Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Non linear dynamics”

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 OSTI2022

Quantum materials for energy-efficient neuromorphic computing: Opportunities and challenges

Neuromorphic computing approaches become increasingly important as we address future needs for efficiently processing massive amounts of data. The unique attributes of quantum materials can help address these needs by enabling new energy-efficient device concepts that implement neuromorphic ideas at the hardware level. In particular, strong correlations give rise to highly non-linear responses, such as conductive phase transitions that can be harnessed for short- and long-term plasticity. Similarly, magnetization dynamics are strongly non-linear and can be utilized for data classification. This Perspective discusses select examples of these approaches and provides an outlook on the current opportunities and challenges for assembling quantum-material-based devices for neuromorphic functionalities into larger emergent complex network systems.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Shallow Soil Response to a Buried Chemical Explosion With Geophones and Distributed Acoustic Sensing

Abstract Shallow sediments can respond non‐linearly to large dynamic strains and undergo a subsequent healing phase as the material gradually recovers following the passing of seismic waves. This study focuses on the physical changes in the subsurface caused by the shaking from a buried chemical explosion detonated in a borehole in Nevada, USA, as a part of the Source Physics Experiment Phase II. The explosion damaged the shallow subsurface and modified the frequency content recorded by 491 geophones and 2240 Distributed Acoustic Sensing (DAS) channels within 2.5 km from surface ground zero. We observe a gradual shift of resonance frequencies in the 10–25 Hz frequency band in the hours following the explosion and develop a method to characterize the related logarithm‐type healing process of the shallow (i.e., upper ∼25 m) subsurface. We find that stronger levels of ground motion increase the relative degree of damage and duration of the subsurface healing; with the spall region exhibiting the largest degree of damage and longest healing recovery time. We observe coherent spatial patterns of damage with the region located to the southeast of the explosion exhibiting more damage than the southwest region. This study demonstrates that both DAS and co‐located geophones capture similar temporal changes associated with the physical processes occurring in the subsurface, with the high‐density sampling of DAS measurements enabling a new capability to monitor the fine‐scale changes of the Earth's shallow subsurface following the detonation of a buried explosion.

Viens, Loïc↗
DOE OSTI2021

Sensor enabled data-driven predictive analytics for modeling and control with high penetration of DERs in distribution systems

The electric power grid is undergoing a tremendous transformation due to the increasing penetration of renewable energy resources beginning with wind and more recently with the distributed energy resources (DERs) such as solar and battery storage. DERs have dramatically changed the role of the distribution systems in the overall power grid, and they are expected to contribute a significant portion of power generation in the future. If current trends for DERs continue, system operation and control will need to change dramatically for improved grid reliability and resiliency. As renewable resources increase in penetration, new and challenging operational, planning, and design problems are expected to emerge. Some of the key challenges that arise in the planning and operation of the future grid are: 1) Quantifying the impact of high DER penetration in distribution systems on bulk grid behavior over multiple time scales. 2) Identifying whether a particular DER configuration/settings have a large impact on the overall grid behavior. These challenges can be addressed in an offline manner using detailed T&D grid models and they can also be addressed in an online manner using sensor measurements. In particular, the advancement and planned growth in sensor technology in power grid over various voltage levels provide us with a unique opportunity to tackle these challenges from a data analytic perspective without needing detailed T&D grid models. A few questions that naturally arise when addressing the challenges from DERs using sensor data are: 1) How can we use limited sensor measurements to monitor & control voltage stability and small signal stability of the bulk system? 2) How can we ensure that the developed data analytic methods are robust to data availability and quality issues? 3) How can we compute the developed analytics in a scalable manner using streaming measurements? In this project, we addressed the aforementioned challenges arising from DERs and answered the questions raised above on how to effectively use the sensor measurements to enhance the reliability and performance of the electric grid. Thus, the overarching goal of this project is to develop effective reduced/representative system models from data that make the computational complexity sufficiently manageable so as to be useful to simulate, analyze, and even control complex non-linear power systems dynamics with large penetrations of DERs. In order to achieve the objective, the project team established a four-fold technical approach 1) Formulated a combined transmission-distribution co-simulation framework for data generation and validation, 2) Derived reduced/representative models of power systems based on data-driven methods for efficient computation and appropriate representation of system behavior, 3) Developed data driven characterization of power system behavior based on transfer operator theory, machine learning and optimization for model estimation, 4) Incorporated a scalable data management and processing architecture using distributed Kafka streaming applications that coordinate input data streams to the developed data analytics. The key accomplishments of the project are: 1) Development of a scalable multi-timescale T&D co-simulation framework (both for steady state and for dynamic co-simulation) using commercial solvers (PSSE and GridLAB-D). The steady-state T&D co-simulation interface is shared with our industry partner (PJM). 2) A structured reduced order dynamic model of distribution systems that can represent partial motor stalling along with a systematic procedure to derive the model parameters. 3) A PMU based online method to monitor, localize and mitigate fault-induced delayed voltage recovery using DER reactive support and load control in distribution systems. 4) Development of linear operator based robust methodologies for dynamic state estimation, uncertainty quantification, system identification and trajectory prediction for power system dynamics. 5) An adaptive damping control for utilizing wind energy resources to provide oscillation damping and system stability. 6) Implementation of Kafka-based framework for efficient processing of streaming data using Linux-based local virtual environment.

DER integration↗
DOE OSTI2024

Complexity: from Turbulence to Accelerators to Poetry

Though it may seem intuitive at times, the term 'complexity' is multifaceted, often encompassing various interacting aspects and components that follow local rules. This interaction leads to non-linearity, randomness, collective dynamics, hierarchy, and emergence. The phenomenological complexity found in large accelerators has recently been addressed by the Snowmass’21 Future Colliders Implementation Task Force (ITF). In this presentation, we will provide a concise overview of the mathematical constructs employed to assess hierarchical complexity, summarize the key findings from the ITF analysis, and offer a few examples demonstrating how this approach can be applied to analyze certain literaryclassics.

43 PARTICLE ACCELERATORS↗
DOE OSTI2020

Quantum Non-Equilibrium Dynamics Prediction of Electronic Transport Coefficients in Non-Linear Regimes

The goal of this work was to develop unique LLNL capabilities for the computational prediction of electrical, optical and thermal transport properties from quantum simulations. Using a recently developed theory of microscopic quantum transport, we were able to model compressed metallic hydrogen and it’s non-linear and out-of-equilibrium contributions in electrical and thermal transport. This theory was implemented in the open-source, real-space time-dependent density functional theory code Octopus. This model is general and widely applicable to high energy density systems that are important to LLNL and NNSA mission areas.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Global System Reduction Order Modeling for Localized Feature Inclusion

The development of reduced-order models remains an active research area, despite advances in computational resources. Here we develop a novel order-reduction approach that is designed to incorporate isolated regions that contain, for example, nonlinearitites or accumulating damage. The approach is designed to use global modes of the overall system response, which are then naturally coupled to the response in the isolated region of interest. Two examples are provided to demonstrate both the accuracy and the computational efficiency of the proposed approach. The performance of this approach is compared to the exact response corresponding to a finite element simulation for the chosen problems. In addition, the accuracy and computational efficiency are shown relative to a standard Galerkin reduction based on the linear normal modes. It is found that the proposed reduction offer computational efficiency comparable to a Galerkin reduction, but more accurately represents the response of the system when both are compared to the finite element simulation.

42 ENGINEERING↗
DOE OSTI2021

Topological or rotational non-Abelian gauge fields from Einstein-Skyrme holography

We report analytically known states at non-zero temperature which may serve as a powerful tool to reveal common topological and thermodynamic properties of systems ranging from the QCD phase diagram to topological phase transitions in condensed matter materials. In the holographically dual gravity theory, these are analytic solutions to a five-dimensional non-linear-sigma (Skyrme) model dynamically coupled to Einstein gravity. This theory is shown to be holographically dual to \( \mathcal{N} \) = 4 Super-Yang-Mills theory coupled to an SU(2)-current. All solutions are fully backreacted asymptotically Anti-de Sitter (AdS) black branes or holes. One family of global AdS black hole solutions contains non-Abelian gauge field configurations with positive integer Chern numbers and finite energy density. Larger Chern numbers increase the Hawking-Page transition temperature. In the holographically dual field theory this indicates a significant effect on the deconfinement phase transition. Black holes with one Hawking temperature can have distinct Chern numbers, potentially enabling topological transitions. A second family of analytic solutions, rotating black branes, is also provided. These rotating solutions induce states with propagating charge density waves in the dual field theory. We compute the Hawking temperature, entropy density, angular velocity and free energy for these black holes/branes. These correspond to thermodynamic data in the dual field theory. For these states the energy-momentum tensor, (non-)conserved current, and topological charge are interpreted.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Non-linear MHD modelling of edge localized modes suppression by resonant magnetic perturbations in ITER

Edge localized modes (ELMs) suppression by resonant magnetic perturbations (RMPs) was studied with the non-linear magneto-hydro-dynamic (MHD) code JOREK for the ITER H-mode scenarios at 15 MA, 12.5 MA, 10 MA/5.3 T. In this study, the main aim was to demonstrate that ELMs can be suppressed by RMPs while the divertor 3D footprints of heat and particle fluxes remain within divertor material limits. The unstable peeling–ballooning modes responsible for ELMs without RMPs were modelled first for each scenario using numerically accessible parameters for ITER. Then the stabilization of ELMs by RMPs was modelled with the same parameters. RMP spectra, optimized by the linear MHD MARS-F code, with main toroidal harmonics N = 2, N = 3, N = 4 have been used as boundary conditions of the computational domain of JOREK, including realistic RMP coils, main plasma, scrape off layer (SOL) divertor and realistic first wall. The model includes all relevant plasma flows: toroidal rotation, two fluid diamagnetic effects and neoclassical poloidal friction. With RMPs, the main toroidal harmonic and the non-linearly coupled harmonics remain dominant at the plasma edge, producing saturated modes and a continuous MHD turbulent transport thereby avoiding ELM crashes in all scenarios considered here. The threshold for ELM suppression was found at a maximum RMP coils current of 45 kAt–60 kAt compared to the coils maximum capability of 90 kAt. In the high beta poloidal steady-state 10 MA/5.3 T scenario, a rotating QH-mode without ELMs was observed even without RMPs. In this scenario with RMPs N = 3, N = 4 at 20 kAt maximum current in RMP coils, similar QH-mode behaviour was observed however with dominant edge harmonic corresponding to the main toroidal number of RMPs. The present MHD modelling was limited in time by few tens of ms after RMPs were switched on until the magnetic energy of the modes saturates. As a consequence the thermal energy was still evolving on this time scale, far from the ITER confinement time scale and hence only the form of 3D footprints on the divertor targets can be indicated within this set-up. Also note, that the divertor physics was missing in this model, so realistic values of fluxes are out of reach in this modelling. However the stationary 3D divertor and particle fluxes could be simply extrapolated from these results to the stationary situation considering that a large power fraction should be radiated in the core and SOL and only about 50 MW power is going to the divertor, which is an arbitrary, but reasonable number used here. The 3D footprints with RMPs show the characteristic splitting with the main RMP toroidal symmetry. The maximum radial extension of the footprints typically was ~20 cm in inner divertor and ~40 cm in outer divertor with stationary heat fluxes decreasing further out from the initial strike point from ~5 MW m ₋2 to ~1 MW m ₋2 assuming a total power in the divertor and walls is 50 MW. The heat fluxes remain within the divertor target and baffle areas, however with rather small margin in the outer divertor which could be an issue for the first wall especially in transient regimes when part of the plasma thermal energy is released due to switching on the RMP coils. This fact should be considered when RMPs are applied with a more favorable application before or soon after the L–H transition, although optimization is required to avoid increasing the L–H power threshold with RMPs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Alaskan carbon-climate feedbacks will be weaker than inferred from short-term experiments

Climate warming is occurring fastest at high latitudes. Based on short-term field experiments, this warming is projected to stimulate soil organic matter decomposition, and promote a positive feedback to climate change. We show here that the tightly coupled, nonlinear nature of high-latitude ecosystems implies that short-term (<10 year) warming experiments produce emergent ecosystem carbon stock temperature sensitivities inconsistent with emergent multi-decadal responses. We first demonstrate that a well-tested mechanistic ecosystem model accurately represents observed carbon cycle and active layer depth responses to short-term summer warming in four diverse Alaskan sites. We then show that short-term warming manipulations do not capture the non-linear, long-term dynamics of vegetation, and thereby soil organic matter, that occur in response to thermal, hydrological, and nutrient transformations belowground. Our results demonstrate significant spatial heterogeneity in multi-decadal Arctic carbon cycle trajectories and argue for more mechanistic models to improve predictive capabilities.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Alaskan carbon-climate feedbacks will be weaker than inferred from short-term manipulations: Alaskan Benchmark Data and Model runs

This submission aimed to assess differences in short-term step warming manipulations and long-term chronic response to climate change in Alaskan ecosystems. Briefly, climate warming is occurring fastest at high latitudes. Based on short-term field experiments, this warming is projected to stimulate soil organic matter decomposition, and promote a positive feedback to climate change. We show here that the tightly coupled, nonlinear nature of high-latitude ecosystems implies that short-term (< 10 year) warming experiments produce emergent ecosystem carbon stock temperature sensitivities inconsistent with emergent multi-decadal responses. We first demonstrate that a well-tested mechanistic ecosystem model accurately represents observed carbon cycle and active layer depth responses to short-term summer warming in four diverse Alaskan sites. We then show that short-term warming manipulations do not capture the non-linear, long-term dynamics of vegetation, and thereby soil organic matter, that occur in response to thermal, hydrological, and nutrient transformations belowground. Our results demonstrate significant spatial heterogeneity in multi-decadal Arctic carbon cycle trajectories and argue for more mechanistic models to improve predictive capabilities.The model used in the current study is available publicly (https://github.com/jinyun1tang/ECOSYS), and the current submission contains the python/ matlab codes for analyzing output from the model (includng a readme file to explain the codes). The benchmark data, also enclosed, was collected from a range of published and publicly available sources (extracted using GRABIT: https://www.mathworks.com/matlabcentral/fileexchange/7173-grabit). These sources describe warming induced changes in tundra/ boreal ecosystems.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Numerical simulation of parametric resonance in point absorbers using a simplified model

Abstract Parametric resonance is a non‐linear phenomenon in which a system can oscillate at a frequency different from its exciting frequency. Some wave energy converters are prone to this phenomenon, which is usually detrimental to their performance. Here, a computationally efficient way of simulating parametric resonance in point absorbers is presented. The model is based on linear potential theory, so the wave forces are evaluated at the mean position of the body. However, the first‐order variation of the body's centres of gravity and buoyancy is taken into account. This gives essentially the same result as a more rigorous approach of keeping terms in the equation of motion up to second order in the body motions. The only difference from a linear model is the presence of non‐zero off‐diagonal elements in the mass matrix. The model is benchmarked against state‐of‐the‐art non‐linear Froude–Krylov and computational fluid dynamics models for free decay, regular wave, and focused wave group cases. It is shown that the simplified model is able to simulate parametric resonance in pitch to a reasonable accuracy even though no non‐linear wave forces are included. The simulation speed on a standard computer is up to two orders of magnitude faster than real time.

16 TIDAL AND WAVE POWER↗
DOE OSTI2025

Technical note: A modified formulation of dynamic energy budget theory for faster computation of biological growth

Abstract. The mass conservation equation in the presence of boundary fluxes and chemical reactions from non-equilibrium thermodynamics is used to derive a modified dynamic energy budget (mDEB) model. Compared to the standard dynamic energy budget (sDEB) model (Kooijman, 2009), this modified formulation does not place the dilution effect in the mobilization kinetics of reserve biomass, and it maintains the partition principle for reserve mobilization dynamics for both linear and non-linear kinetics. Overall, the mDEB model shares most features with the sDEB model. However, for biological growth that requires multiple nutrients, the mDEB model is computationally much more efficient by not requiring numerical iterations for obtaining the specific growth rate. In an example of modeling the growth of Thalassiosira weissflogii in a nitrogen-limiting chemostat, the mDEB model was found to have almost the same accuracy as the sDEB model while requiring almost half of the computing time of the sDEB model. Since the sDEB model has been successfully applied in numerous studies, we believe that the mDEB model can help improve the modeling of biological growth and the associated ecosystem processes in various contexts.

Tang, Jinyun↗
DOE OSTI2024

Dynamic Control of Sodium Cold Trap Purification Temperature Using LSTM System Identification

This study investigates the dynamic regulation of the sodium cold trap purification temperature at Argonne National Laboratory’s liquid sodium test facility, employing long short-term memory (LSTM) system identification techniques. The investigation introduces an innovative hybrid approach by integrating model predictive control (MPC) based on first principles dynamic models with a multi-step time–frequency LSTM model in predicting the temperature profiles of a sodium cold trap purification system. The long short-term memory–model predictive controller (LSTM-MPC) model employs a sliding window scheme to gather training samples for multi-step prediction, leveraging historical data to construct predictive models that capture the non-linearities of the complex system dynamics without explicitly modeling the underlying physical processes. The performance of the LSTM-MPC and MPC were evaluated through simulation experiments, where both models were assessed on their capacity to maintain the cold trap temperature within predefined set-points while minimizing deviations and overshoots. Results obtained show how the data-driven LSTM-MPC model demonstrates stability and adaptability. In contrast, the traditional MPC model exhibits irregularities, particularly evident as overshoots around set-point limits, which can potentially compromise its effectiveness over long prediction time intervals. The findings obtained offer valuable insights into integrating data-driven techniques for enhancing real-time monitoring systems.

LSTM-MPC↗
DOE OSTI2023

Domain wall motion across microstructural features in polycrystalline ferroelectric films

This paper describes the effect of microstructural features such as grain boundaries and triple points on the pinning of domain wall motion in perovskite Pb(Zr 0.52 Ti 0.48 )O 3 (PZT) films on polycrystalline SrRuO 3 /SrTiO 3 substrates. Here, spatial variability in the collective domain wall dynamics was assessed using non-linearity mapping via Band Excitation Piezoresponse Force Microscopy (BE-PFM). Collocating the non-linearity maps with triple point locations (as visualized by EBSD) allowed for exploration of the effects that local microstructure (e.g., grain boundary) have on domain wall motion. It was found that the extrinsic behavior varied with both the misorientation angle and the proximity to the grain boundary. The width of influence of individual grain boundaries on the motion of domain walls was a function of the character of the grain boundary; random grain boundaries exhibit deeper minima in α d /d 33,initial and larger widths of influence (up to 905 nm) compared to coincident site lattice (CSL) boundaries (up to 572 nm). Additionally, triple points containing larger numbers of random boundaries exhibited non-Rayleigh behavior to greater distances, suggesting that the triple point provides either a deep potential minimum or a region where domain wall motion is unfavorable.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Linear Discriminant Analysis-Based Machine Learning and All-Atom Molecular Dynamics Simulations for Probing Electro-Osmotic Transport in Cationic-Polyelectrolyte-Brush-Grafted Nanochannels

Deciphering the correct mechanisms governing certain phenomena in polyelectrolyte (PE) brush grafted systems, revealed through atomistic simulations, is an extremely challenging problem. In a recent study, our all-atom molecular dynamics (MD) simulations revealed a non-linearly large electroosmotic (EOS) flow (in the presence of an applied electric field) in nanochannels grafted with PMETAC [Poly(2-(methacryloyloxy)ethyl trimethylammonium chloride] brushes. Given the lack of any formal procedure that would have directed us to identify the correct factors responsible for such an occurrence, we needed to spend several months and devote significant analyses to unravel the involved mechanisms. In this paper, we propose a Linear Discriminant Analysis (LDA) based Machine Learning (ML) approach to address this gap. At first, we obtain data on certain basic features from the all-atom MD data. These basic features represent the number of atoms of certain species around one atom of another (or same) species. Here, we obtain such data on basic features for a reference case (case of an EOS flow in PMETAC-brush-grafted nanochannels with a smaller electric field) and a perturbed case (case of an EOS flow in PMETAC-brush-grafted nanochannels with a larger electric field) in bins in which the nanochannel half height has been divided into. These datasets are high-dimensional dataset, to which the LDA is applied. This leads to the projection of the data (between the reference and the perturbed states) in a highly separated form on a 1D line. From such LDA calculations, we are able to identify the relative importance of the different basic features in ensuring this separation of the data (between the reference and the perturbed states) on the 1D line. This relative importance of the different basic features is quantified as “importance scores” for the different features, which in turn tell us what to study and where to study. Such knowledge enables us to rapidly identify the key factors responsible for the non-linearly large EOS transport in PMETAC-brush-grafted nanochannels.

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

Solving differential‐algebraic equations in power system dynamic analysis with quantum computing

Abstract Power system dynamics are generally modeled by high dimensional non‐linear differential‐algebraic equations (DAEs) given a large number of components forming the network. These DAEs' complexity can grow exponentially due to the increasing penetration of distributed energy resources, whereas their computation time becomes sensitive due to the increasing interconnection of the power grid with other energy systems. This paper demonstrates the use of quantum computing algorithms to solve DAEs for power system dynamic analysis. We leverage a symbolic programming framework to equivalently convert the power system's DAEs into ordinary differential equations (ODEs) using index reduction methods and then encode their data into qubits using amplitude encoding. The system non‐linearity is captured by Hamiltonian simulation with truncated Taylor expansion so that state variables can be updated by a quantum linear equation solver. Our results show that quantum computing can solve the power system's DAEs accurately with a computational complexity polynomial in the logarithm of the system dimension. We also illustrate the use of recent advanced tools in scientific machine learning for implementing complex computing concepts, that is, Taylor expansion, DAEs/ODEs transformation, and quantum computing solver with abstract representation for power engineering applications.

computational complexity↗
DOE OSTI2022

The DREAM Endstation at the Linac Coherent Light Source

Free-electron lasers (FEL), with their ultrashort pulses, ultrahigh intensities, and high repetition rates at short wavelength, have provided new approaches to Atomic and Molecular Optical Science. One such approach is following the birth of a photo electron to observe ion dynamics on an ultrafast timescale. Such an approach presents the opportunity to decipher the photon-initiated structural dynamics of an isolated atomic and molecular species. It is a fundamental step towards understanding single- and non-linear multi-photon processes and coherent electron dynamics in atoms and molecules, ultimately leading to coherent control following FEL research breakthroughs in pulse shaping and polarization control. A key aspect for exploring photoinduced quantum phenomena is visualizing the collective motion of electrons and nuclei in a single reaction process, as dynamics in atoms/ions proceed at femtosecond (10 –15 s) timescales while electronic dynamics take place in the attosecond timescale (10 –18 s). Here, we report on the design of a Dynamic Reaction Microscope (DREAM) endstation located at the second interaction point of the Time-Resolved Molecular and Optical (TMO) instrument at the Linac Coherent Light Source (LCLS) capable of following the photon–matter interactions by detecting ions and electrons in coincidence. The DREAM endstation takes advantage of the pulse properties and high repetition rate of LCLS-II to perform gas-phase soft X-ray experiments in a wide spectrum of scientific domains. With its design ability to detect multi-ions and electrons in coincidence while operating in step with the high repetition rate of LCLS-II, the DREAM endstation takes advantage of the inherent momentum conservation of reaction product ions with participating electrons to reconstruct the original X-ray photon–matter interactions. In this report, we outline in detail the design of the DREAM endstation and its functionality, with scientific opportunities enabled by this state-of-the-art instrument.

47 OTHER INSTRUMENTATION↗
DOE OSTI2023

$\text{GPLaSDI}$: Gaussian Process-based interpretable Latent Space Dynamics Identification through deep autoencoder

Numerically solving partial differential equations (PDEs) can be challenging and computationally expensive. This has led to the development of reduced-order models (ROMs) that are accurate but faster than full order models (FOMs). Recently, machine learning advances have enabled the creation of non-linear projection methods, such as Latent Space Dynamics Identification (LaSDI). LaSDI maps full-order PDE solutions to a latent space using autoencoders and learns the system of ODEs governing the latent space dynamics. By interpolating and solving the ODE system in the reduced latent space, fast and accurate ROM predictions can be made by feeding the predicted latent space dynamics into the decoder. In this paper, we introduce GPLaSDI, a novel LaSDI-based framework that relies on Gaussian process (GP) for latent space ODE interpolations. Using GPs offers two significant advantages. First, it enables the quantification of uncertainty over the ROM predictions. Second, leveraging this prediction uncertainty allows for efficient adaptive training through a greedy selection of additional training data points. This approach does not require prior knowledge of the underlying PDEs. Consequently, GPLaSDI is inherently non-intrusive and can be applied to problems without a known PDE or its residual. Here we demonstrate the effectiveness of our approach on the Burgers equation, Vlasov equation for plasma physics, and a rising thermal bubble problem. Our proposed method achieves between 200 and 100,000 times speed-up, with up to 7% relative error.

97 MATHEMATICS AND COMPUTING↗