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Results for “multistep methods”
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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Interface flux recovery framework for constructing partitioned heterogeneous time-integration methods
A common approach for the development of partitioned schemes employing different time integrators on different subdomains is to lag the coupling terms in time. This can lead to accuracy issues, especially in multistage methods. Here, in this article, we present a novel framework for partitioned heterogeneous time-integration methods, which allows the coupling of arbitrary multistage and multistep methods without reducing their order of accuracy. At the core of our approach are accurate estimates of the interface flux obtained from the Schur complement of an auxiliary monolithic system. We use these estimates to construct a polynomial-in-time approximation of the interface flux over the current time coupling window. This approximation provides the interface boundary conditions necessary to decouple the subdomain problems at any point within the coupling window. In so doing our framework enables a flexible choice of time-integrators for the individual subproblems without compromising the time-accuracy at the coupled problem level. This feature is the main distinction between our framework and other approaches. To demonstrate the framework, we construct a family of partitioned heterogeneous time-integration methods, combining multistage and multistep methods, for a simplified tracer transport component of the coupled air-sea system in Earth system models. We report numerical tests evaluating accuracy and flux conservation for different pairs of time-integrators from the explicit Runge-Kutta and Adams-Moulton families.
SDYN-GANs: Adversarial learning methods for multistep generative models for general order stochastic dynamics
We introduce adversarial learning methods for data-driven generative modeling of dynamics of nth-order stochastic systems. Our approach builds on Generative Adversarial Networks (GANs) with generative model classes based on stable m-step stochastic numerical integrators. From observations of trajectory samples, we introduce methods for learning long-time predictors and stable representations of the dynamics. Our approaches use discriminators based on Maximum Mean Discrepancy (MMD), training protocols using both conditional and marginal distributions, and methods for learning dynamic responses over different time-scales. We show how our approaches can be used for modeling physical systems to learn force-laws, damping coefficients, and noise-related parameters. Our adversarial learning approaches provide methods for obtaining stable generative models for dynamic tasks including long-time prediction and developing simulations for stochastic systems.
Equilibrium-gated pattern formation: How molecular dissociation thermodynamics drive emergent behavior in dissipative polymeric systems
Emergent patterns in biological systems arise through dissipative processes that balance reaction and transport phenomena, producing highly functional properties from self-regulating mechanisms. Synthetic fabrication, by contrast, often relies on user-controlled, multistep methods that lack the self-organizing capabilities of natural systems. Inspired by nature, we sought chemical systems that integrate strongly coupled reaction and transport phenomena, identifying frontal ring-opening metathesis polymerization (FROMP) as a method capable of creating diverse forms and functions through reactive processing. By employing discrete molecular initiators, FROMP allows precise control of key reaction steps—inhibition, initiation, and propagation. Using an integrated computational and experimental framework, we uncover how near-equilibrium inhibition dynamics, coupled with far-from-equilibrium reaction kinetics, drive pattern formation in frontally polymerized synthetic materials. We propose the concept of equilibrium-gated pattern formation, demonstrating how initiator chemistry can be tuned to achieve programmable macroscale properties. Our study reveals a surprising insight: Emergent behavior in FROMP systems arises from the inhibition-dominated regime of resin composition, expanding prior observations that such behavior is confined to a narrow compositional space near the boundary between front quenching and uniform front propagation. We identify a broader compositional window, far from the quenching regime, where emergent behavior reliably manifests. This expanded design space significantly enhances the operational flexibility of reactive systems and their capacity for self-organization. Furthermore, these insights provide a roadmap for designing bioinspired materials with self-organizing capabilities, unlocking possibilities in synthetic manufacturing.
MULTISTEP AND CONTINUOUS PHYSICS-INFORMED NEURAL NETWORK METHODS FOR LEARNING GOVERNING EQUATIONS AND CONSTITUTIVE RELATIONS
In this work, we investigate the applicability and relative merit of discrete and continuous versions of physics-informed neural network (PINN) methods for learning unknown governing equations or constitutive relations in a nonlinear dynamical system. In the case of unknown dynamics, entire right-hand-side (RHS) equations of the ordinary differential equations are unknown. In the case of unknown constitutive relations, however, the RHS equations are known up to the specification of constitutive relations (that may depend on the state of the system). We use a deep neural network to model unknown governing equations or constitutive relations. The discrete PINN approach combines classical multistep discretization methods for dynamical systems with neural-network-based machine learning methods. On the other hand, the continuous versions utilize deep neural networks to minimize the residual function for the continuous governing equations. We use the case of a fedbatch bioreactor system to study the effectiveness of these approaches and discuss conditions for their applicability. Our results indicate that the accuracy of the trained neural network models is much higher for the cases where we only have to learn a constitutive relation instead of all dynamics. This finding corroborates the well-known fact from scientific computing that building as much structural information as is available into an algorithm can enhance its efficiency and/or accuracy.
Energy filtering–induced ultrahigh thermoelectric power factors in Ni 3 Ge
Traditional thermoelectric materials rely on low thermal conductivity to enhance their efficiency but suffer from inherently limited power factors. Innovative pathways to optimize electronic transport are thus crucial. Here, we achieve ultrahigh power factors in Ni 3 Ge-based systems through an unconventional thermoelectric materials design principle. When overlapping flat and dispersive bands are engineered to the Fermi level, charge carriers can undergo intense interband scattering, yielding an energy filtering effect similar to what has long been predicted in certain nanostructured materials. Via a multistep DFT-based screening method developed here, we find a family of L1 2 -ordered binary compounds with ultrahigh power factors up to 11 mW m −1 K −2 near room temperature, which are driven by an intrinsic phonon-mediated energy filtering mechanism. Our comprehensive experimental and theoretical study of these intriguing materials paves the way for understanding and designing high-performance scattering-tuned metallic thermoelectrics.
Stable Simulation of the Community Atmosphere Model Using Machine‐Learning Physical Parameterization Trained With Experience Replay
In recent years, machine learning (ML) models have been used to improve physical parameterizations of general circulation models (GCMs). A significant challenge of integrating ML models into GCMs is the online instability when they are coupled for long‐term simulation. We present a new strategy that demonstrates robust online stability when the physical parameterization package of an atmospheric GCM is replaced by a deep ML model. The method uses experience replay with a multistep training scheme of the ML model in which the model's own output at the previous time step is used in the training. Predicted physics tendencies in the replay buffer with the most recent errors in the training iterations are reused, making the ML model learn from its own errors. The training method reduces the gap between the offline and online environments of the ML model. The method is used to train the ML model as the physical parameterization of the Community Atmosphere Model (CAM5) with training data from the Multi‐scale Modeling Framework high resolution simulations. Three 6‐year online simulations of the CAM5 are carried out by using the ML physics package. The simulated spatial distributions of precipitation, surface temperature and zonally averaged atmospheric fields demonstrate overall better accuracy than that of the standard CAM5 and benchmark model even without the use of additional physical constraints or tuning. This work is the first to demonstrate a solution to address the online instability problem in climate modeling with ML physics by using experience replay.
Fundamental mechanistic insights into the catalytic reactions of Li-S redox by Co single-atom electrocatalysts via operando methods
Lithium-sulfur batteries represent an attractive option for energy storage applications. A deeper understanding of the multistep lithium-sulfur reactions and the electrocatalytic mechanisms are required to develop advanced, high-performance batteries. We have systematically investigated the lithium-sulfur redox processes catalyzed by a cobalt single-atom electrocatalyst (Co-SAs/NC) via operando confocal Raman microscopy and x-ray absorption spectroscopy (XAS). The real-time observations, based on potentiostatic measurements, indicate that Co-SAs/NC efficiently accelerates the lithium-sulfur reduction/oxidation reactions, which display zero-order kinetics. Under galvanostatic discharge conditions, the typical stepwise mechanism of long-chain and intermediate-chain polysulfides is transformed to a concurrent pathway under electrocatalysis. In addition, operando cobalt K-edge XAS studies elucidate the potential-dependent evolution of cobalt’s oxidation state and the formation of cobalt-sulfur bonds. Our work provides fundamental insights into the mechanisms of catalyzed lithium-sulfur reactions via operando methods, enabling a deeper understanding of electrocatalysis and interfacial dynamics in electrical energy storage systems.
Divide and conquer: Learning chaotic dynamical systems with multistep penalty neural ordinary differential equations
Forecasting high-dimensional dynamical systems is a fundamental challenge in various fields, such as geosciences and engineering. Neural Ordinary Differential Equations (NODEs), which combine the power of neural networks and numerical solvers, have emerged as a promising algorithm for forecasting complex nonlinear dynamical systems. However, classical techniques used for NODE training are ineffective for learning chaotic dynamical systems. In this work, we propose a novel NODE-training approach that allows for robust learning of chaotic dynamical systems. Here, our method addresses the challenges of non-convexity and exploding gradients associated with underlying chaotic dynamics. Training data trajectories from such systems are split into multiple, non-overlapping time windows. In addition to the deviation from the training data, the optimization loss term further penalizes the discontinuities of the predicted trajectory between the time windows. The window size is selected based on the fastest Lyapunov time scale of the system. Multi-step penalty(MP) method is first demonstrated on Lorenz equation, to illustrate how it improves the loss landscape and thereby accelerates the optimization convergence. MP method can optimize chaotic systems in a manner similar to least-squares shadowing with significantly lower computational costs. Our proposed algorithm, denoted the Multistep Penalty NODE, is applied to chaotic systems such as the Kuramoto-Sivashinsky equation, the two-dimensional Kolmogorov flow, and ERA5 reanalysis data for the atmosphere. It is observed that MP-NODE provide viable performance for such chaotic systems, not only for short-term trajectory predictions but also for invariant statistics that are hallmarks of the chaotic nature of these dynamics.
Mechanistic Insights into Nonoxidative Ethanol Dehydrogenation on NiCu Single-Atom Alloys
Ethanol dehydrogenation presents a promising pathway towards the production of acetaldehyde, a valuable building block in chemicals production. Under non-oxidative conditions, the reaction is facilitated by supported Cu nanoparticles which afford reasonable activity and high selectivity. The stability issues associated with Cu nanoparticle sintering can be addressed by the addition of small amounts of Ni, which further boost reactivity while retaining selectivity. Despite the promise of NiCu single-atom alloys for non-oxidative ethanol dehydrogenation, little is known about the role of each component and the pathway of this mechanistically complex process. Herein, kinetic investigations from reactor tests identify C-H bond scission as the rate limiting step, while 1-hydroxyethyl is detected as the intermediate via IR spectroscopy. Temperature program desorption studies are employed to examine the effect of Ni coverage and to demonstrate that Ni atoms activate ethanol selectively at lower temperatures, resulting in higher acetaldehyde yield than pure Cu. Temperature program desorption experiments also reveal the spillover of intermediates from the Ni atom to neighboring Cu sites as a relevant step in the reaction pathway. Density functional theory calculations are used to investigate the 2 reaction energetics and to confirm that C-H bond scission is the initial reaction step, while a clear effect of H 2 partial pressure on the reaction pathway is realized. Further, counter to the expected behavior that all reaction steps take place on the Ni atoms, our degree of rate control analysis reveals that a mechanism involving spillover of the 1-hydroxyethyl intermediate from the Ni atom to the Cu surface, where it will dehydrogenate further, is more likely. Furthermore, our combined kinetic, spectroscopic, and theoretical approach sheds light on this complex reaction mechanism and represents a promising method for the understanding and designing of highly active, selective, and stable single-atom alloys for other multistep catalytic processes.
Grey-box and ANN-based building models for multistep-ahead prediction of indoor temperature to implement model predictive control
Model-based predictive control (MPC) strategies for heating, ventilation, and air-conditioning (HVAC) systems present an opportunity to lower building energy consumption and operational costs. Such approaches rely on the development of a model to precisely forecast building thermal dynamics, such as room air temperature or heating/cooling rate, and make control-related decisions. The control-oriented modeling of building energy systems should be accurate in predicting indoor conditions and present low computational complexity. These features are the key challenge of implementing advanced control methods such as MPC. Extant studies on building modeling for MPC have focused on step-ahead forecasting techniques to forecast building thermal dynamics, while multistep-ahead forecasting is essential. Moreover, machine learning model suitable in case of the domain-based engineering expertise are also not available. To this aim, we perform a comparative analysis of the grey-box model based on a resistance-capacitance (RC) thermal network and a machine learning model composed of an artificial neural network (ANN) for multistep-ahead prediction of building thermal dynamics using current and historical data. Actual experimental data obtained from the Flexible Research Platform (FRP) in Oak Ridge National Laboratory (US) are used for estimation and validation purposes. The average root mean squared error (RMSE) of the grey-box and ANN models are 0.89 °C and 1.02°C, respectively. Finally, the results indicate that the grey-box model outperforms the ANN model in the considered validation periods in terms of accuracy and prediction stability.
Voltage-Based Strategies for Preventing Battery Degradation under Diverse Fast-Charging Conditions
Maintaining safe operating conditions is a key challenge for high-performance lithium-ion battery applications. The lithium-plating reaction remains a risk during charging, but limited studies consider the highly variable charging conditions possible in commercial cells. Here we combine pseudo-2D electrochemical modeling with data visualization methods to reveal important relationships between the measurable cell voltage and difficult-to-predict Li-plating onset criteria. An extensively validated model is used to compute Li plating for thousands of multistep charging conditions spanning diverse rates, temperatures, states-of-charge, and cell aging. Here we observe an empirical cell operating voltage limit below which plating does not occur across all conditions, and this limit varies with the battery state-of-charge and aging. A model sensitivity analysis also indicates that, when comparing two charging voltage profiles, the capacity difference at 4.0 V correlates well with the difference in the plating onset capacity. These results encourage simple strategies for Li-plating prevention that are complementary to existing battery controls.
Constraining calculations of Pu 239 ( n , γ ) cross sections with multistep cascade γ -ray spectra measured at the DANCE facility
Measurements of multistep cascade gamma-ray spectra from several low-lying 1 + resonances in the Pu 239 ( n , γ ) reaction were made using the DANCE detector. The measured spectra are compared to spectra simulated using several models for the photon strength function and the nuclear level density, representing the first analysis of this nature on a fissile nucleus. In general, models of the photon strength function that included a strong M 1 “scissors mode” contribution coupled with a Gilbert-Cameron nuclear level density provided a reasonable description of the spectra. Simulations using photon strength functions and nuclear level densities specifically for Pu 240 , extracted by the Oslo method, resulted in a very good representation of the measured spectra. Neutron-capture cross section calculations that included the scissors mode provided a good estimate of the previously measured values, without additional normalization. However, the scissors-mode energy that produced the best description of the multistep cascade spectra was different from the value that best reproduced the capture cross section. In addition, the 〈 Γ γ 〉 inferred from the multistep cascade calculations was somewhat less than the tabulated value, which was determined from resonance analysis. Published by the American Physical Society 2025
Quantitatively controlled electrophoretic deposition of nanocrystal films from non-aqueous suspensions
This study presents a novel method to correlate the mass and charge transfer kinetics during the electrophoretic deposition of nanocrystal films by using a purpose-built double quartz crystal microbalance combined with simultaneous current-measurement. Our data support a multistep process for film formation: generation of charged nanocrystal flux, charge transfer at the electrode, and polarization of neutral nanocrystals near the electrode surface. The polarized particles are then subject to dielectrophoretic forces that reduce diffusion away from the interface, generating a sufficiently high neutral particle concentration at the interface to form a film. The correlation of mass and charge transfer enables quantification of the nanocrystal charge, the fraction of charged nanocrystals, and the initial sticking coefficient of the particles. These quantities permit calculation of the film thickness, providing a theoretical basis for using concentration and voltage as process parameters to grow films of targeted thicknesses.
Observation of formation and local structures of metal-organic layers via complementary electron microscopy techniques
Abstract Metal-organic layers (MOLs) are highly attractive for application in catalysis, separation, sensing and biomedicine, owing to their tunable framework structure. However, it is challenging to obtain comprehensive information about the formation and local structures of MOLs using standard electron microscopy methods due to serious damage under electron beam irradiation. Here, we investigate the growth processes and local structures of MOLs utilizing a combination of liquid-phase transmission electron microscopy, cryogenic electron microscopy and electron ptychography. Our results show a multistep formation process, where precursor clusters first form in solution, then they are complexed with ligands to form non-crystalline solids, followed by the arrangement of the cluster-ligand complex into crystalline sheets, with additional possible growth by the addition of clusters to surface edges. Moreover, high-resolution imaging allows us to identify missing clusters, dislocations, loop and flat surface terminations and ligand connectors in the MOLs. Our observations provide insights into controllable MOL crystal morphology, defect engineering, and surface modification, thus assisting novel MOL design and synthesis.
Transient Pulse-Response Time-of-Flight Mass Spectrometry for Complex, Deactivating Heterogeneous Catalytic Systems: Application to Ethane Dehydroaromatization
The study of complex, multistep bond-forming and -breaking reactions in heterogeneous catalytic systems often encounters challenges associated with the involvement of large numbers of intermediates among branching pathways. Kinetic information obtained from traditional steady-state measurements can be complemented with that from time-resolved methods to uncover details of the underlying chemistry. Herein, we describe an approach for tracking the complete time-resolved chemical composition (ca. 4–200 u) of a reactor effluent in response to a reactant pulse. We use a six-port rotary valve with a metered sampling loop to pulse reactants at ambient pressure into a flow reactor packed with a catalyst bed within the isothermal region of a heated furnace. The temporal evolution of effluent species is tracked using time-resolved molecular-beam time-of-flight mass spectrometry. We highlight the possibilities that this method has to offer by studying the complex bifunctional mechanism of ethane dehydroaromatization over an HZSM-5-supported platinum catalyst. We demonstrate that energy-tunable ionization sources, which facilitate isomer resolution, enable the measurement of the full mass spectral time-dependent system response. This includes the evolution of major products and mechanistically relevant reactive intermediates such as 1,3-butadiene and cyclopentadiene; these species have not previously been observed from this reaction. In additional studies, we also assess the role of platinum in the catalyst by examining temporal responses to ethane and ethylene feeds. Results show that two temporally distinct formation pathways exist for methane and benzene, and that their importance depends on both catalyst composition and reactant identity. Additionally, characteristics of catalyst deactivation are uniquely observable in the time-resolved mass spectral response, including the selective deactivation of a benzene formation pathway. The combination of time-of-flight mass spectrometry with tunable ionization enables the simultaneous observation of all effluents in a complex mixture of intermediates with isomer/isobar differentiation capabilities that can be applied to any complex reaction system.
Insights into co-pyrolysis of polyethylene terephthalate and polyamide 6 mixture through experiments, kinetic modeling and machine learning
The non-isothermal pyrolysis of polyethylene terephthalate (PET), polyamide 6 (PA6), and their mixtures was studied in a thermogravimetric analyzer at different heating rates. Temperature of maximum decomposition (T max ) decreased by 25–45 °C and 35–55 °C for the PET:PA6 mixtures (3:1, 1:1, 1:3) compared to PET and PA6, respectively. The kinetic analysis was initially carried out using isoconversional method. However, the dependency of activation energy on conversion was observed for the co-pyrolysis of PET and PA6 that suggested the occurrence of multi-step reactions in the mixtures. Distributed activation energy model (DAEM) was used in this study to describe the multistep reactions occurring during pyrolysis of PET:PA6 mixtures. Here, in this work, a four-parallel reaction DAEM was developed to describe the pyrolysis kinetics of PET:PA6 mixtures. The apparent mean activation energies (E o ) for PET, PA6, and mixtures varied in the range of 244–255, 140–215, and 138–255 kJ mol –1 , respectively. The mass loss profiles of PET and PA6 mixtures were also modeled using artificial neural network (ANN). Out of 155 ANN models, the best prediction was made by ANN511 with R 2 greater than 0.997 for both test and unseen data. The interaction effects observed through TGA experiments and subsequent kinetic analysis were further assessed in terms of product composition using analytical pyrolysis coupled with gas chromatograph/mass spectrometer (Py-GC/MS). Co-pyrolysis of PET and PA6 resulted in the formation of new aromatic compounds with nitrogen-containing functional groups, which were not detected when PET or PA6 were pyrolyzed individually.
Scalable multiplexed machine learning gas sensor chips for food classification
Multiplexed gas sensor arrays combined with machine learning have unlocked previously inaccessible applications for scent-based sensing. Current platforms are limited by overlapping sensing materials with similar compositions, leading to highly correlated responses, or multistep deposition processes that hinder scalability. In this work, we developed a 16-element monolithic chip with fully distinct sensing layers, enabling a truly heterogeneous array. The system consists of highly sensitive carbon nanotube field effect transistors that are functionalized through a single-step microdispensing method compatible with automated pipetting systems. The resulting chip produces characteristic signal patterns in response to object-specific scent profiles and, when combined with machine learning algorithms, can perform automated object identification. We demonstrate the classification of 16 different objects, including food spoilage and nut allergens, with a 92.6% overall prediction accuracy.