Search NASA⌕ Search

SEARCH · Search NASA

Results for “Exponential integrator”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Sparse Cholesky factorization for solving nonlinear PDEs via Gaussian processes

In recent years, there has been widespread adoption of machine learning-based approaches to automate the solving of partial differential equations (PDEs). Among these approaches, Gaussian processes (GPs) and kernel methods have garnered considerable interest due to their flexibility, robust theoretical guarantees, and close ties to traditional methods. They can transform the solving of general nonlinear PDEs into solving quadratic optimization problems with nonlinear, PDE-induced constraints. However, the complexity bottleneck lies in computing with dense kernel matrices obtained from pointwise evaluations of the covariance kernel, and its partial derivatives, a result of the PDE constraint and for which fast algorithms are scarce. The primary goal of this paper is to provide a near-linear complexity algorithm for working with such kernel matrices. We present a sparse Cholesky factorization algorithm for these matrices based on the near-sparsity of the Cholesky factor under a novel ordering of pointwise and derivative measurements. The near-sparsity is rigorously justified by directly connecting the factor to GP regression and exponential decay of basis functions in numerical homogenization. We then employ the Vecchia approximation of GPs, which is optimal in the Kullback-Leibler divergence, to compute the approximate factor. This enables us to compute ϵ-approximate inverse Cholesky factors of the kernel matrices with complexity O(N log d (N/ϵ)) in space and O(N log 2d (N/ϵ)) in time. We integrate sparse Cholesky factorizations into optimization algorithms to obtain fast solvers of the nonlinear PDE. We numerically illustrate our algorithm’s near-linear space/time complexity for a broad class of nonlinear PDEs such as the nonlinear elliptic, Burgers, and Monge-Ampère equations. In summary, we provide a fast, scalable, and accurate method for solving general PDEs with GPs and kernel methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A multiscale model to understand the interface chemistry, contacts, and dynamics during lithium stripping

A reversible Li-metal electrode, paired with a solid electrolyte, is critical for attaining higher energy density and safer batteries beyond the current lithium-ion cells. A stable stripping process may be even harder to attain as the stripping process will remove Li-atoms from the surface, and naturally reduce surface contact area, if not self-corrected by other mechanisms, such as diffusion and plastic deformation under an applied external stack pressure. Here, we capture these mechanisms occurring at multiple length- and time- scales, i.e., interface interactions, vacancy hopping, and plastic deformation, by integrating density functional theory (DFT) simulations, kinetic Monte Carlo (KMC), and continuum finite element method (FEM). By assuming the self-affine nature of multiscale contacts, we predict the steady-state contact area as a function of stripping current density, interface wettability, and stack pressure. We further estimate the exponential increase of overpotential due to contact area loss to maintain the same stripping current density. We demonstrate that a lithiophilic interface requires less stack pressure to reach the same steady-state contact area fraction than a lithiophobic interface. A “tolerable steady-state” contact area loss for maintaining stable stripping is estimated at 20 %, corresponding to a 10 % increase in overpotential. To constrain contact loss within the tolerance, the required stack pressure is 0.1, 0.5, and 2 times the yield strength of lithium metal for three distinct interfaces, lithiophilic Li/lithium oxide(Li2O), Li/lithium lanthanum zirconium oxide(LLZO), and lithiophoblic Li/lithium fluoride(LiF), respectively. The modeling results agree with experiments on the impact of the stack pressure quantitatively, while the discrepancy in stripping rate sensitivity is attributed to the simplifying interface interaction in our simulations. Overall, this multiscale simulation framework demonstrates the importance of electrochemical-mechanical coupling in understanding the dynamics of the Li/SE interface during stripping.

Feng, Min↗
DOE OSTI2026

From Rules to Reasoning: A Survey of Large Language Model-Based Approaches to Scientific Hypothesis and Idea Generation

Scientific hypothesis generation represents a fundamental challenge in contemporary research due to exponentially expanding literature volumes and increasing disciplinary specialization. Large language models (LLMs) have emerged as transformative tools for automated scientific discovery, moving beyond traditional rule-based and literature-mining approaches. Four paradigmatic approaches define current LLM-driven hypothesis generation: direct prompting and fine-tuning methods, knowledge-enhanced frameworks integrating retrieval-augmented generation (RAG), multi-agent collaborative systems simulating research teams, and reasoning-focused approaches implementing cognitive architectures. Domain-specific applications demonstrate statistical equivalence to human expert performance in social psychology, experimental validation in biomedical research, and near-expert quality in astronomy. Evaluation methodologies encompass human expert assessment, LLM-as-judge frameworks, and comprehensive benchmarking systems. Technical challenges include hallucination management, knowledge integration limitations, and balancing novelty with feasibility. Future directions emphasize hybrid neural-symbolic architectures and sophisticated human-AI collaboration models for responsible scientific discovery acceleration.

AI-driven discovery↗
DOE OSTI2026

Efficient and flexible multirate temporal adaptivity

In this work we present two new families of multirate time step adaptivity controllers, that are designed to work with embedded multirate infinitesimal (MRI) time integration methods for adapting time steps when solving problems with multiple time scales. We compare these controllers against competing approaches on two benchmark problems, showing that the proposed methods offer dramatically improved performance and flexibility. The combination of embedded MRI methods and the proposed controllers enable adaptive simulations of problems with a potentially arbitrary number of time scales, achieving high accuracy while maintaining low computational cost. Additionally, we introduce a new set of embeddings for the family of explicit multirate exponential Runge–Kutta (MERK) methods of orders 2 through 5, resulting in the first-ever fifth-order embedded MRI method. Finally, we compare the performance of a wide range of embedded MRI methods on our benchmark problems to provide guidance on how to select an appropriate MRI method and multirate controller.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Pyrolysis of high-density polyethylene: Degradation behaviors, kinetics, and product characteristics

Pyrolysis is a promising technology for converting plastic waste into valuable raw materials while offering a potential solution to the global plastic pollution crisis. In this study, the thermal pyrolysis of high-density polyethylene (HDPE) is investigated in a drop tube reactor under nearly isothermal conditions. The impact of reaction temperature and gas/volatile residence time on carbon conversion and product distribution is examined across a range of 500–900°C and 3.6–32.2s, respectively. Non-condensable gas products detected by online mass spectrometry are H 2 , CH 4 , C 2 H 4 , C 2 H 6 , C 3 H 6 , and C 3 H 8 . At elevated temperatures and prolonged residence time, H 2 yield reaches as high as 8.6 wt% of the initial HDPE mass due to intensified cracking reactions of C 2 –C 3 hydrocarbons and long-chain aliphatic compounds. Consequently, pyrolysis tars consist mainly of polycyclic aromatic hydrocarbons (PAHs) with 5–7 rings, accompanied by visible coke deposition within the reactor. HDPE decomposition to volatiles is an endothermic process and it is complete at a temperature between 492°C and 525°C, depending on the heating rate employed, from non-isothermal thermogravimetric analysis and differential scanning calorimetry (TGA-DSC) measurements. The thermal degradation of HDPE pellets follows the two-dimensional nucleation growth model for conversion levels up to 0.8 with an apparent activation energy of 259–270 kJ/mol and a pre-exponential factor of 4.83 × 10 17 –1.37 × 10 19 min -1 , determined from various isoconversional methods such as Flynn-Wall-Ozawa (FWO), Kissinger-Akahira-Sunose (KAS), and Starink, along with Criado's master plots. Further, these findings provide valuable insights into optimizing process parameters and refining reactor design for pyrolysis, which can be integrated with gasification and reforming processes to enhance hydrogen production on a larger scale.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Hadamard products and BPS networks

We study examples of fourth-order Picard-Fuchs operators that are Hadamard products of two second-order Picard-Fuchs operators. Each second-order Picard-Fuchs operator is associated with a family of elliptic curves, and the Hadamard product computes period integrals on the fibred product of the two elliptic surfaces. We construct 3-cycles on this geometry as the union of 2-cycles in the fibre over contours on the base. We then use the special Lagrangian condition to constrain the contours on the base. This leads to a construction that is reminiscent of spectral networks and exponential networks that have previously appeared in string theory literature.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Dehydroxylation kinetics of kaolinite and montmorillonite examined using isoconversional methods

The use of calcined clays as supplementary cementitious materials (SCMs) in concrete is a promising strategy towards decarbonizing the cement and concrete industry. This is especially relevant considering the ever-increasing demand for concrete. Comprehensive understanding of the kinetics of calcination is essential towards maximizing the potential reactivity of clay minerals while ensuring energy efficiency. In this study, the kinetics of the dehydroxylation of kaolinite and montmorillonite are investigated under non-isothermal conditions at constant heating rate. Activation energies ( E a ) are determined via Friedman differential and advanced Vyazovkin incremental methods over the isoconversional range; these are devoid of computational approximations, thus allowing kinetic analysis without assuming a specific reaction model. Kinetic equations—in the differential form as well as a combination of differential and integral forms are compared against the experimentally determined reaction models to identify the most probable dehydroxylation mechanism for kaolinite and montmorillonite. A reaction order mechanism is established for dehydroxylation of kaolinite, while montmorillonite is noted to undergo dehydroxylation via a single-step reversible diffusion-controlled process. Kinetic triplet—comprising activation energy, reaction model and pre-exponential factor—is used to predict isothermal calcination conditions, which is further verified using analytical techniques. Heat release rates of clay-portlandite blends from isothermal calorimetry are used within a thermodynamic framework to quantify reactivity of the calcined clays. Here, the study demonstrates a general approach based on isoconversional methods to predict calcination conditions for different clays that can be used in efficient and optimized production of blended cements or SCMs.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Streaming Readout and Data-Stream Processing With ERSAP

With the exponential growth in the volume and complexity of data generated at high-energy physics and nuclear physics research facilities, there is an imperative demand for innovative strategies to process this data in real or near-real-time. Given the surge in the requirement for high-performance computing, it becomes pivotal to reassess the adaptability of current data processing architectures in integrating new technologies and managing streaming data. This paper introduces the ERSAP framework, a modern solution that synergizes flow-based programming with the reactive actor model, paving the way for distributed, reactive, and high performance in data stream processing applications. Additionally, we unveil a novel algorithm focused on time-based clustering and event identification in data streams. The efficacy of this approach is further exemplified through the data-stream processing outcomes obtained from the recent beam tests of the EIC prototype calorimeter at DESY.

Vardan, Gyurjyan↗
DOE OSTI2025

Hybrid learning techniques for scientific data reduction with performance guarantees

The research initiatives supported by the U.S. Department of Energy (DOE) Grant DE-SC0022265 are fundamentally aimed at pioneering advanced machine learning (ML) techniques for scientific data compression within high-performance computing (HPC) environments. This comprehensive body of work addresses the critical challenge posed by the exponential growth of data generated by scientific simulations in domains such as fusion energy, climate modeling, and computational fluid dynamics (CFD). A core objective is to develop compression algorithms that achieve substantial data reduction—often by orders of magnitude—while rigorously ensuring the fidelity of both the primary data (PD) and scientifically crucial derived quantities of interest (QoI). The methodologies deployed under this grant integrate sophisticated deep learning architectures, prominently featuring autoencoders, advanced generative models like conditional diffusion, and hybrid learning techniques. Key innovations include the development of Guaranteed Autoencoders (GAE) and the Guaranteed Conditional Diffusion with Tensor Correction (GCDTC) framework, which provide explicit, instance-level error bounds on reconstructed data. Furthermore, specialized strategies such as nonlinear constraint satisfaction are employed to preserve the integrity of QoI, a vital requirement for the trustworthiness of downstream scientific analyses. This research also focuses on the design and implementation of scalable, GPU-accelerated software pipelines that seamlessly integrate into existing HPC workflows, ensuring both computational efficiency and practical applicability. The CAESAR framework, for example, unifies foundation and generative models to create an adaptive and efficient compression solution for spatio-temporal scientific data. Collectively, these efforts represent a significant advancement in mitigating the scientific data deluge, enabling more effective data management, accelerated scientific discovery, and optimized utilization of HPC resources.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Final report- UFL - RAPIDS2: A SciDAC Institute for Computer Science, Data, and Artificial Intelligence

The research initiatives supported by the U.S. Department of Energy (DOE) Grant DE-SC0022265 are fundamentally aimed at pioneering advanced machine learning (ML) techniques for scientific data compression within high-performance computing (HPC) environments. This comprehensive body of work addresses the critical challenge posed by the exponential growth of data generated by scientific simulations in domains such as fusion energy, climate modeling, and computational fluid dynamics (CFD). A core objective is to develop compression algorithms that achieve substantial data reduction—often by orders of magnitude—while rigorously ensuring the fidelity of both the primary data (PD) and scientifically crucial derived quantities of interest (QoI). The methodologies deployed under this grant integrate sophisticated deep learning architectures, prominently featuring autoencoders, advanced generative models like conditional diffusion, and hybrid learning techniques. Key innovations include the development of Guaranteed Autoencoders (GAE) and the Guaranteed Conditional Diffusion with Tensor Correction (GCDTC) framework, which provide explicit, instance-level error bounds on reconstructed data. Furthermore, specialized strategies such as nonlinear constraint satisfaction are employed to preserve the integrity of QoI, a vital requirement for the trustworthiness of downstream scientific analyses. This research also focuses on the design and implementation of scalable, GPU-accelerated software pipelines that seamlessly integrate into existing HPC workflows, ensuring both computational efficiency and practical applicability. The CAESAR framework, for example, unifies foundation and generative models to create an adaptive and efficient compression solution for spatio-temporal scientific data. Collectively, these efforts represent a significant advancement in mitigating the scientific data deluge, enabling more effective data management, accelerated scientific discovery, and optimized utilization of HPC resources.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Formation of the oxyl’s potential energy surface by the spectral kinetics of a vibrational mode

One of the most reactive intermediates for oxidative reactions is the oxyl radical, an electron-deficient oxygen atom. The discovery of a new vibration upon photoexcitation of the oxygen evolution catalysis detected the oxyl radical at the SrTiO3 surface. The vibration was assigned to a motion of the sub-surface oxygen underneath the titanium oxyl (Ti–O●−) created upon hole transfer to (or electron extraction from) a hydroxylated surface site. Evidence for such an interfacial mode is derived from its spectral shape, which exhibited a Fano resonance—a coupling of a sharp normal mode to continuum excitations. Here, this Fano resonance is utilized to derive precise formation kinetics of the oxyl radical and its associated potential energy surface (PES). From the Fano lineshape, the formation kinetics are obtained from the anti-resonance (the kinetics of the coupling factor), the resonance (the kinetics of the coupled continuum excitations), and the frequency integrated spectrum (the kinetics of the normal mode’s cross-section). All three perspectives yield logistic function growth with a half-rise of 2.3 ± 0.3 ps and a time constant of 0.48 ± 0.09 ps. A non-equilibrium transient associated with photoexcitation is separated from the rise of the equilibrated PES. The logistic function characterizes the oxyl coverage at the very initial stages (t ∼ 0) to have an exponential growth rate that quickly decreases toward zero as a limiting coverage is reached. Such time-dependent reaction kinetics identify a dynamic activation barrier associated with the formation of a PES and quantify it for oxyl radical coverage.

Chemistry↗
DOE OSTI2025

Bottom-Up Simulation, Reconstruction, and Quantification of Macromolecule Sequences from Experimental Polymerizations

Motivated by the canonical sequence–structure–function paradigm, tools to characterize chemical patterning in natural biomacromolecules, from proteins to nucleic acids, have grown exponentially in recent years. However, analogous strategies for synthetic macromolecules remain in nascent stages, complicated by sequence polydispersity and analytical limitations. To address this, we have developed a comprehensive and open-source Python package, PRISM (polymer rate insights and sequence modeling), an end-to-end workflow that provides a path from experimental kinetics measurements to quantitative and qualitative metrics for describing chemical patterning in stochastic polymers. First, a numerical integration strategy was constructed to simulate and fit experimental data from reversible addition–fragmentation chain transfer (RAFT) polymerization kinetics, enabling the facile estimation of relevant reactivity ratios. These ratios were then used in a mechanism-specific stochastic kinetic simulation strategy to simulate sequence ensembles corresponding to model systems spanning experimental copolymers, classes of statistical polymers (e.g., alternating, block, and gradient), and multiblock copolymers. Lastly, inspired by sequence homology metrics from bioinformatics, we introduce visualization strategies and quantitative metrics to facilitate comparisons of different sequence ensembles. As the sequence–structure–function paradigm becomes increasingly central in de novo design of synthetic macromolecules, this toolkit provides a first step toward accurate and representative sequence description and featurization.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

ENSO Recharge Oscillator Theory Integrating the Southward Wind Shift

The El Niño–Southern Oscillation (ENSO) is one of the most‐well understood climate phenomena, and the Recharge Oscillator (RO) theory is widely used to conceptualize its physics in observations and models. ENSO‐associated equatorial zonal wind anomalies shift southward in boreal winter, contributing to ENSO termination. Thus far, this effect has not been explicitly described in the RO framework. Here we derive a new form of the RO under the low‐frequency limit that incorporates the seasonal migration of zonal wind anomalies. In our theory, the Bjerknes feedback depends on the central latitude of zonal wind anomalies, decaying exponentially as winds shift away from the equator. Meanwhile, wind anomalies centered off the equator induce equatorial wave adjustment and thereby have a delayed effect on sea surface temperature anomalies. A stochastic RO simulation with a prescribed wind shift reproduces about half the amplitude of ENSO seasonal synchronization as well as ENSO combination tones.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

The gravitational path integral from an observer’s point of view

One of the fundamental problems in quantum gravity is to describe the experience of a gravitating observer in generic spacetimes. In this paper, we develop a framework for describing non-perturbative physics relative to an observer using the gravitational path integral. We apply our proposal to an observer that lives in a closed universe and one that falls behind a black hole horizon. We find that the Hilbert space that describes the experience of the observer is much larger than the Hilbert space in the absence of an observer. In the case of closed universes, the Hilbert space is not one-dimensional, as calculations in the absence of the observer suggest. Rather, its dimension scales exponentially with ${G}_{N}^{-1}$. Similarly, from an observer’s perspective, the dimension of the Hilbert space in a two-sided black hole is increased. We compute various observables probing the experience of a gravitating observer in this Hilbert space. We find that an observer experiences non-trivial physics in the closed universe in contrast to what it would see in a one-dimensional Hilbert space. In the two-sided black hole setting, our proposal implies that non-perturbative corrections to effective field theory for an infalling observer are suppressed until times exponential in the black hole entropy, resolving a recently-raised puzzle in black hole physics. While the framework that we develop is exemplified in the toy-model of JT gravity, most of our analysis can be extended to higher dimensions and, in particular, to generic spacetimes not admitting a conventional holographic description, such as cosmological universes or black hole interiors.

2D gravity↗
DOE OSTI2025

A consumer-centric approach to quantify efficiency of receiving goods purchased via online

Virtual participation in shopping activities has increased exponentially in the past four years compared to the last couple of decades. E-tailing or online shopping offers the convenience of goods reaching a consumer instead of a consumer traveling to a store, but it has downsides like geographical service variability and negative social externalities such as increased energy consumption and emissions. This study proposes a novel approach to quantify e-tailing efficiency from the consumers’ viewpoint. The methodology is innovative in its integration of accessibility theory with energy and cost impedance factors and consideration of delivering and picking up goods purchased via online. The methodology is implemented for the San Francisco Bay Area and is subject to scenarios that see enhancements to various facets of online shopping delivery. Results demonstrate that increasing the frequency of e-commerce deliveries helps improve e-tailing efficiency in rural locations, while improvements in energy and cost aspects of delivery modes are seen to improve e-tailing efficiencies in the central parts of the region. The approach proposed can provide valuable insights on where people have limited benefits from online shopping and how emerging delivery mechanisms can change the quality of the e-commerce experience within a city. This research offers a replicable framework for assessing e-commerce systems in diverse geographic contexts, contributing to the development of equitable and environmentally sustainable urban freight systems.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2025

Modeling Cyber Supply Chain Incidents with Multilayered Graph Motifs

As noted within the literature, supply chain includes people and organizations---manufacturers, integrators, and third-party vendors---that are involved in one or more stages of a product lifecycle. Since supply chains, by definition, include organizations and people, supply chain risk management activities must consider dependencies between an organization's business processes and third-party resources. Just as adversarial tactics can be implemented via techniques implemented via networked computer systems, so can such tactics be expressed via legal business relationships. A cyber incident may have an exponential impact downstream, for example, by leveraging a product's distribution channel (e.g. malicious updates in SolarWinds, buggy updates in CrowdStrike). Similarly, legitimate and legal business relationships also affect the attack surface exposure of systems, enabling long-term persistence and/or unknown impacts to product quality that are hard to detect. This paper catalogs several recent digital supply chain incidents and applies a multilayered network formalism to develop structural indicators (graph motifs) that reflect potentially-adversarial behavior. Finally, we compare and contrast the characteristics of adversarial tactics (e.g. Loss of Availability, Data Collection) that leverage cyber-physical dependencies to those that leverage legal organizational relationships.

97 - MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Blockchain-Enabled Secure Device-to-Device Communication in Software-Defined Networking

The Internet of Things (IoT) continues to increase the demand for seamless communication among IoT devices. The rapid growth of IoT devices has led to an exponential increase in device-to-device (D2D) communication within the Software-Defined Networking (SDN), though it enables a flexible archi-tecture for managing network resources. However, traditional security models face challenges (e.g., Security, privacy, and trust) in addressing the dynamic and decentralized nature of these communications. Despite of these challenges, this paper proposes a novel approach that leverages blockchain technology to enhance the security, privacy, and trustworthiness of D2D communication within an SDN environment. The proposed approach integrates blockchain nodes in sDN components to establish a decentralized ledger for transparent and verifiable records. Smart contracts enforce authentication rules to ensure that only authenticated devices can access the network and engage in transactions securely. It also automates the security policies to ensure temper resistance execution using the cryptographic mechanism for data integrity and authentic communication. The Implementation of the proposed algorithms validates the resilience of the proposed approach against cyberattacks. Overall, the proposed approach enables efficient and secure D2D communication for resilient SDN infrastructure in IoT ecosystems.

Das, Debashis↗
DOE OSTI2024

Electroweak three-body decays in the presence of two- and three-body bound states

Recently, formalism has been derived for studying electroweak transition amplitudes for three-body systems both in infinite and finite volumes. The formalism provides exact relations that the infinite-volume amplitudes must satisfy, as well as a relationship between physical amplitudes and finite-volume matrix elements, which can be constrained from lattice QCD calculations. This formalism poses additional challenges when compared with the analogous well-studied two-body equivalent one, including the necessary step of solving integral equations of singular functions. In this work, we provide some non-trivial analytical and numerical tests on the aforementioned formalism. In particular, we consider a case where the three-particle system can have three-body bound states as well as bound states in the two-body subsystem. For kinematics below the three-body threshold, we demonstrate that the scattering amplitudes satisfy unitarity. We also check that for these kinematics the finite-volume matrix elements are accurately described by the formalism for two-body systems up to exponentially suppressed corrections. Finally, we verify that in the case of the three-body bound state, the finite-volume matrix element is equal to the infinite-volume coupling of the bound state, up to exponentially suppressed errors.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗