongly influenced by the number of both upper- and lower-level generations. Moreover, the success of experiments with large-scale problems is closely linked to the choice of small population sizes.

Dufek, Amanda S↗
DOE OSTI2025

Nyström type exponential integrators for strongly magnetized charged particle dynamics

Solving for charged particle motion in electromagnetic fields (i.e. the particle pushing problem) is a computationally intensive component of particle-in-cell (PIC) methods for plasma physics simulations. This task is especially challenging when the plasma is strongly magnetized due numerical stiffness arising from the wide range of time scales between highly oscillatory gyromotion and long term macroscopic behavior. A promising approach to solve these problems is by a class of methods known as exponential integrators that can solve linear problems exactly and are A-stable. This work extends the standard exponential integration framework to derive Nyström-type exponential integrators that integrates the Newtonian equations of motion as a second-order differential equation directly. In particular, we derive second-order and third-order Nyström-type exponential integrators for strongly magnetized particle pushing problems. Numerical experiments show that the Nyström-type exponential integrators exhibit significant improvement in computation speed over the standard exponential integrators.

general physics↗
DOE OSTI2023

Direct Estimation of Parameters in ODE Models Using WENDy: Weak-Form Estimation of Nonlinear Dynamics

Abstract We introduce the Weak-form Estimation of Nonlinear Dynamics (WENDy) method for estimating model parameters for non-linear systems of ODEs. Without relying on any numerical differential equation solvers, WENDy computes accurate estimates and is robust to large (biologically relevant) levels of measurement noise. For low dimensional systems with modest amounts of data, WENDy is competitive with conventional forward solver-based nonlinear least squares methods in terms of speed and accuracy. For both higher dimensional systems and stiff systems, WENDy is typically both faster (often by orders of magnitude) and more accurate than forward solver-based approaches. The core mathematical idea involves an efficient conversion of the strong form representation of a model to its weak form, and then solving a regression problem to perform parameter inference. The core statistical idea rests on the Errors-In-Variables framework, which necessitates the use of the iteratively reweighted least squares algorithm. Further improvements are obtained by using orthonormal test functions, created from a set of $$C^{\infty }$$ C ∞ bump functions of varying support sizes.We demonstrate the high robustness and computational efficiency by applying WENDy to estimate parameters in some common models from population biology, neuroscience, and biochemistry, including logistic growth, Lotka-Volterra, FitzHugh-Nagumo, Hindmarsh-Rose, and a Protein Transduction Benchmark model. Software and code for reproducing the examples is available at https://github.com/MathBioCU/WENDy .

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Scientific Discovery with Physics-Informed System Identification (Abbreviated Report)

My fellowship research focused on making physics-based simulations faster and more useful through machine learning. Many problems in science and engineering are governed by partial differential equations, but high-fidelity simulations are often too expensive to run repeatedly. I worked on improving Latent Space Dynamics Identification (LaSDI), a reduced-order modeling framework that compresses large simulation data sets into a smaller representation and then learns how that representation evolves over time. The motivation was to develop reduced models that remain accurate for more challenging systems, especially when predictions must remain reliable over long time intervals or when the underlying dynamics are more complicated than standard methods can easily handle. I also contributed to related work on Quandary, a high-performance software effort for simulation and control of open quantum systems, before focusing primarily on Latent Space Dynamics Identification methods. The main outcomes of the fellowship were two new algorithms (both of which were published), Rollout-LaSDI and Higher-Order LaSDI, together with supporting work on multi-stage Latent Space Dynamics Identification. Rollout-LaSDI improved long-term prediction by training the model to stay accurate over extended time horizons, and Higher-Order LaSDI broadened the method so it could model systems with higher-order time dynamics. My contributions to multistage Latent Space Dynamics Identification also helped show that its later training stages could be simplified without losing effectiveness, and that this behavior held across different model architectures and training strategies. Taken together, these advances improved the accuracy, flexibility, and practical value of reduced-order modeling tools for computational science.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1983

Measurement of ultrasonic fields in transparent media using a scanning differential interferometer

An experimental system for the detection of three dimensional acoustic fields in optically transparent media using a dual beam differential interferometer is described. In this system, two coherent, parallel, focused laser beams are passed through the specimen and the interference fringe pattern which results when these beams are combined shifts linearly by an amount which is related to the optical pathlength difference between the two beams. It is shown that for small signals, the detector output is directly proportional to the amplitude of the acoustic field integrated along the optical beam path through the specimen. A water tank and motorized optical platform were constructed to allow these dual beams to be scanned through an ultrasonic field generated by a piezoelectric transducer at various distances from the transducer. Scan data for the near, Fresnel, and far zones of a uniform, circular transducer are presented and an algorithm for constructing the radial field profile from this integrated optical data, assuming cylindrical symmetry, is described.

Dockery, G. D.↗
DOE OSTI2021

Growth differentiation factor-15 promotes immune escape of ovarian cancer via targeting CD44 in dendritic cells

Immune escape is the main cause of the low response rate to immunotherapy for cancer, including ovarian cancer. Growth differentiation factor-15 (GDF-15) inhibits immune cell function. However, only few reports described the mechanism. Therefore, the aim of this study was to investigate the mechanism of immune escape regulated by GDF-15 in ovarian cancer. Ovarian cancer patients and healthy women were enrolled in this study. Immunohistochemistry and ELISA were performed to measure GDF-15 expression. Immunoprecipitation combined with mass spectrometry, surface plasmon resonance, and co-immunoprecipitation assay were used to evaluate the interaction between GDF-15 and the surface molecules of DCs. Immunofluorescence analysis, flow cytometry and transwell assay were used to evaluate additional effects of GDF-15 on DCs. The results showed that GDF-15 expression was higher in the ovarian cancer patients compared to that in the healthy women. The TIMER algorithm revealed that highly GDF-15 expression is associated with immune DC infiltration in immunoreactive high-grade serous carcinoma. A further study showed that GDF-15 suppressed DCs maturation, as well as IL-12p40 and TNF-α secretion, the length and number of protrusions and the migration. More importantly, CD44 in the surface of DCs interacted with GDF-15. The overexpression of CD44 in DCs resulted in the suppression of the inhibitory effect of GDF-15 on the length and number of DC synapses. In DCs overexpressing CD44 the inhibition of GDF-15 on the expression of CD11c, CD83 and CD86 was decreased, while in DCs with a knockdown of CD44 the inhibition was further enhanced. Knockdown of CD44 in DCs enhanced the inhibitory effect of GDF-15 on DC migration, while the overexpression of CD44 inhibited the inhibitory effect of GDF-15 on DC migration. In conclusion, the present study suggested that GDF-15 might facilitate ovarian cancer immune escape by interacting with CD44 in DCs to inhibit their function.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2020

On the Derivation of Quasi-Newton Formulas for Optimization in Function Spaces

Newton’s method is usually preferred when solving optimization problems due to its superior convergence properties compared to gradient-based or derivative-free optimization algorithms. However, deriving and computing second-order derivatives needed by Newton’s method often is not trivial and, in some cases, not possible. In such cases quasi-Newton algorithms are a great alternative. In this paper, we provide a new derivation of well-known quasi-Newton formulas in an infinite-dimensional Hilbert space setting. Furthermore, it is known that quasi-Newton update formulas are solutions to certain variational problems over the space of symmetric matrices. In this paper, we formulate similar variational problems over the space of bounded symmetric operators in Hilbert spaces. By changing the constraints of the variational problem we obtain updates (for the Hessian and Hessian inverse) not only for the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method but also for Davidon–Fletcher–Powell (DFP), Symmetric Rank One (SR1), and Powell-Symmetric-Broyden (PSB). In addition, for an inverse problem governed by a partial differential equation (PDE), we derive DFP and BFGS “structured” secant formulas that explicitly use the derivative of the regularization and only approximates the second derivative of the misfit term. We show numerical results that demonstrate the desired mesh-independence property and superior performance of the resulting quasi-Newton methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Symbol alphabets from plabic graphs

Symbol alphabets of n-particle amplitudes in N = 4 super-Yang-Mills theory are known to contain certain cluster variables of Gr(4, n) as well as certain algebraic functions of cluster variables. In this paper we suggest an algorithm for computing these symbol alphabets from plabic graphs by solving matrix equations of the form C ∙ Z = 0 to associate functions on Gr(m, n) to parameterizations of certain cells of Gr(k, n) indexed by plabic graphs. For m = 4 and n = 8 we show that this association precisely reproduces the 18 algebraic symbol letters of the two-loop NMHV eight-particle amplitude from four plabic graphs.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

On the Investigation of Phase Fault Classification in Power Grid Signals: A Case Study for Support Vector Machines, Decision Tree and Random Forest

In monitoring the power grid, an ability to differentiate between fault types is essential to ensuring electrical safety. Accordingly, this study introduces a fault detection and classification method by considering different machine learning (ML) and feature extraction (FE) methods combinations. Specifically, the proposed method is established in two classification layers; the first layer determines the fault, and the second layer distinguishes the type of fault. Based on the proposed system model, this study seeks to determine the influential data attributes in a power grid signal using FE methods, including fast Fourier transform, power spectral density (PSD), auto-correlation, and wavelet transform (WT). A cross-comparison of the effectiveness of the Support Vector Machine (SVM), Decision Tree (DT), and Random Forest (RF) is also performed to accomplish the classification layers of the proposed method. The designed algorithm is analyzed under the various combinations of FE and ML methods, and outcomes are presented by considering the trade-off between computational complexity and prediction accuracy. The results reveal that the RF-based ML algorithm shows the most accurate classification performance with PSD, and the most time-saving of the models is the DT WT. Also, SVM emerges superior on a subsequent test of the simulated models on real-world signals.

Galbraith, Kelli↗
NASA NTRS1988

A feedback linearization approach to spacecraft control using momentum exchange devices

Recent developments in the area of nonlinear control theory have shown how coordiante changes in the state and input spaces can be used with nonlinear feedback to transform certain nonlinear ordinary differential equations into equivalent linear equations. These feedback linearization techniques are applied to resolve two problems arising in the control of spacecraft equipped with control moment gyroscopes (CMGs). The first application involves the computation of rate commands for the gimbals that rotate the individual gyroscopes to produce commanded torques on the spacecraft. The second application is to the long-term management of stored momentum in the system of control moment gyroscopes using environmental torques acting on the vehicle. An approach to distributing control effort among a group of redundant actuators is described that uses feedback linearization techniques to parameterize sets of controls which influence a specified subsystem in a desired way. The approach is adapted for use in spacecraft control with double-gimballed gyroscopes to produce an algorithm that avoids problematic gimbal configurations by approximating sets of gimbal rates that drive CMG rotors into desirable configurations. The momentum management problem is stated as a trajectory optimization problem with a nonlinear dynamical constraint. Feedback linearization and collocation are used to transform this problem into an unconstrainted nonlinear program. The approach to trajectory optimization is fast and robust. A number of examples are presented showing applications to the proposed NASA space station.

Dzielski, John Edward↗
NASA NTRS1988

Adaptive independent joint control of manipulators - Theory and experiment

The author presents a simple decentralized adaptive control scheme for multijoint robot manipulators based on the independent joint control concept. The proposed control scheme for each joint consists of a PID (proportional integral and differential) feedback controller and a position-velocity-acceleration feedforward controller, both with adjustable gains. The static and dynamic couplings that exist between the joint motions are compensated by the adaptive independent joint controllers while ensuring trajectory tracking. The proposed scheme is implemented on a MicroVAX II computer for motion control of the first three joints of a PUMA 560 arm. Experimental results are presented to demonstrate that trajectory tracking is achieved despite strongly coupled, highly nonlinear joint dynamics. The results confirm that the proposed decentralized adaptive control of manipulators is feasible, in spite of strong interactions between joint motions. The control scheme presented is computationally very fast and is amenable to parallel processing implementation within a distributed computing architecture, where each joint is controlled independently by a simple algorithm on a dedicated microprocessor.

Seraji, H.↗
DOE OSTI2022

Brill-Noether-general limit root bundles: absence of vector-like exotics in F-theory Standard Models

Root bundles appear prominently in studies of vector-like spectra of 4d F-theory compactifications. Of particular importance to phenomenology are the Quadrillion F-theory Standard Models (F-theory QSMs). In this work, we analyze a superset of the physical root bundles whose cohomologies encode the vector-like spectra for the matter representations ($3$, $2$) 1/6 , ($\overline{3}$, $1$) -2/3 and ($1$, $1$) 1 . For the family B 3 (Δ$^{°}_{4}$) consisting of $\mathcal{O}$(10 11 ) F-theory QSM geometries, we argue that more than 99.995% of the roots in this superset have no vector-like exotics. This indicates that absence of vector-like exotics in those representations is a very likely scenario in the O(10 11 ) QSM geometries B 3 (Δ$^{°}_{4}$). The QSM geometries come in families of toric 3-folds B 3 (Δ°) obtained from triangulations of certain 3-dimensional polytopes Δ°. The matter curves in X Σ $\large{ϵ}$ B 3 (Δ°) can be deformed to nodal curves which are the same for all spaces in B 3 (Δ°). Therefore, one can probe the vector-like spectra on the entire family B 3 (Δ°) from studies of a few nodal curves. We compute the cohomologies of all limit roots on these nodal curves. In our applications, for the majority of limit roots the cohomologies are determined by line bundle cohomology on rational tree-like curves. For this, we present a computer algorithm. The remaining limit roots, corresponding to circuit-like graphs, are handled by hand. The cohomologies are independent of the relative position of the nodes, except for a few circuits. On these jumping circuits, line bundle cohomologies can jump if nodes are specially aligned. This mirrors classical Brill-Noether jumps. B 3 (Δ°) admits a jumping circuit, but the root bundle constraints pick the canonical bundle and no jump happens.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1991

Data analysis using scale-space filtering and Bayesian probabilistic reasoning

This paper describes a program for analysis of output curves from Differential Thermal Analyzer (DTA). The program first extracts probabilistic qualitative features from a DTA curve of a soil sample, and then uses Bayesian probabilistic reasoning to infer the mineral in the soil. The qualifier module employs a simple and efficient extension of scale-space filtering suitable for handling DTA data. We have observed that points can vanish from contours in the scale-space image when filtering operations are not highly accurate. To handle the problem of vanishing points, perceptual organizations heuristics are used to group the points into lines. Next, these lines are grouped into contours by using additional heuristics. Probabilities are associated with these contours using domain-specific correlations. A Bayes tree classifier processes probabilistic features to infer the presence of different minerals in the soil. Experiments show that the algorithm that uses domain-specific correlation to infer qualitative features outperforms a domain-independent algorithm that does not.

Kulkarni, Deepak↗
NASA NTRS2008

Development of Position-sensitive Transition-edge Sensor X-ray Detectors

We report on the development of position-sensitive transition-edge sensors (PoST's) for future x-ray astronomy missions such as the International X-ray Observatory (IXO), currently under study by NASA and ESA. PoST's consist of multiple absorbers each with a different thermal coupling to one or more transition-edge sensor (TES). This differential thermal coupling between absorbers and TES's results in different characteristic pulse shapes and allows position discrimination between the different pixels. The development of PoST's is motivated by a desire to achieve maximum focal-plane area with the least number of readout channels and as such. PoST's are ideally suited to provide a focal-plane extension to the Constellation-X microcalorimeter array. We report the first experimental results of our latest one and two channel PoST's, which utilize fast thermalizing electroplated Au/Bi absorbers coupled to low noise Mo/Au TES's - a technology already successfully implemented in our arrays of single pixel TES's. We demonstrate 6 eV energy resolution coupled with spatial sensitivity in the keV energy range. We also report on the development of signal processing algorithms to optimize energy and position sensitivity of our detectors.

Smith, S. J.↗
NASA NTRS2019

Use of Polarimetric Radar Measurements to Constrain Simulated Convective Cell Evolution: A Pilot Study with Lagrangian Tracking

To probe the potential value of a radar-driven field campaign to constrain simulation of isolated convection subject to a strong aerosol perturbation, convective cells observed by the operational KHGX weather radar in the vicinity of Houston, Texas, are examined individually and statistically. Cells observed in a single case study of onshore flow conditions during July 2013 are first examined and compared with cells in a regional model simulation. Observed and simulated cells are objectively identified and tracked from observed or calculated positive specific differential phase (K(sub DP)) above the melting level, which is related to the presence of supercooled liquid water. Several observed and simulated cells are subjectively selected for further examination. Below the melting level, we compare sequential cross sections of retrieved and simulated raindrop size distribution parameters. Above the melting level, we examine time series of KDP and radar differential reflectivity (Z(sub DR)) statistics from observations and calculated from simulated supercooled rain properties, alongside simulated vertical wind and supercooled rain mixing ratio statistics. Results indicate that the operational weather radar measurements offer multiple constraints on the properties of simulated convective cells, with substantial value added from derived K(sub DP) and retrieved rain properties. The value of collocated three-dimensional lightning mapping array measurements, which are relatively rare in the continental US, supports the choice of Houston as a suitable location for future field studies to improve the simulation and understanding of convective updraft physics. However, rapid evolution of cells between routine volume scans motivates consideration of adaptive scan strategies or radar imaging technologies to amend operational weather radar capabilities. A 3-year climatology of isolated cell tracks, prepared using a more efficient algorithm, yields additional relevant information. Isolated cells are found within the KHGX domain on roughly 40 % of days year-round, with greatest concentration in the northwest quadrant, but roughly 5-fold more cells occur during June through September. During this enhanced occurrence period, the cells initiate following a strong diurnal cycle that peaks in the early afternoon, typically follow a south-to-north flow, and dissipate within 1 h, consistent with the case study examples. Statistics indicate that ∼ 150 isolated cells initiate and dissipate within 70 km of the KHGX radar during the enhanced occurrence period annually, and roughly 10 times as many within 200 km, suitable for multi-instrument Lagrangian observation strategies. In addition to ancillary meteorological and aerosol measurements, robust vertical wind speed retrievals would add substantial value to a radar-driven field campaign.

Fridlind, Ann M.↗