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DOE OSTI2024

A taxonomy of automatic differentiation pitfalls

Automatic differentiation is a popular technique for computing derivatives of computer programs. While automatic differentiation has been successfully used in countless engineering, science, and machine learning applications, it can sometimes nevertheless produce surprising results. In this paper, we categorize problematic usages of automatic differentiation, and illustrate each category with examples such as chaos, time-averages, discretizations, fixed-point loops, lookup tables, linear solvers, and probabilistic programs, in the hope that readers may more easily avoid or detect such pitfalls. We also review debugging techniques and their effectiveness in these situations.

Autodiff↗

DOE OSTI2021

Non-intrusive data-driven model reduction for differential–algebraic equations derived from lifting transformations

In this paper we present a non-intrusive data-driven approach for model reduction of nonlinear systems. The approach considers the particular case of nonlinear partial differential equations (PDEs) that form systems of partial differential–algebraic equations (PDAEs) when lifted to polynomial form. Such systems arise, for example, when the governing equations include Arrhenius reaction terms (e.g., in reacting flow models) and thermodynamic terms (e.g., the Helmholtz free energy terms in a phase-field solidification model). Using the known structured form of the lifted algebraic equations, the approach computes the reduced operators for the algebraic equations explicitly, using straightforward linear algebra operations on the basis matrices. The reduced operators for the differential equations are inferred from lifted snapshot data using operator inference, which solves a linear least squares regression problem. The approach is illustrated for the nonlinear model of solidification of a pure material. The lifting transformations reformulate the solidification PDEs as a system of PDAEs that have cubic structure. The operators of the lifted system for this solidification example have affine dependence on key process parameters, permitting us to learn a parametric reduced model with operator inference. Numerical experiments show the effectiveness of the resulting reduced models in capturing key aspects of the solidification dynamics.

42 ENGINEERING↗

DOE OSTI2023

Learning subgrid-scale models with neural ordinary differential equations

We propose a new approach to learning the subgrid-scale model when simulating partial differential equations (PDEs) solved by the method of lines and their representation in chaotic ordinary differential equations, based on neural ordinary differential equations (NODEs). Solving systems with fine temporal and spatial grid scales is an ongoing computational challenge, and closure models are generally difficult to tune. Machine learning approaches have increased the accuracy and efficiency of computational fluid dynamics solvers. In this approach neural networks are used to learn the coarse- to fine-grid map, which can be viewed as subgrid-scale parameterization. We propose a strategy that uses the NODE and partial knowledge to learn the source dynamics at a continuous level. Our method inherits the advantages of NODEs and can be used to parameterize subgrid scales, approximate coupling operators, and improve the efficiency of low-order solvers. Numerical results with the two-scale Lorenz 96 ODE, the convection-diffusion PDE, and the viscous Burgers' PDE are used to illustrate this approach.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Collocation methods for nonlinear differential equations on low-rank manifolds

We introduce new methods for integrating nonlinear differential equations on low-rank manifolds. These methods rely on interpolatory projections onto the tangent space, enabling low-rank time integration of vector fields that can be evaluated entry-wise. A key advantage of our approach is that it does not require the vector field to exhibit low-rank structure, thereby overcoming significant limitations of traditional dynamical low-rank methods based on orthogonal projection. To construct the interpolatory projectors, we develop a sparse tensor sampling algorithm based on the discrete empirical interpolation method (DEIM) that parameterizes tensor train manifolds and their tangent spaces with cross interpolation. Using these projectors, we propose two time integration schemes on low-rank tensor train manifolds. The first scheme integrates the solution at selected interpolation indices and constructs the solution with cross interpolation. The second scheme generalizes the well-known orthogonal projector-splitting integrator to interpolatory projectors. We demonstrate the proposed methods with applications to several tensor differential equations arising from the discretization of partial differential equations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Improved evaluation of safeguards parameters from spent fuel measurements with the Differential Die-Away (DDA) instrument

The Differential Die-Away (DDA) technique is a highly sensitive non-destructive assay method for characterizing and detecting the presence of fissile material within an item of interest. DDA utilizes a series of pulses from a neutron generator (NG) to actively interrogate an item of interest. The die-away time of the neutron population induced by this active interrogation and the integral of the total differential die-away signal can be used to characterize items such as nuclear waste drums and spent nuclear fuel assemblies. In this work, Los Alamos National Laboratory (LANL) conceptualized, designed, and fabricated a DDA instrument that was deployed for field test measurements at the Central Interim Storage Facility for Spent Nuclear Fuel (Clab) in Oskarshamn, Sweden. The instrument performed multiple static measurements at fixed locations and dynamic axial scans of 15 pressurized water reactor (PWR) and 10 boiling water reactor (BWR) spent fuel assemblies, collecting both passive and active measurement data. The static assays of the assemblies measured the differential die-away signal, die-away time, and total passive neutron emission rate to create calibration curves for the evaluation of assembly multiplication, burnup, initial enrichment, effective fissile mass, and total elemental plutonium mass. Each calibration curve was optimized by minimizing the relative root mean square error (RRMSE) of assembly assay results compared to declared assembly parameters. The same quantities were also measured with the axial scans, and the resulting data were applied in two ways: (1) in the creation of calibration curves to improve evaluation of the same safeguards parameters as static assays, and (2) for comparison to simulation. In most cases, across both PWR and BWR assemblies, axial scan data improved the estimation of the above parameters, quantified by decreasing the calibration curve RRMSE. These axial scan results demonstrate the ability of the DDA instrument and analysis method to characterize spent PWR and BWR fuel as well as, or better than, a static assay of the same assembly. Furthermore, the DDA instrument’s unique ability to obtain both active and passive data in a single, axial scan of an entire spent fuel assembly represents a more efficient and accurate way of assaying spent fuel for verification purposes. These results represent a significant advancement for characterizing spent nuclear fuel compared to current technologies.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2021

Optimized simple and affordable procedure for differentiation of monocyte-derived dendritic cells from LRF: An accessible and valid alternative biological source

Dendritic cells are one of the most popular immune cells, which plays a remarkable role in both immunotherapy and tolerance induction. Due to unwanted side effects of leukocyte presence in donated blood, the policy of blood service is the pre-storage reduction of leukocytes, which today, filtration is the most common method for this purpose. The filtration method has led to diminished access to Buffy coat as a generally used conventional source of biological cells. We developed a simple, affordable, and reproducible method for dendritic cell differentiation from filter-derived monocytes and, the results of the filter study were compared with differentiated DCs from the conventional buffy coat-derived monocytes. The Monocytes were recovered from leukoreduction filter using an optimized protocol with supplemented PBS buffer. Following the adhesion method, CD14{sup +} Monocyte-enriched population with the purity of 94 % was obtained. After cytokine stimulation over a 6-day period and maturation induction by LPS, differentiated DCs were evaluated for morphology, surface markers (CD86, CD40, CD83 and, HLA-DR), antigen uptake potency and IL-12 secretion. Analysis and comparison of the results represented no significant difference between the two groups. Accordingly, we conclude that leukoreduction filters could be introduced as a reliable and research-grade source of monocyte for DC generation in biological research.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2020

Coupled Time-Lapse Full-Waveform Inversion for Subsurface Flow Problems Using Intrusive Automatic Differentiation

We describe a novel framework for estimating subsurface properties, such as rock permeability and porosity, from time-lapse observed seismic data by coupling full-waveform inversion (FWI), subsurface flow processes, and rock physics models. For the inverse modeling, we handle the back propagation of gradients by an intrusive automatic differentiation strategy that offers three levels of user control: (1) At the wave physics level, we adopted the discrete adjoint method in order to use our existing high-performance FWI code; (2) at the rock physics level, we used built-in automatic differentiation operators from the TensorFlow backend; (3) at the flow physics level, we implemented customized partial differential equation (PDE) operators for the multiphase flow equations. The three-level coupled inversion strategy strikes a good balance between computational efficiency and programming efforts, and when the gradients are chained together, it constitutes a coupled inverse system. Our numerical experiments demonstrate that the three-level coupled inverse problem is superior in terms of accuracy to a traditional decoupled inversion strategy. Additionally, our method is able to simultaneously invert for parameters in empirical relationships such as the rock physics models. Our proposed inverted model can be used for reservoir performance prediction and reservoir management/optimization purposes.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Qualitative and quantitative enhancement of parameter estimation for model-based diagnostics using automatic differentiation with an application to inertial fusion

Parameter estimation using observables is a fundamental concept in the experimental sciences. Mathematical models that represent the physical processes can enable reconstructions of the experimental observables and greatly assist in parameter estimation by turning it into an optimization problem which can be solved by gradient-free or gradient-based methods. In this work, the recent rise in flexible frameworks for developing differentiable scientific computing programs is leveraged in order to dramatically accelerate data analysis of a common experimental diagnostic relevant to laser–plasma and inertial fusion experiments, Thomson scattering. A differentiable Thomson-scattering data analysis tool is developed that uses reverse-mode automatic differentiation (AD) to calculate gradients. By switching from finite differencing to reverse-mode AD, three distinct outcomes are achieved. First, gradient descent is accelerated dramatically to the extent that it enables near real-time usage in laser–plasma experiments. Second, qualitatively novel quantities which require $\mathcal{O}(10^3)$ parameters can now be included in the analysis of data which enables unprecedented measurements of small-scale laser–plasma phenomena. Third, uncertainty estimation approaches that leverage the value of the Hessian become accurate and efficient because reverse-mode AD can be used for calculating the Hessian.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Correspondence between open bosonic systems and stochastic differential equations

Bosonic mean-field theories can approximate the dynamics of systems of $n$ bosons provided that $n \gg 1$. Here, we show that there can also be an exact correspondence at finite $n$ when the bosonic system is generalized to include interactions with the environment and the mean-field theory is replaced by a stochastic differential equation. When the $n \to \infty$ limit is taken, the stochastic terms in this differential equation vanish, and a mean-field theory is recovered. Besides providing insight into the differences between the behavior of finite quantum systems and their classical limits given by $n \to \infty$, the developed mathematics can provide a basis for quantum algorithms that solve some stochastic nonlinear differential equations. We discuss conditions on the efficiency of these quantum algorithms, with a focus on the possibility for the complexity to be polynomial in the log of the stochastic system size. A particular system with the form of a stochastic discrete nonlinear Schrödinger equation is analyzed in more detail.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Fast Computational Algorithms for Partial Differential Equations and Uncertainty Quantifications

This project concerned the construction, testing and analysis of computational algorithms for solving parameterized and stochastic partial differential equations. The study and understanding of equations of this type is of fundamental importance in numerous engineering and scientific applications. Examples include simulation of plasma dynamics in models of electric propulsion and nuclear fusion, simulation of multiphase flows, such as the flow of water, gas and oil in reservoirs, and structural analysis of the dependence of structures on materials. Parametrization is used in such settings when properties of the models such as viscosity of fluids or electric resistivity of materials are not precisely understood and instead are treated as random variables. The resulting solutions are themselves random, and having such solutions will enable engineers to use probabilistic methods to assess the likelihood of events, for example, whether a pollutant in a liquid will exceed a limit, and to use such analyses to develop ways to ensure positive outcomes. Construction of accurate (high resolution) computational solutions is expensive, requiring significant computer time and computational resources, and there is need to reduce computational cost to make simulation useful and effective. The aim of the project was to construct algorithms to efficiently compute surrogate solutions to parameterized problems to allow for efficient and accurate simulation. The technical approach used focused on two related strategies, based on rank-reduction methods and reduced-order models. These methods construct surrogate solutions of parameter-dependent models by projection or interpolation into low-dimensional approximation spaces. Cost savings are achieved if the low-dimensional spaces can be identified and constructed efficiently and if the resulting low-dimensional algebraic systems can be solved cheaply. Accomplishments include: Theoretical and empirical demonstration of the effectiveness of fast multigrid solution strategies for computing low-rank representations of parameter-dependent solutions to discrete partial differential equations, including the first proof establishing so-called textbook convergence properties for low-rank methods. Development of efficient solution algorithms for solving nonlinear parameter-dependent partial differential equations used in models of fluid dynamics. Developent of efficient algorithms for low-rank representation of solutions of time-dependent simulations of fluid dynamics using multi-dimensional tensor representations of solutions.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1990

Morphometric analysis of epidermal differentiation in primary roots of Zea mays

Epidermal differentiation in primary roots of Zea mays was divided into six cell types based on cellular shape and cytoplasmic appearance. These six cell types are: 1) apical protoderm, located at the tip of the root pole and characterized by periclinally flattened cells; 2) cuboidal protoderm, located approximately 230 microns from the root pole and characterized by cuboidal cells; 3) tabular epidermis, located approximately 450 microns from the root pole and characterized by anticlinally flattened cells; 4) cuboidal epidermis, located approximately 900 microns from the root pole and characterized by cuboidal cells having numerous small vacuoles; 5) vacuolate cuboidal epidermis, located approximately 1,500 microns from the root pole and characterized by cuboidal cells containing several large vacuoles; and 6) columnar epidermis, located approximately 2,200 microns from the root pole (i.e., at the beginning of the zone of elongation) and characterized by elongated cells. We also used stereology to quantify the cellular changes associated with epidermal differentiation. The quiescent center and the apical protoderm have significantly different ultrastructures. The relative volume of dictyosomes increases dramatically during the early stages of epidermal differentiation. This increase correlates inversely with the amount of coverage provided by the root cap and mucilage.

NASA Discipline Plant Biology↗

NASA NTRS2000

Growth and differentiation of human lens epithelial cells in vitro on matrix

PURPOSE: To characterize the growth and maturation of nonimmortalized human lens epithelial (HLE) cells grown in vitro. METHODS: HLE cells, established from 18-week prenatal lenses, were maintained on bovine corneal endothelial (BCE) extracellular matrix (ECM) in medium supplemented with basic fibroblast growth factor (FGF-2). The identity, growth, and differentiation of the cultures were characterized by karyotyping, cell morphology, and growth kinetics studies, reverse transcription-polymerase chain reaction (RT-PCR), immunofluorescence, and Western blot analysis. RESULTS: HLE cells had a male, human diploid (2N = 46) karyotype. The population-doubling time of exponentially growing cells was 24 hours. After 15 days in culture, cell morphology changed, and lentoid formation was evident. Reverse transcription-polymerase chain reaction (RT-PCR) indicated expression of alphaA- and betaB2-crystallin, fibroblast growth factor receptor 1 (FGFR1), and major intrinsic protein (MIP26) in exponential growth. Western analyses of protein extracts show positive expression of three immunologically distinct classes of crystallin proteins (alphaA-, alphaB-, and betaB2-crystallin) with time in culture. By Western blot analysis, expression of p57(KIP2), a known marker of terminally differentiated fiber cells, was detectable in exponential cultures, and levels increased after confluence. MIP26 and gamma-crystallin protein expression was detected in confluent cultures, by using immunofluorescence, but not in exponentially growing cells. CONCLUSIONS: HLE cells can be maintained for up to 4 months on ECM derived from BCE cells in medium containing FGF-2. With time in culture, the cells demonstrate morphologic characteristics of, and express protein markers for, lens fiber cell differentiation. This in vitro model will be useful for investigations of radiation-induced cataractogenesis and other studies of lens toxicity.

Non-NASA Center↗

NASA NTRS1993

Cell proliferation and differentiation in chemical leukemogenesis

In tissues such as bone marrow with normally high rates of cell division, proliferation is tightly coordinated with cell differentiation. Survival, proliferation and differentiation of early hematopoietic progenitor cells depend on the growth factors, interleukin 3 (IL-3) and/or granulocyte-macrophage colony stimulating factor (GM-CSF) and their synergism with other cytokines. We provide evidence that a characteristic shared by a diverse group of compounds with demonstrated leukemogenic potential is the ability to act synergistically with GM-CSF. This results in an increase in recruitment of a resting population of hematopoietic progenitor cells normally unresponsive to the cytokine and a twofold increase in the size of the proliferating cell population normally regarded to be at risk of transformation in leukemogenesis. These findings support the possibility that transient alterations in hematopoietic progenitor cell differentiation may be an important factor in the early stages of development of leukemia secondary to chemical or drug exposure.

Non-NASA Center↗

NASA NTRS1992

Morphologic differentiation of colon carcinoma cell lines HT-29 and HT-29KM in rotating-wall vessels

A new low shear stress microcarrier culture system has been developed at NASA's Johnson Space Center that permits three-dimensional tissue culture. Two established human colon adenocarcinoma cell lines, HT-29, an undifferentiated, and HT-29KM, a stable, moderately differentiated subline of HT-29, were grown in new tissue culture bioreactors called Rotating-Wall Vessels (RWVs). RWVs are used in conjunction with multicellular cocultivation to develop a unique in vitro tissue modeling system. Cells were cultivated on Cytodex-3 microcarrier beads, with and without mixed normal human colonic fibroblasts, which served as the mesenchymal layer. Culture of the tumor lines in the absence of fibroblasts produced spheroidlike growth and minimal differentiation. In contrast, when tumor lines were co-cultivated with normal colonic fibroblasts, initial growth was confined to the fibroblast population until the microcarriers were covered. The tumor cells then commenced proliferation at an accelerated rate, organizing themselves into three-dimensional tissue masses that achieved 1.0- to 1.5-cm diameters. The masses displayed glandular structures, apical and internal glandular microvilli, tight intercellular junctions, desmosomes, cellular polarity, sinusoid development, internalized mucin, and structural organization akin to normal colon crypt development. Differentiated samples were subjected to transmission and scanning electron microscopy and histologic analysis, revealing embryoniclike mesenchymal cells lining the areas around the growth matrices. Necrosis was minimal throughout the tissue masses. These data suggest that the RWV affords a new model for investigation and isolation of growth, regulatory, and structural processes within neoplastic and normal tissue.

Colonic Neoplasms/pathology↗

NASA NTRS2004

Design of an Auto-zeroed, Differential, Organic Thin-film Field-effect Transistor Amplifier for Sensor Applications

Organic strain gauge and other sensors require high-gain, precision dc amplification to process their low-level output signals. Ideally, amplifiers would be fabricated using organic thin-film field-effect transistors (OTFT's) adjacent to the sensors. However, OTFT amplifiers exhibit low gain and high input-referred dc offsets that must be effectively managed. This paper presents a four-stage, cascaded differential OTFT amplifier utilizing switched capacitor auto-zeroing. Each stage provides a nominal voltage gain of four through a differential pair driving low-impedance active loads, which provide common-mode output voltage control. p-type pentacence OTFT's are used for the amplifier devices and auto-zero switches. Simulations indicate the amplifier provides a nominal voltage gain of 280 V/V and effectively amplifies a 1-mV dc signal in the presence of 500-mV amplifier input-referred dc offset voltages. Future work could include the addition of digital gain calibration and offset correction of residual offsets associated with charge injection imbalance in the differential circuits.

large-area electronics↗

NASA NTRS2017

Improving X-Ray Optics via Differential Deposition

Differential deposition, a post-fabrication figure correction technique, has the potential to significantly improve the imaging quality of grazing-incidence X-ray optics. DC magnetron sputtering is used to selectively coat the mirror in order to minimize the figure deviations. Custom vacuum chambers have been developed at NASA MSFC that will enable the implementation of the deposition on X-ray optics. A factor of two improvement has been achieved in the angular resolution of the full-shell X-ray optics with first stage correction of differential deposition. Current efforts are focused on achieving higher improvements through efficient implementation of differential deposition.

differential deposition grazing↗

DOE OSTI2024

SUNDIALS time integrators for exascale applications with many independent systems of ordinary differential equations

Many complex systems can be accurately modeled as a set of coupled time-dependent partial differential equations (PDEs). However, solving such equations can be prohibitively expensive, easily taxing the world’s largest supercomputers. One pragmatic strategy for attacking such problems is to split the PDEs into components that can more easily be solved in isolation. This operator splitting approach is used ubiquitously across scientific domains, and in many cases leads to a set of ordinary differential equations (ODEs) that need to be solved as part of a larger “outer-loop” time-stepping approach. The SUNDIALS library provides a plethora of robust time integration algorithms for solving ODEs, and the U.S. Department of Energy Exascale Computing Project (ECP) has supported its extension to applications on exascale-capable computing hardware. In this paper, we highlight some SUNDIALS capabilities and its deployment in combustion and cosmology application codes (Pele and Nyx, respectively) where operator splitting gives rise to numerous, small ODE systems that must be solved concurrently.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Single Bimodular Sensor for Differentiated Detection of Multiple Oxidative Gases

Semiconductive metal-oxide sensors suffer from cross-sensitivities under mixed chemical condition, specifically upon mixture of multiple oxidative or reductive gases. Herein, a single bimodular sensor is demonstrated for smart differentiation of multiple oxidative analytes by relating the resistance-metric mode to impedance-metric mode. The sensor construct based on ZnO nanorods readily outputs three response datasets upon exposure of oxidative-gas mixture including O 2 , SO 2 , and NO 2 , the resistance, real part impedance, and imaginary part impedance. The differentiative and correlated nature between these response signals allows such a single sensor platform to differentiate these oxidative gases accurately and robustly. Linear and non-linear decision boundaries are established over a large gas-concentration range from 2 ppm to 3% through a combination of principal component analysis and artificial neural network training. A facile user interface is demonstrated for recognition and measurement of unknown gas analytes, with the error of the predicted analyte-concentration as low as 2%.

36 MATERIALS SCIENCE↗