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Results for “differential transformation”

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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Transformer Health Monitoring via Synchrophasors

Traditional transformer protection schemes such as differential protection operate once the transformer is in a critical state. Proactive means of transformer health evaluation such as Sweep Frequency Response Analysis, can only be performed periodically with the transformer out-of-service. This work presents a framework where the health and structural integrity of transformers is monitored via synchrophasors in real-time. Synchrophasors and subspace estimation techniques are used to build reduced-order models which are then analyzed across multiple domains. A diagnostics algorithm is developed and tested via Matlab simulations. Test results are promising, opening up new prospects in transformer protection research.

cyber-physical security↗
DOE OSTI2023

Differentiable Quantum Programming with Unbounded Loops

The emergence of variational quantum applications has led to the development of automatic differentiation techniques in quantum computing. Existing work has formulated differentiable quantum programming with bounded loops, providing a framework for scalable gradient calculation by quantum means for training quantum variational applications. However, promising parameterized quantum applications, e.g., quantum walk and unitary implementation, cannot be trained in the existing framework due to the natural involvement of unbounded loops. To fill in the gap, we provide the first differentiable quantum programming framework with unbounded loops, including a newly designed differentiation rule, code transformation, and their correctness proof. Technically, we introduce a randomized estimator for derivatives to deal with the infinite sum in the differentiation of unbounded loops, whose applicability in classical and probabilistic programming is also discussed. We implement our framework with Python and Q# and demonstrate a reasonable sample efficiency. Through extensive case studies, we showcase an exciting application of our framework in automatically identifying close-to-optimal parameters for several parameterized quantum applications.

Computer Science↗
DOE OSTI2026

ssys

`ssys` is a Python toolkit for exact algebraic transformation of ordinary differential equation (ODE) models into canonical S-system or Generalized Mass Action (GMA) form. Given a model in Antimony or SBML format, `ssys` produces a mathematically equivalent representation. The transformation introduces auxiliary variables as needed to decompose a broad class of nonlinearities into products of power-law terms. The recast is exact: the original and transformed systems have identical dynamics on the invariant constraint manifold defined by auxiliary variable definitions, given consistent initial conditions.

Hlavacek, William [Los Alamos National Laboratory]↗
DOE OSTI2024

Towards reverse mode automatic differentiation of Kokkos-based codes

Derivative computation is a key component of optimization, sensitivity analysis, uncertainty quantification, and the solving of nonlinear problems. Automatic differentiation (AD) is a powerful technique for evaluating such derivatives, and in recent years, has been integrated into programming environments such as Jax, PyTorch, and TensorFlow to support derivative computations needed for training of machine learning models, facilitating wide-spread use of these technologies. The C++ language has become the de facto standard for scientific computing due to numerous factors, yet language complexity has made the wide-spread adoption of AD technologies for C++ difficult, hampering the incorporation of powerful differentiable programming approaches into C++ scientific simulations. This is exacerbated by the increasing emergence of architectures, such as GPUs, with limited memory capabilities and requiring massive thread-level concurrency. C++ AD tools must effectively use these environments to bring novel scientific simulations to next-generation DOE experimental and observational facilities. In this project, we investigated source transformation-based automatic differentiation using LLVM compiler infrastructure to automatically generate portable and efficient gradient computations of Kokkos-based code. We have demonstrated that our proposed strategy is feasible by investigating the usage of a prototype LLVM-based source transformation tool to generate gradients of simple functions made of sequences of simple Kokkos parallel regions. Speedups of up to 500x compared to Sacado were observed on NVIDIA V100 GPU.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Biobased Semi-Interpenetrating Polymer Networks of Poly(ε-caprolactone) and Epoxidized Soybean Oil with Nanoscale Morphology, Shape-Memory Effect, and Biocompatibility

Creating biobased polymer blends with outstanding properties, nanoscale morphology, shape-memory capability, and biocompatibility is very crucial and requires a fundamental understanding of the phase behavior, macromolecular structure, and biological compatibility of the polymer blends with living cells. It is very critical to understand the complex relationships among the polymer structure, morphology, and performance of multifunctional smart materials under conditions that they are likely to encounter during use, particularly in biomedical applications. Biobased semi-interpenetrating polymer networks of poly(ε-caprolactone) and epoxidized soybean oil with nanoscale morphology have been successfully synthesized via in situ cationic polymerization and compatibilization in a homogeneous solution. Varies analytical and characterization techniques, such as Fourier transform infrared spectroscopy, differential scanning calorimetry, dynamic mechanical analysis, transmission electron microscopy, X-ray scattering, cell toxicity, and shape-memory effects (SMEs), have been employed to understand the structure–properties relationship of these smart, biobased nanostructured polymer blends. The synthesized nano blends were nontoxic or biocompatible and supported attachment of human vein endothelial cells, showing their potential use in biomedical applications. The current versatile, low-cost strategy for synthesizing the nanoscale morphology of semi-interpenetrating polymer networks with SMEs and biocompatibility should be widely applicable for polymer systems. This study is also considered as a continuation to our efforts in the area of biobased polymers to develop innovative technologies to transform natural resources into smart multifunctional materials for a wide range of applications, including coatings, adhesives, and medical devices.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Quantitative phase imaging by gradient retardance optical microscopy

Abstract Quantitative phase imaging (QPI) has become a vital tool in bioimaging, offering precise measurements of wavefront distortion and, thus, of key cellular metabolism metrics, such as dry mass and density. However, only a few QPI applications have been demonstrated in optically thick specimens, where scattering increases background and reduces contrast. Building upon the concept of structured illumination interferometry, we introduce Gradient Retardance Optical Microscopy (GROM) for QPI of both thin and thick samples. GROM transforms any standard Differential Interference Contrast (DIC) microscope into a QPI platform by incorporating a liquid crystal retarder into the illumination path, enabling independent phase-shifting of the DIC microscope's sheared beams. GROM greatly simplifies related configurations, reduces costs, and eradicates energy losses in parallel imaging modalities, such as fluorescence. We successfully tested GROM on a diverse range of specimens, from microbes and red blood cells to optically thick (~ 300 μm) plant roots without fixation or clearing.

47 OTHER INSTRUMENTATION↗
DOE OSTI2026

Design of digital acquisition for beam current monitor

As a part of the Proton Improvement Plan – II (PIP-II) at Fermilab, instrumentation systems are being modernized to take advantage of the higher speeds and ease of use offered by standardized embedded systems like MicroTCA. A rear-transition module (RTM) is being designed to interface with said embedded systems. In each of the four identical channels on the RTM, the differential signal from an alternating-current current transformer (ACCT) transimpedance amplifier will again be amplified by a differential operation-amplifier, then filtered by a low-pass topology. The conditioned signal is then digitized at a maximum of 10MS/s by an analog to digital converter (ADC) integrated circuit. After digitization, the ADC passes the data to an off the shelf AdvancedMC (AMC) Xilinx FPGA module using low voltage differential signals. This paper will describe the simulation of analog circuitry for signal conditioning, simulation of digital signal integrity based on physical design as well as verification of design characteristics critical to signal integrity. This work aims to create a methodology that can be applied to future RTMs requiring application of high-speed digital design principles.

White, R.Turner [Fermilab]↗
DOE OSTI2025

Design of Digital Acquisition for Beam Current Monitor

As a part of the Proton Improvement Plan II (PIP-II) at Fermilab, instrumentation systems are being modernized to take advantage of the higher speeds and ease of use offered by standardized embedded systems like MicroTCA. A rear-transition module (RTM) is being designed to interface with said embedded systems. In each of the four identical channels on the RTM, the differential signal from an alternating-current current transformer (ACCT) transimpedance amplifier will again be amplified by a differential operation-amplifier, then filtered by a low-pass topology. The conditioned signal is then digitized at a maximum of 10MS/s by an analog to digital converter (ADC) integrated circuit. After digitization, the ADC passes the data to an off the shelf AdvancedMC (AMC) Xilinx FPGA module using low voltage differential signals. This paper will describe the simulation of analog circuitry for signal conditioning, simulation of digital signal integrity based on physical design as well as verification of design characteristics critical to signal integrity. This work aims to create a methodology that can be applied to future RTMs requiring application of high-speed digital design principles.

White, Turner [Fermilab] (ORCID:0009000348159256)↗
DOE OSTI2026

Multiscale Modeling and Experimental Insights into High-Temperature Soil Biodegradation Dynamics of Semi-Crystalline Poly(Lactic Acid) Nonwoven Fabrics

This study investigates the biodegradation of semi-crystalline poly(lactic acid) (PLA) nonwovens (NWs) in soil at 58 °C using both experimental and mathematical modeling approaches. The model utilizes a system of parabolic diffusion-reaction partial differential equations (PDEs) to elucidate chemical transformations over time and in space. It accounts for phenomena such as the diffusion of water and lactic acid monomers through the polymer matrix and into the surrounding soil, along with their microbial breakdown. It also accounts for the initial PLA crystallinity and predicts its evolution in time. The model is solved numerically for a single filament, and the results were used to shed light on PLA NW transformations observed in soil over a 180-day incubation period. Various characterization techniques, including scanning electron microscopy (SEM), differential scanning calorimetry (DSC), and Raman spectroscopy, were employed to assess morphological changes, crystallinity, and molecular changes in the NWs throughout the experiment. By comparing the experimental data with the model predictions, the hydrolysis rate coefficient was found to be 3.37 × 10 -7 s -1 , while the rate of microbial degradation of lactic acid monomers was faster, of the order of 9.63 × 10 -7 s -1 . The findings highlight the significant role of crystallinity in the biodegradation process. The PLA degradation ceases when no amorphous material remains, and the crystallinity reaches 0.8, as observed in the experiments by day 120. Furthermore, this research contributes to a deeper understanding of PLA biodegradation dynamics and offers insights for effectively managing biodegradable materials in environmental settings.

Diffusion−reaction modeling↗
DOE OSTI2024

CurvilinearGrids.jl: A Julia package for curvilinear coordinate transformations

Finite-difference discretizations of partial differential equations are widespread throughout the scientific community. Oftentimes finite-differences are used to compute spatial gradients of fields on a discrete grid, which is typically a uniform or rectilinear Cartesian mesh. Arbitrary multidimensional geometry is difficult to discretize directly with finite differences, however, due to non-uniform grid spacing and non-orthogonality. Curvilinear coordinate transformations can be used as a strategy to enable arbitrary geometry. While these curvilinear transformations are straightforward, the governing PDEs require additional terms (metrics) and must adhere to strict conservation laws; these criteria complicate the application of the transformation and require careful implementation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Evaluating switch lifetime in soft-switched single-stage differential-mode SST

The reliability of semiconductor switches in single-stage differential-mode solid-state transformers (DM-SSTs) has not been systematically evaluated under soft-switching operation and realistic grid conditions. This paper presents a switch-level reliability analysis for soft-switched and hard-switched DM-SST configurations by integrating converter-specific power loss modeling with empirical lifetime prediction. Analytical derivation of device current profiles specific to the DM-SST is used to characterize electrothermal stress, which is then mapped to lifetime using degradation models obtained from power cycling tests (PCTs). Applied to realistic SST load profiles and grid voltage variations, this approach provides a probabilistic prediction of switch lifetime for the DM-SST. Lifetime estimates for both SiC MOSFETs and Si IGBTs are presented, offering insight into device degradation under converter operating conditions. The results quantify the reliability benefits of soft switching in single-stage SSTs, highlighting how switching dynamics influence long-term switch degradation.

14 SOLAR ENERGY↗
DOE OSTI2026

Laplace Transform–Based Quantum Eigenvalue Transformation via Linear Combination of Hamiltonian Simulation

Eigenvalue transformations, which include solving time-dependent differential equations as a special case, have a wide range of applications in scientific and engineering computation. While quantum algorithms for singular value transformations are well studied, eigenvalue transformations are distinct, especially for nonnormal matrices. Here, we propose an efficient quantum algorithm for performing a class of eigenvalue transformations that can be expressed as a certain type of matrix Laplace transformation. This allows us to significantly extend the recently developed linear combination of Hamiltonian simulation method [D. An, J.-P. Liu, and L. Lin, Phys. Rev. Lett., 131 (2023), 150603; D. An, A. M. Childs, and L. Lin, Commun. Math. Phys. 407, 19 (2026)] to represent a wider class of eigenvalue transformations, such as powers of the matrix inverse, 𝐴 −𝑘 , and the exponential of the matrix inverse, 𝑒 −𝐴 −1 . The latter can be interpreted as the solution of a mass-matrix differential equation of the form form 𝐴⁢𝑢′⁡⁡(𝑡) =−𝑢⁡(𝑡). We demonstrate that our eigenvalue transformation approach can solve this problem without explicitly inverting 𝐴, thereby reducing the computational complexity.

Laplace transform↗
DOE OSTI2024

The melt memory effects in polymer crystallization

This paper presents a systematic review of the literature on the melt memory effects observed in polymers, an area that has engendered considerable debate for over 50 years. Recent advances in experimental techniques have provided fresh insights into how a polymer's thermal history influences its recrystallization behavior. It has been observed that given other conditions unchanged, the crystallization temperature during recrystallization decreases with an increase in the melt temperature T s above the melting point T m until a critical melt temperature is attained. This phenomenon also extends to the half-time of crystallization and the secondary structures, such as lamellar thickness, of semi-crystalline polymers. Despite these findings, a comprehensive constitutive model that encapsulates polymer melt memory effects remains elusive. Cutting-edge instrumentation, including in situ small and wide-angle X-ray scattering, temperature-controlled Fourier transform infrared spectroscopy, and flash differential scanning calorimetry, have posed significant challenges to the traditional nucleation and growth models established in the 1970s. These models are foundational to our understanding of polymer crystallization, which is an integral part of polymer processing and production. In this review, the historical contours of this discourse are traced, with an examination of both the recent experimental breakthroughs and theoretical advancements pertinent to polymer melt memory effects. In conclusion, this paper delves into the prevailing theories of polymer nucleation and crystallization and engages with theoretical discussions and numerical simulations that attempt to elucidate and rationalize these melt memory phenomena.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Gradient flow based phase-field modeling using separable neural networks

Allen–Cahn equation is a reaction–diffusion equation and is widely used for modeling phase separation. Machine learning methods for solving the Allen–Cahn equation in its strong form suffer from inaccuracies in collocation techniques, errors in computing higher-order spatial derivatives, and the large system size required by the space–time approach. To overcome these challenges, we propose solving the gradient flow of the Ginzburg–Landau free energy functional, which is equivalent to the Allen–Cahn equation, thereby avoiding the second-order spatial derivatives associated with the Allen–Cahn equation. A minimizing movement scheme is employed to solve the gradient flow problem, eliminating the complexities of a space–time approach. We utilize a separable neural network that efficiently represents the phase field through low-rank tensor decomposition. As we use the minimizing movement scheme to numerically solve the gradient flow problem, we thus, refer to the proposed method as the Separable Deep Minimizing Movement (SDMM) method. The evaluation of the functional in the minimizing movement scheme using the Gauss quadrature technique bypasses the inaccuracies associated with collocation techniques traditionally used to solve partial differential equations. A hyperbolic tangent transformation is introduced on the phase field prior to the evaluation of the functional to ensure that it remains strictly bounded within the values of the two phases. For this transformation, theoretical guarantee for energy stability of the minimizing movement scheme is established. Our results suggest that this transformation helps to improve the accuracy and efficiency significantly. The proposed method resolves the challenges faced by state-of-the-art machine learning techniques, outperforming them in both accuracy and efficiency. It is also the first machine learning method to achieve an order of magnitude speed improvement over the finite element method. In addition to its formulation and computational implementation, several case studies illustrate the applicability of the proposed method.

42 ENGINEERING↗
DOE OSTI2025

SwinCell: a 3D transformer and flow-based framework for improved cell segmentation

Segmentation of three-dimensional (3D) cellular images is fundamental for studying and understanding cell structure and function. However, 3D cellular segmentation is challenging, particularly for dense cells and tissues. This challenge arises mainly from the complex contextual information within 3D images, anisotropic properties, and the sensitivity to internal cellular structures, which often lead to incorrect segmentation. In this work, we introduce SwinCell, a 3D transformer-based framework that leverages Swin-transformer to predict flow and differentiate individual cell instances. We demonstrate SwinCell’s utility in the segmentation of nuclei, colon tissue cells, and densely cultured cells. SwinCell strikes a balance between maintaining detailed local feature recognition and understanding broader contextual information. Through extensive testing with both public and in-house 3D cell imaging datasets, SwinCell shows utility in segmenting dense cells, making it a valuable tool for 3D segmentation in cellular analysis that could expedite research in cell biology and tissue engineering.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2026

Neural operator transformers capture bifurcating drift-wave turbulence in fusion plasma simulations

Self-consistent modeling of turbulence-driven transport is critical for optimizing confinement in magnetically confined fusion plasmas, such as tokamaks and stellarators. In particular, capturing the long-term co-evolution of turbulence, flow, and background plasma profiles remains computationally challenging. Direct numerical simulation of these multiscale, highly nonlinear processes is often demanding and impractical for real-time control or design optimization. To address this bottleneck, we investigate transformer-based neural operator partial differential equation surrogates for emulating the dynamics of drift-wave turbulence bifurcation mediated by zonal flows, using the modified Hasegawa–Wakatani (MHW) model as a prototypical system. We find that the finetuned neural operator model has excellent performance in capturing the multi-spatiotemporal-scales of MHW turbulence bifurcation and is robust to testing on rare and out-of-distribution dynamics. Specifically, we demonstrate that a single unified model accurately predicts both quasi-steady-state turbulence and a wide range of dynamical transition processes, such as nonlinear saturation, spontaneous suppression of turbulence, and the emergence of macroscopic zonal flows, over time horizons vastly exceeding the local turbulence correlation time. This computationally efficient approach establishes a strong foundation for fast, AI-based modeling of complex, multiscale phenomena in magnetized fusion plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Forecasting high-dimensional spatio-temporal systems from sparse measurements

This paper introduces a new neural network architecture designed to forecast high-dimensional spatio-temporal data using only sparse measurements. The architecture uses a two-stage end-to-end framework that combines neural ordinary differential equations (NODEs) with vision transformers. Initially, our approach models the underlying dynamics of complex systems within a low-dimensional space; and then it reconstructs the corresponding high-dimensional spatial fields. Many traditional methods involve decoding high-dimensional spatial fields before modeling the dynamics, while some other methods use an encoder to transition from high-dimensional observations to a latent space for dynamic modeling. In contrast, our approach directly uses sparse measurements to model the dynamics, bypassing the need for an encoder. This direct approach simplifies the modeling process, reduces computational complexity, and enhances the efficiency and scalability of the method for large datasets. We demonstrate the effectiveness of our framework through applications to various spatio-temporal systems, including fluid flows and global weather patterns. Although sparse measurements have limitations, our experiments reveal that they are sufficient to forecast system dynamics accurately over long time horizons. Our results also indicate that the performance of our proposed method remains robust across different sensor placement strategies, with further improvements as the number of sensors increases. This robustness underscores the flexibility of our architecture, particularly in real-world scenarios where sensor data is often sparse and unevenly distributed.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Development of Fixtures and Methods to Assess the Durability of Balance of Systems Components

The degradation of photovoltaic (PV) balance of systems (BoS) components is not well studied, but the consequences include offline modules, strings, and inverters; system shutdown; arc faults; and fires. A utility provider experienced a ~30% failure rate in their power transfer chain, originally attributed to branch connectors. Field-failed specimen assemblies were, therefore, examined, consisting of cable connector, branch connector, and discrete fuse components. In this study, unused field-vintage specimens are examined using a benchtop prototype fixture to identify the most influential environmental stressors on BoS components as well as the effect of external mechanical perturbation. The prototype fixture was used to develop a perturbation capability for future use in the combined-accelerated stress testing chamber. The benchtop experiments were also used to develop the in-situ data acquisition of specimen current, voltage, and temperature. A significant increase in operating temperature (~100 °C from ~40 °C) and a different failure mode (arcing at the metal pins rather than overheating of the fuse filament) were observed promptly once periodic mechanical perturbation was applied. The current at failure was decreased from 35 A (measured for static specimens, with failure occurring in the fuses) to 15 A (for tests with mechanical perturbation, with failure at the male/female metal pin connection). After initial examination using X-ray computed tomography, the external plastic was machined away from failed specimens to allow for failure analysis, including the extraction of the internal convolute springs for morphological examination (optical and electron microscopy). Chemical composition analysis included energy-dispersive X-ray spectroscopy, differential scanning calorimetry, and Fourier transform infrared spectroscopy.

14 SOLAR ENERGY↗