SEARCH · Engineering Papers

Results for “Time step adaptivity”

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.

SourceResearch connectionFrom yearThrough year

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

At least 19 records

All sources NASA NTRS DOE OSTI

DOE OSTI2024

Adaptive time stepping for the two-time integro-differential Kadanoff-Baym equations

The nonequilibrium Green's function gives access to one-body observables for quantum systems. Of particular interest are quantities such as density, currents, and absorption spectra which are important for interpreting experimental results in quantum transport and spectroscopy. We present an integration scheme for the Green's function's equations of motion, the Kadanoff-Baym equations (KBE), which is both adaptive in the time integrator step size and method order as well as the history integration order. We analyze the importance of solving the KBE self-consistently and show that adapting the order of history integral evaluation is important for obtaining accurate results. To examine the efficiency of our method, we compare runtimes to a state-of-the-art fixed time step integrator for several test systems and show an order of magnitude speedup at similar levels of accuracy. Published by the American Physical Society 2024

97 MATHEMATICS AND COMPUTING↗

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 OSTI2026

Explicit Monotone Stable Super-Time-stepping Methods for Finite Time Singularities

We explore a novel way to numerically resolve the scaling behavior of finite-time singularities in solutions of nonlinear parabolic PDEs. The Runge–Kutta–Legendre (RKL) and Runge–Kutta–Gegenbauer (RKG) super-time-stepping methods were originally developed for nonlinear complex physics problems with diffusion. These are multistage single step second-order, forward-in-time methods with no implicit solves. The advantage is that the time-step size for stability scales with stage number 𝑠 as $\mathcal{O}$⁡(𝑠 2 ). Many interesting nonlinear PDEs have finite-time singularities, and the presence of diffusion often limits one to using implicit or semi-implicit time-step methods for stability constraints. Finite-time singularities are particularly challenging due to the large range of scales that one desires to resolve, often with adaptive spatial grids and adaptive time steps. Here, in this study, we show two examples of nonlinear PDEs for which the self-similar singularity structure has time and space scales that are resolvable using the RKL and RKG methods, without forcing even smaller time steps. Compared to commonly used implicit numerical methods, we achieve a significantly smaller run time while maintaining comparable accuracy. We also prove numerical monotonicity for both the RKL and RKG methods under their linear stability conditions for the constant coefficient heat equation, in the case of infinite domain and periodic boundary condition, leading to a theoretical guarantee of the superiority of the RKL and RKG methods over traditional super-time-stepping methods, such as the Runge-Kutta-Chebyshev and the orthogonal Runge-Kutta-Chebyshev methods. Code can be found at https://github.com/ZT220501/SRK-Singularity.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Robust Implicit Adaptive Low Rank Time-Stepping Methods for Matrix Differential Equations

In this work, we develop implicit rank-adaptive schemes for time-dependent matrix differential equations. The dynamic low rank approximation (DLRA) is a well-known technique to capture the dynamic low rank structure based on Dirac–Frenkel time-dependent variational principle. In recent years, it has attracted a lot of attention due to its wide applicability. Our schemes are inspired by the three-step procedure used in the rank adaptive version of the unconventional robust integrator (the so called BUG integrator) (Ceruti et al. in BIT Numer Math 62(4):1149–1174, 2022) for DLRA. First, a prediction (basis update) step is made computing the approximate column and row spaces at the next time level. Second, a Galerkin evolution step is invoked using an implicit solves for the small core matrix. Finally, a truncation is made according to a prescribed error threshold. Since the DLRA is evolving the differential equation projected on to the tangent space of the low rank manifold, the error estimate of the BUG integrator contains the tangent projection (modeling) error which cannot be easily controlled by mesh refinement. This can cause convergence issue for equations with cross terms. To address this issue, we propose a simple modification, consisting of merging the row and column spaces from the explicit step truncation method together with the BUG spaces in the prediction step. In addition, we propose an adaptive strategy where the BUG spaces are only computed if the residual for the solution obtained from the prediction space by explicit step truncation method, is too large. Here, we prove stability and estimate the local truncation error of the schemes under assumptions. We benchmark the schemes in several tests, such as anisotropic diffusion, solid body rotation and the combination of the two, to show robust convergence properties.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Towards modelling AR Sco: generalized particle dynamics and strong radiation-reaction regimes

Numerical simulations of relativistic plasmas have become more feasible, popular, and crucial for various astrophysical sources with the availability of computational resources. The necessity for high-accuracy particle dynamics is especially highlighted in pulsar modelling due to the extreme associated electromagnetic fields and particle Lorentz factors. Including the radiation-reaction force in the particle dynamics adds even more complexity to the problem, but is crucial for such extreme astrophysical sources. We have also realized the need for such modelling concerning magnetic mirroring and particle injection models proposed for AR Sco, the first white dwarf pulsar. This paper demonstrates the benefits of using higher-order explicit numerical integrators with adaptive time-step methods to solve the full particle dynamics with radiation-reaction forces included. We show that for standard test scenarios, namely various combinations of uniform E- and B-fields and a static dipole B-field, the schemes we use are equivalent to and in extreme field cases outperform standard symplectic integrators in accuracy. We show that the higher-order schemes have massive computational time improvements due to the adaptive time-steps we implement, especially in non-uniform field scenarios and included radiation reaction where the particle gyro-radius rapidly changes. When balancing accuracy and computational time, we identified the adaptive Dormand–Prince eighth-order scheme to be ideal for our use cases. The schemes we use maintain accuracy and stability in describing the particle dynamics and we indicate how a charged particle enters radiation-reaction equilibrium and conforms to the analytical Aristotelian Electrodynamics expectations.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2026

TANTE: Time-adaptive operator learning via neural Taylor expansion

Operator learning for time-dependent partial differential equations (PDEs) has seen rapid progress in recent years, enabling efficient approximation of complex spatiotemporal dynamics. However, most existing methods rely on fixed time step sizes during rollout, which limits their ability to adapt to varying temporal complexity and often leads to error accumulation. In this work, we propose the Time-Adaptive Transformer with Neural Taylor Expansion (TANTE), a novel operator-learning framework that produces continuous-time predictions with adaptive step sizes. TANTE predicts future states by performing a Taylor expansion at the current state, where neural networks learn both the higher-order temporal derivatives and the local radius of convergence. This allows the model to dynamically adjust its rollout based on the local behavior of the solution, thereby reducing cumulative error and improving computational efficiency. We demonstrate the effectiveness of TANTE across a wide range of PDE benchmarks, achieving superior accuracy and adaptability compared to fixed-step baselines, delivering accuracy gains of 60-80 % and speed-ups of 30-40 % at inference time.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

An iterative dynamic chemical stiffness removal method for reacting flow simulations

Abstract An iterative dynamic chemical stiffness removal method (IDCSR) based on quasi-steady-state approximation (QSSA) is proposed. The IDCSR method is built on a previously developed non-iterative method which has proved to work well for small timestep sizes. A novel iterative procedure is designed in IDCSR to enable explicit time integration of stiff chemistry at relatively large timestep sizes relevant to practical reacting flow simulations. The effectiveness of the iterative procedure is first demonstrated with a toy problem and homogeneous auto-ignition with fixed integration step sizes, showing that larger timestep sizes can be allowed for explicit time integration using IDCSR compared with the previous non-iterative method. IDCSR is then compared with existing explicit chemistry solvers for simulations of homogeneous auto-ignition and shows similar or lower computational cost but significantly higher accuracy across a wide range of timestep sizes. IDCSR is further combined with an automatic adaptive time-stepping scheme for simulations of 0-D homogeneous auto-ignition and a 2-D laminar lifted n -dodecane jet flame. For the 0-D auto-ignition simulations, IDCSR is shown to reduce both the error (by 43%–90%) and computational cost (by 6–15 times) compared with existing explicit solvers, while achieving speed-up factors of up to 400 compared with VODE for a wide range of timestep sizes and reaction mechanisms. For the 2-D jet flame simulations, speed-up factors of 15 and 31 for chemistry integration, and 5 and 9 for overall simulation, are achieved by IDCSR compared with CVODE with and without analytic Jacobian, respectively.

Xu, Chao (ORCID:0000000153074159)↗

DOE OSTI2025

Numerical schemes for 3-wave kinetic equations: A complete treatment of the collision operator

In our previous work Walton and Tran (2023), numerical schemes for a simplified version of 3-wave kinetic equations, in which only the simple forward-cascade terms of the collision operators are kept, have been successfully designed, especially to capture the long time dynamics of the equation given the multiple blow-up time phenomenon. In this second work in the series, we propose numerical treatments for the complete 3-wave kinetic equations, in which the complete, much more complicated collision operators are fully considered based on a novel conservative form of the equation. Here we then derive an implicit finite volume scheme to solve the equation. The new discretization uses an adaptive time-stepping method which allows for the simulations to be carried to very long times. Our computed solutions are compared with previously derived long-time asymptotic estimates for the decay rate of total energy of time-dependent solutions of 3-wave kinetic equations and found to be in excellent agreement.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Towards modelling AR Sco: calibration – reproducing high-energy pulsar emission and testing convergence to Aristotelian electrodynamics

In recent years, kinetic simulations have been crucial to further our understanding of pulsar electrodynamics. Yet, due to the large-scale separation between the gyro-period and the stellar rotation period, resolving the particle gyration has been computationally unfeasible for realistic pulsar parameters. The main aim of this work is comparing our gyro-phase-resolved model with a gyro-centric pulsar model, where our model solves the general equations of motion with included radiation reaction using a higher order numerical solver with adaptive time-steps. Specifically, we aim to (i) reproduce a pulsar’s high-energy emission maps, namely one with 10 per cent of the surface B-field strength of Vela, and the spectra produced by an independent gyro-centric pulsar emission model; and (ii) test convergence of these results to the radiation-reaction limit of Aristotelian electrodynamics. (iii) Additionally, we identify the effect that a large $E_{\parallel }$-field has on the trajectories and radiation calculations. We find that we can reproduce the curvature radiation emission maps and spectra well, using 10 per cent field strengths of the Vela pulsar and injecting our particles at a higher altitude in the magnetosphere. Using sufficiently large $E_{\parallel }$-fields, our numeric results converge to the analytic radiation-reaction limit trajectories. Additionally, we illustrate the importance of accounting for the $\mathbf {E}\times \mathbf {B}$-drift in the particle trajectories and radiation calculations, validating the Harding and collaborators’ model approach. Lastly, we found that our model deals very well with the high-radiation-reaction and high-field regimes present in pulsars.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Development of a Performance Portable Non-Equilibrium Plasma Fluid Solver on Adaptive Grids

This presentation will describe the numerical techniques, programming paradigms, verification, and performance of a non-equilibrium plasma fluid solver that can effectively utilize current and upcoming central processing and graphics processing unit (CPU+GPU) architectures. Our plasma fluid model solves the conservation equations for self-consistent electrostatic Poisson, electron and heavy species transport, and electron temperature on adaptive Cartesian grids. Our solver is written using performance portable adaptive mesh management library, AMReX (Zhang et al., JOSS, 4 (37) 1370, 2019), and can be built and run on widely available vendor specific GPU architectures (NVIDIA/AMD/Intel). We utilize a non-subcycled second order semi-implicit time-stepping method where all adaptive mesh refinement (AMR) levels are advanced with the same time step. The composite multi-level multigrid solver from within AMReX is used for each of the governing equations that are cast into a Helmholtz equation form. We have also developed a python based chemical mechanism parser framework that uses a similar format as CANTERA (Goodwin et al., Zenodo, 2018) yaml files as input. Our custom parser reads the yaml file and provides C++ files with transport and production rate functions that can be executed on both host (CPU) and device (GPU). We present verification of our solver using method of manufactured solutions that indicate formal second order accuracy with central diffusion and fifth order weighted-essentially-non-oscillatory (WENO) advection scheme. We also verify our solver with published literature on low-pressure capacitive and high-pressure streamer discharges. Our initial performance studies indicate 10X speed-up using 20 NVIDIA GPUs versus 200 CPUs for an atmospheric streamer discharge problem solved on a 512 x 1024 x 512 grid.

graphics processing units↗

DOE OSTI2025

Advancing simulations of coupled electron and phonon nonequilibrium dynamics using adaptive and multirate time integration

Electronic structure calculations in the time domain provide a deeper understanding of nonequilibrium dynamics in materials. The real-time Boltzmann equation (rt-BTE), used in conjunction with accurate interactions computed from first principles, has enabled reliable predictions of coupled electron and lattice dynamics. However, the timescales and system sizes accessible with this approach are still limited, with two main challenges being the different timescales of electron and phonon interactions and the cost of computing collision integrals. As a result, only a few examples of these calculations exist, mainly for two-dimensional (2D) materials. Here we leverage adaptive and multirate time integration methods to achieve a major step forward in solving the coupled rt-BTEs for electrons and phonons. Relative to conventional (non-adaptive) time-stepping, our approach achieves a 10x speedup for a target accuracy, or greater accuracy by 3–6 orders of magnitude for the same computational cost, enabling efficient calculations in both 2D and bulk materials. This efficiency is showcased by computing the coupled electron and lattice dynamics in graphene up to ~100 ps, as well as modeling ultrafast lattice dynamics and thermal diffuse scattering maps in bulk materials (silicon and gallium arsenide). In addition to improved efficiency, our adaptive method can resolve the characteristic rates of different physical processes, thus naturally bridging different timescales. This enables simulations of longer timescales and provides a framework for modeling multiscale dynamics of coupled degrees of freedom in matter. Our work opens new opportunities for quantitative studies of nonequilibrium physics in materials, including driven lattice dynamics with phonons coupled to electrons, spin, and other degrees of freedom.

Yao, Jia [California Institute of Technology (CalT↗

DOE OSTI2025

Accelerating phase field simulations through a hybrid adaptive Fourier neural operator with U-net backbone

Prolonged contact between a corrosive liquid and metal alloys can cause progressive dealloying. For one such process as liquid-metal dealloying (LMD), phase field models have been developed to understand the mechanisms leading to complex morphologies. However, the LMD governing equations in these models often involve coupled non-linear partial differential equations (PDE), which are challenging to solve numerically. In particular, numerical stiffness in the PDEs requires an extremely refined time step size (on the order of 10 -12 s or smaller). This computational bottleneck is especially problematic when running LMD simulation until a late time horizon is required. This motivates the development of surrogate models capable of leaping forward in time, by skipping several consecutive time steps at-once. In this paper, we propose a U-shaped adaptive Fourier neural operator (U-AFNO), a machine learning (ML) based model inspired by recent advances in neural operator learning. U-AFNO employs U-Nets for extracting and reconstructing local features within the physical fields, and passes the latent space through a vision transformer (ViT) implemented in the Fourier space (AFNO). We use U-AFNOs to learn the dynamics of mapping the field at a current time step into a later time step. We also identify global quantities of interest (QoI) describing the corrosion process (e.g., the deformation of the liquid-metal interface, lost metal, etc.) and show that our proposed U-AFNO model is able to accurately predict the field dynamics, in spite of the chaotic nature of LMD. Most notably, our model reproduces the key microstructure statistics and QoIs with a level of accuracy on par with the high-fidelity numerical solver, while achieving a significant 11, 200 × speed-up on a high-resolution grid when comparing the computational expense per time step. Finally, we also investigate the opportunity of using hybrid simulations, in which we alternate forward leaps in time using the U-AFNO with high-fidelity time stepping. We demonstrate that while advantageous for some surrogate model design choices, our proposed U-AFNO model in fully auto-regressive settings consistently outperforms hybrid schemes.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Numerical challenges in modeling gravothermal collapse in Self-Interacting Dark Matter halos

When dark matter has a large cross section for self scattering, halos can undergo a process known as gravothermal core collapse, where the inner core rapidly increases in density and temperature. To date, several methods have been used to implement Self-Interacting Dark Matter (SIDM) in N-body codes, but there has been no systematic study of these different methods or their accuracy in the core-collapse phase. In this paper, we compare three different numerical implementations of SIDM, including the standard methods from the GIZMO and Arepo codes, by simulating idealized dwarf halos undergoing significant dark matter self interactions (σ/m = 50 cm 2 /g). When simulating these halos, we also vary the mass resolution, time-stepping criteria, and gravitational force-softening scheme. The various SIDM methods lead to distinct differences in a halo's evolution during the core-collapse phase, as each results in spurious scattering rate differences and energy gains/losses. The use of adaptive force softening for gravity can lead to numerical heating that artificially accelerates core collapse, while an insufficiently small simulation time step can cause core evolution to stall or completely reverse. Additionally, particle numbers must be large enough to ensure that the simulated halos are not sensitive to noise in the initial conditions. Even for the highest-resolution simulations tested in this study (10 6 particles per halo), we find that variations of order 10% in collapse time are still present. Here, the results of this work underscore the sensitivity of SIDM modeling on the choice of numerical implementation and motivate a careful study of how these results generalize to halos in a cosmological context.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Cardinal: Seismic and Geoacoustic Array Processing

Data collected via seismic and infrasound array deployments are leveraged in the geosciences to detect and characterize a myriad of natural and anthropogenic sources. These deployments consist of numerous sensors placed in a predetermined configuration to amplify signal strength and improve the efficacy of array processing techniques used to measure signal directionality and waveform coherence. High‐fidelity feature extraction is often predicated on interstation distance as well as the frequency content and wavelength of an incident signal. Numerous array processing softwares analyze data in sequential frequency bands to obtain a more detailed characterization of a signal. However, current algorithms are limited in their ability to determine optimal array configuration for each band. We introduce an open‐source Python code, called Cardinal, to process seismic and infrasound array data in discretized time–frequency space with the option of applying an adaptive array design to determine optimal subarray configuration for each frequency band. To reduce computational time, the array processing step can be run in parallel using multithreading. Furthermore, the software has the capability to aggregate array processing results from different time–frequency pixels to produce separate sets of detections, or families, with added utility via the application of an adaptive semblance threshold, which aids in isolating signals‐of‐interest from coherent background noise. Upon appropriate configuration, Cardinal exhibits the potential to combine distinct seismic and infrasound phases into separate families.

Adaptive Array↗

DOE OSTI2025

Intelligent Triggers for Rare Event Detection in Liquid Argon Detectors

Next-generation neutrino experiments like SBND and DUNE rely on Liquid Argon Time Projection Chambers (LArTPCs), which produce exceptionally detailed data at high volume. Capturing rare or unexpected events in real-time is a major challenge. Our project explores the use of machine learning, specifically autoencoder-based anomaly detection, to identify unusual activity directly from raw detector signals. Inspired by successes at the CMS experiment, we demonstrate that such methods can be adapted to LArTPCs and show promising results in both simulated studies and early steps toward real-time hardware deployment. This approach could open new avenues for detecting signals from physics beyond the Standard Model.

Chung, Seokju [Columbia U. (main)]↗

DOE OSTI2024

An Orbital Basis Set for Double Photoionization of Atoms and Molecules

The ab initio theoretical treatment of one-photon double photoionization processes has been limited to atoms and diatomic molecules by the challenges posed by large grid-based representations of the double ionized continuum wave function. To provide a path for extensions to polyatomics, an energy-adapted orbital basis approach is demonstrated that reduces the dimensions of such representations and simultaneously allows larger time steps in time-dependent computational descriptions of double ionization. Additionally, an algorithm that exploits the diagonal nature of the two-electron integrals in the grid basis and dramatically accelerates the transformation between grid and orbital representations is presented. Excellent agreement between the present results and benchmark theoretical calculations is found for H – and Be atoms, as well as the hydrogen molecule, including for the triply differential cross sections that relate the angular distribution and energy sharing of all of the particles in the molecular frame.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Adaptive X-ray imaging with reinforcement learning

X-ray imaging is a powerful technique to scan samples in a variety of contexts including biological, environmental and materials science, but commonly requires a synchrotron light source to produce X-rays at sufficient intensity. As these facilities are expensive to operate, the available beam time is limited and always in high demand. Particularly if the illuminated samples are sparse, standard raster scanning methods can be time-consuming, with a majority of that time being spent on areas of the image that carry little information. To increase the efficiency and maximize the information gain for a given time budget, we split the scanning process into a series of steps where previous measurements are used to inform the decision making and adapt the exposure distribution at later stages of the sequence. We formulate this task as a reinforcement learning problem where the goal is to produce a sequence of exposure maps that maximize a predefined scalar metric. We demonstrate the potential of this approach in simulations where the adaptive illumination can accelerate the measurement process by up to an order of magnitude compared with standard raster scanning. Finally, we present the first results from deploying the trained agents on an X-ray fluorescence beamline at the Stanford Synchrotron Radiation Lightsource.

Reinforcement Learning↗

DOE OSTI2024

A Measurement-Based Adaptive Voltage Regulation Method Considering Topology Changes

This paper proposes an online adaptive data-driven distributed energy resource (DER) dispatch optimization method for voltage control considering topology changes. By using a local sensitivity factor (LSF)-enabled voltage control, traditional DER control can be reformulated into a linear programming (LP) problem, leading to faster computation speeds. Power injection alteration and topology changes are two common operational changes in the distribution network that can affect the LSF and voltage control performance. To address this issue, a robust estimation method is developed to adjust the sensitivity matrix at each time step for the time-varying power injection changes. When topology changes occur, only the allocated predominant LSF submatrices are updated based on measurement data, allowing for a fast adaptation to the system reconfiguration. Results obtained from a real distribution feeder in Southern California demonstrate its robustness as compared to traditional volt-var control and constant LSF matrix dispatch control methods.

DERs↗