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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

An Improved Convection Parameterization with Detailed Aerosol–Cloud Microphysics for a Global Model

Abstract A new microphysical treatment that includes aerosol–cloud interactions and secondary ice production (SIP) mechanisms is implemented in the convection scheme of the Community Atmosphere Model, version 6 (CAM6). The approach is to embed a 1D Lagrangian parcel model in the bulk convective plume of the existing deep convection parameterization. Aerosol activation, growth processes including collision/coalescence, and three processes of SIP mechanisms, two of which are normally overlooked in atmospheric models, are represented in this embedded parcel model. These microphysical processes are treated with a hybrid bin/bulk scheme and a high spatial and temporal resolution for the integration of the embedded parcel in 1D, allowing vertical velocity to determine the microphysical evolution following the in-cloud motion during ascent. Simulations of an observed case (Midlatitude Continental Convective Clouds Experiment) of a mesoscale convective system in Oklahoma, United States, with a single-column model (SCAM) version of CAM, are compared with aircraft in situ and ground-based observations of microphysical properties from the convection and precipitation. Results from the validation show the new microphysical scheme has a good representation of the ice initiation in the bulk convective plume, including the known and empirically quantified pathways of primary and secondary initiation, with benefits for the accuracy of properties of its supercooled cloud liquid. The sensitivity simulations and use of tagging tracers for the validated simulation confirm that the newly included SIP mechanisms are of paramount importance for convective microphysics and can be successfully treated in the global model.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Slow Wake Recovery and Low Turbulence Behind Wind Farms Parameterized in Mesoscale Simulations

Numerical weather prediction (NWP) and climate models equipped with wind-farm parameterizations (WFPs) can simulate cluster wake effects affecting downstream wind farms in both onshore and offshore environments. This study evaluates wake recovery behind a wind farm represented by the NWP-WFP approach in the Weather Research and Forecasting (WRF) model using either the Fitch et al. (2012) or Ma et al. (2022a, b) WFPs. Results are benchmarked against large-eddy simulations (LES) of an idealized offshore wind farm with aligned and staggered layouts under neutral atmospheric stability. Near-farm wake recovery is underestimated in NWP-WFP simulations due to its representation on a coarse mesoscale grid. This limitation leads to slow wake recovery through two interconnected mechanisms: (i) spatial gradients in the wind velocity field are weaker compared to LES and (ii) turbulence kinetic energy (TKE) remains low not because of excessive dissipation but due to insufficient shear production caused by these weakened gradients. For the scenario considered here, a wind-speed bias develops in the near-farm wake and persists into the far wake. Differences between the NWP-WFP simulations and LES emerge within a short distance downstream of the farm exit, where the mesoscale simulations recover too slowly. This reduced recovery contributes approximately 0.15-0.50 m s-1 to the near-farm wind-speed bias. The bias established in this region is not subsequently compensated for downstream but instead propagates into the far wake, where wind-speed differences of approximately 0.4-0.6 m s-1 remain up to 50 km downstream. Higher-resolution mesoscale simulations partially reduce this bias. Increasing turbine-added TKE or including subgrid wake effects provides additional improvement, but neither fully addresses the underlying cause. The slow wake recovery is not caused by limitations of the WFPs themselves, as it also occurs outside their region of influence, and adding subgrid wake effects does not significantly impact recovery. Rather, the slow wake recovery is a consequence of mesoscale flow representation. This behavior is not limited to regions downstream of the wind farm but is less visible within the farm, where wake recovery occurs simultaneously with turbine-induced momentum extraction. These results highlight the need for improved representations of wake recovery both within and downstream of wind farms. While enhanced subgrid modeling, shear-driven TKE production, and refined WFP formulations may improve intra-farm dynamics, accurately capturing near-farm wake recovery downstream remains challenging, as WFPs do not act in this region.

17 WIND ENERGY↗
DOE OSTI2024

Sensitivity of Fine‐Resolution Urban Heat Island Simulations to Soil Moisture Parameterization

ABSTRACT Urban areas experience the impact of natural disasters, such as heatwaves and flash floods, disparately in different neighbourhoods across a city. The demand for precise urban hydrometeorological and hydroclimatological modelling to examine this disparity, and the interacting challenges posed by climate change and urbanisation, has thus surged. The Weather Research and Forecasting (WRF) model has served such operational and research purposes for decades. Recent advancements in WRF, including enhanced numerical schemes and sophisticated urban atmospheric‐hydrological parameterizations, have empowered the simulation of urban geophysical processes at high resolution (~1 km), but even this resolution misses significant urban microclimate variability. This study applies the large‐eddy simulations (LES) mode within WRF, coupled with single‐layer urban canopy models (SLUCM), to enable even finer‐scale modelling (150 m) of the Urban Heat Island (UHI) effect in the Baltimore metropolitan area. We run nine scenarios to evaluate various methods of initializing soil moisture and various spinup lead times, and to assess the impact of WRF's Mosaic approach in depicting subgrid‐scale processes. We evaluate the scenarios by comparing the WRF simulated land surface temperature (LST) against Landsat LST and the WRF simulated hourly 2‐m air temperatures (AT) with observations from eight weather stations across the domain. Results underscore the paramount influence of the lead spinup time on the spatiotemporal distribution of simulated soil moisture, consequently shaping WRF's efficacy in predicting the UHI. Furthermore, interpolating soil moisture‐related parameters from the parent for child domain initialization yields a notable reduction in mean and root‐mean‐squared errors. This improvement was particularly evident in simulations with the longest spinup time, affirming the importance of carefully designing the initialization of soil moisture for improved urban temperature predictions.

Talebpour, Mahdad↗
DOE OSTI2024

NCAP: Noncanonical Amino Acid Parameterization Software for CHARMM Potentials

Noncanonical Amino Acids (NCAAs) provide numerous avenues for introduction of novel functionality to peptides and proteins. NCAAs can be incorporated through solid phase synthesis or genetic code expansion in conjugation with heterologous expression of the encoded protein modification. Due to the difficulty of synthesis, wide chemical space and lack of empirically resolved structures modeling the effects of NCAA mutation is critical for rational protein design. To evaluate the structural and functional perturbations NCAAs introduce we utilize molecular potentials that describe the forces in protein structure. Most potentials such as CHARMM are designed to model canonical residues but can be parameterized in include novel NCAAs. Here, in this work, we introduce NCAP a software package to generate CHARMM compatible parameters from quantum chemical calculation. Unlike currently available tools NCAP is designed to recognize NCAA structure and automatically bridge the gap between DFT calculations and potential parameters. For our software we discuss workflow, validation against canonical parameter sets and comparison to published NCAA-protein structures.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Assessing Clouds in GFDL's AM4.0 With Different Microphysical Parameterizations Using the Satellite Simulator Package COSP

We evaluate cloud simulations using satellite simulators against multiple observational data sets. These simulators have been run within the Geophysical Fluid Dynamics Laboratory's Atmosphere Model version 4.0 (AM4.0), as well as an alternative configuration where a fully two‐moment Morrison‐Gettelman cloud microphysical parameterization with prognostic precipitation (MG2) is applied, denoted as AM4‐MG2. The modeled cloud spatial distributions, vertical profiles, phase partitioning, cloud‐to‐precipitation transitions, and radiative effects compare reasonably well with satellite observations. Model biases include the under‐prediction of total and low‐level clouds, especially optically thin/intermediate clouds with cloud optical depth of less than 23, but the over‐prediction of thick clouds, indicating “too few, too bright” biases. These biases counteract each other, and give rise to reasonable estimates of cloud radiative effects. The underestimate of low‐level clouds is associated with too early and too frequent drizzle/precipitation formation. The precipitation bias is improved in AM4‐MG2, where the autoconversion scheme initiates the precipitation more realistically. There also exist discrepancies between models and observations for midlevel and high‐level clouds. Additional biases include the underestimate of liquid cloud fraction and the overestimate of ice cloud fraction.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Stable Machine‐Learning Parameterization of Subgrid Processes in a Comprehensive Atmospheric Model Learned From Embedded Convection‐Permitting Simulations

Modern climate projections often suffer from inadequate spatial and temporal resolution due to computational limitations, resulting in inaccurate representations of sub-grid processes. A promising technique to address this is the multiscale modeling framework (MMF), which embeds a kilometer-resolution cloud-resolving model (CRM) within each atmospheric column of a host climate model to replace traditional convection and cloud parameterizations. Machine learning offers a unique opportunity to make MMF more accessible by emulating the embedded CRM and reducing its substantial computational cost. Although many studies have demonstrated proof-of-concept success of achieving stable hybrid simulations, it remains a challenge to achieve near operational-level success with real geography and comprehensive variable emulation that includes, for example, explicit cloud condensate coupling. In this study, we present a stable hybrid model capable of integrating for at least 5 years with near operational-level complexity, including coarse-grid geography, seasonality, explicit cloud condensate and wind predictions, and land coupling. Our model demonstrates skillful online performance, achieving a 5-year zonal mean tropospheric temperature bias within 2 K, water vapor bias within 1 g/kg, and a precipitation root mean square error of 0.96 mm/day. Key factors contributing to our online performance include an expressive U-Net architecture and physical thermodynamic constraints for microphysics. With microphysical constraints mitigating unrealistic cloud formation, our work is the first to demonstrate realistic multi-year cloud condensate climatology under the MMF framework. Despite these advances, online diagnostics reveal persistent biases in certain regions, highlighting the need for innovative strategies to further optimize online performance.

Hu, Zeyuan [NVIDIA Corporation, Santa Clara, CA (U↗
DOE OSTI2024

Revealing the hidden structure of disordered materials by parameterizing their local structural manifold

Abstract Durable interest in developing a framework for the detailed structure of glassy materials has produced numerous structural descriptors that trade off between general applicability and interpretability. However, none approach the combination of simplicity and wide-ranging predictive power of the lattice-grain-defect framework for crystalline materials. Working from the hypothesis that the local atomic environments of a glassy material are constrained by enthalpy minimization to a low-dimensional manifold in atomic coordinate space, we develop a generalized distance function, the Gaussian Integral Inner Product (GIIP) distance, in connection with agglomerative clustering and diffusion maps, to parameterize that manifold. Applying this approach to a two-dimensional model crystal and a three-dimensional binary model metallic glass results in parameters interpretable as coordination number, composition, volumetric strain, and local symmetry. In particular, we show that a more slowly quenched glass has a higher degree of local tetrahedral symmetry at the expense of cyclic symmetry. While these descriptors require post-hoc interpretation, they minimize bias rooted in crystalline materials science and illuminate a range of structural trends that might otherwise be missed.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Accurate and efficient parameterization of an atomic cluster expansion (ACE) potential for ammonia under extreme conditions

We present a machine learning interatomic potential for ammonia designed to capture its complex multiphase behavior, including both molecular and superionic phases. The potential is based on the atomic cluster expansion (ACE) formulation and has been parameterized to facilitate high-fidelity molecular dynamics simulations of ammonia under extreme conditions, for pressures up to 100 GPa and for temperatures above 500 K and up to 6000 K. A diverse range of configurations was generated through high-quality ab initio molecular dynamics simulations, covering insulating and superionic ice phases, liquid ammonia, molecular nitrogen (N 2 ) and hydrogen (H 2 ), and metastable compounds that form upon dissociation, including $NH^{+}_{4}$, $H^{+}_{3}$, N 2 H 4 , and N 3 H. We demonstrate that the ammonia ACE potential accurately reproduces experimental and density functional theory predicted isotherms and Hugoniots. Crucially, the potential is able to capture the intricate phase behavior of ammonia, including the transition from insulating molecular fluid to the superionic phase. This work provides a robust interatomic potential that can be used for large-scale, accurate simulations of ammonia under extreme thermodynamic conditions, offering a powerful tool for investigating its behavior in various phases and applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Parameterized anomalous transport model for current-carrying collisionless plasmas in pulsed power inertial confinement fusion

Current delivery in pulsed power inertial confinement fusion is influenced by collisionless current-carrying microturbulent plasmas, which are sourced from electrode surfaces. In this setting, the lower hybrid drift instability—triggered by plasma acceleration—is a leading candidate driver of difficult-to-predict momentum and energy transport. To characterize the nonlinear state of the microturbulent plasma, a parameterized anomalous transport model is developed for the instability, with analytic formulas for anomalous collision frequency, resistivity, and species heating rates. The formulas are expressed in terms of linear-theory variables and four dimensionless parameters that characterize the macroscopic plasma state. The model is built on linear theory analysis, power law analysis, and quasilinear theory analysis, and is validated using a series of nonlinear continuum kinetic Vlasov–Poisson simulations. The theoretical and computational investigation demonstrates that the anomalous collision frequency associated with the instability can be reliably approximated, within about a factor of five or better, by the unscaled linear theory growth rate of the fastest-growing wavenumber mode. This finding enables efficient calculation of anomalous resistivity and species heating rates over a wide range of plasma conditions, resulting in improved predictive capabilities.

Complex functions↗
DOE OSTI2024

Divertor-safe nonlinear burn control based on a SOLPS parameterized core-edge model for ITER

Abstract For ITER operations, the range of desirable burning-plasma regimes with high fusion power output will be restricted by various operational constraints. These constraints include the saturation of ITER’s various heating and fueling actuators such as the neutral beam injectors, the ion and electron cyclotron heating systems, the gas puffing system, and the deuterium–tritium pellet injectors. In addition to these actuator constraints, the H-mode power threshold, divertor detachment, and the heat load on the divertor targets may apply limitations to ITER’s operational space. In this work, Plasma Operation Contour (POPCON) plots that map the aforementioned constraints to the temperature-density space are used to investigate which constraints are most limiting towards accessing regimes with high fusion power output. The presented POPCON plots are based on a control-oriented core-edge model that couples the nonlinear density and energy response models for the core-plasma region with SOLPS4.3 parameterizations for conditions in the edge-plasma regions (scrape-off-layer and divertor). Using this control-oriented core-edge model, a nonlinear burn controller, which aims to regulate the plasma temperature and density in the core-plasma region, is constructed in this work. This controller is augmented with an online optimization scheme that governs the control references such that the plasma can be guided towards regimes with high fusion powers while protecting the divertor targets from dangerously high heat loads. A closed-loop simulation study illustrates the capability of this burn control scheme.

Physics↗
DOE OSTI2024

Machine learning visualization tool for exploring parameterized hydrodynamics

We are interested in the computational study of shock hydrodynamics, i.e. problems involving compressible solids, liquids, and gases that undergo large deformation. These problems are dynamic and nonlinear and can exhibit complex instabilities. Due to advances in high performance computing it is possible to parameterize a hydrodynamic problem and perform a computational study yielding $\mathscr{O} (TB)$ of simulation state data. We present an interactive machine learning tool that can be used to compress, browse, and interpolate these large simulation datasets. This tool allows computational scientists and researchers to quickly visualize 'what-if' situations, perform sensitivity analyses, and optimize complex hydrodynamic experiments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A mixture parameterized biologically based dosimetry model to predict body burdens of polycyclic aromatic hydrocarbons in developmental zebrafish toxicity assays

Polycyclic aromatic hydrocarbons (PAHs) are a group of environmental toxicants found ubiquitously as complex mixtures in human-impacted environments. Developmental zebrafish exposures have been used widely to study PAH toxicity, but most studies report nominal exposure concentrations. Nominal exposure concentrations can be unreliable dose metrics due to differences in toxicant bioavailability resulting from disparate exposure methodologies and chemical properties. Toxicokinetic modeling can predict toxicant tissue doses to facilitate comparison between exposures of different chemicals, methodologies, and biological models. We parameterize a biologically based dosimetry model for developmental zebrafish toxicity assays for 9 PAHs. The model was optimized with measurements from media, tissue, and plastic plate walls throughout a static developmental exposure to a mixture of 10 PAHs of high abundance within the Portland Harbor Superfund Site. Plate binding, volatilization, zebrafish permeability, and tissue—media partitioning coefficients vary widely between PAHs. Model predictions accounted for 83% and 54% of 48 hpf body burdens within a factor of 2 resulting from exposures to mixtures and individual PAHs, respectively. Accounting for solubility significantly improves model performance. Competition for active sites in metabolizing enzymes may change biotransformation kinetics between individual PAH and mixture exposures. Area under the curve estimations of concentrations in zebrafish resulted in altered hazard rankings from nominal exposure concentrations. Future work will be oriented to generalizing the model to other PAHs. This PAH dosimetry model improves the interpretability of developmental zebrafish toxicity assays by providing time-resolved body burdens from nominal exposure concentrations.

63 RADIATION, THERMAL, AND OTHER ENVIRON. POLLUTAN↗
DOE OSTI2025

NCAP - Non-Canonical Amino Acid Parameterization

Our software is designed to only work on novel NCAA side chains and parameterize for the CHARMM potential. This works around the detailed analysis and manual parameter fitting of many existing software programs. Our approach is also more specific than those used in Rosetta where we calculate parameters specific for each NCAA rather than assuming transferability.

Overstreet, Richard [Pacific Northwest National La↗
DOE OSTI2025

Performance of Convection-Permitting and Convection-Parameterized Models in Reproducing the Extreme Precipitation Intensity Relationship with Surface Conditions

Here, this study investigates the warm-season extreme precipitation–temperature scaling relationship in CONUS404, a convection-permitting (4 km) Weather Research and Forecasting (WRF) Model simulation over the conterminous United States for the past four decades, and compares it with the WRF-Thermodynamic Global Warming (WRF-TGW) historical simulation at a coarser resolution (12 km) using parameterized convection. We also analyze the NCEP stage IV and NASA Integrated Multi-satellitE Retrievals for the Global Precipitation Measurement (IMERG) datasets as observational benchmarks. We examine how extreme precipitation intensity (EPI) varies with temperature and saturation deficit over representative regions based on hourly data. The stage IV and IMERG data show a similar pattern of EPI variation with temperature and saturation deficit, except that the EPI peak is lower in IMERG than in stage IV. Under dry and hot conditions, EPI decreases too rapidly with elevated saturation deficit in both CONUS404 and WRF-TGW compared to observations, but the performance of CONUS404 is superior to WRF-TGW. When the near-surface atmosphere is saturated or close to saturated, both CONUS404 and WRF-TGW produce higher peak values of EPI relative to the observational references; IMERG exhibits scaling rates close to the Clausius–Clapeyron (C–C) relationship, while CONUS404, WRF-TGW, and stage IV all demonstrate super-C–C scaling behaviors. Despite marked warming over the past four decades, in both CONUS404 and WRF-TGW, the scaling relationship between EPI and temperature in a saturated atmosphere remains stable and robust. This indicates a strong potential for the EPI–temperature scaling rate under saturation to be used as an emergent constraint in reducing uncertainties of future extreme precipitation projection.

Atmosphere↗
DOE OSTI2025

Videos, photos, and AI-derived grain size data associated with “High-throughput AI Video Surveys Enable Reproducible Multiscale Sediment Size Mapping, with Implications for Hydrobiogeochemical Parameterization”

NOTE: The manuscript associated with this data package is currently in review. The data may be revised based on reviewer feedback. Upon manuscript acceptance, this data package will be updated with the final dataset and additional metadata. This data package is associated with the manuscript “High-throughput AI Video Surveys Enable Reproducible Multiscale Sediment Size Mapping, with Implications for Hydrobiogeochemical Parameterization” under review. This data package includes five data types: 1) raw photos and videos from drone survey and walking smartphone surveys; 2) images derived from raw videos; 3) manual labeling of reference scales; 4) metadata for all images and photo resolution derived from artificial intelligence (AI) models or manual labels, 5) grain size data obtained from AI models for all photos, 6) metadata and grain size data after quality control, 7) summaries of sample efficiency for all data, and 8) computational fluid dynamics (CFD) data used to support hydro-biogeochemical (HBGC) parameter estimation. Such data is used to 1) demonstrate significant improvements in accuracy, efficiency, and quality control for grain size data collection with the help of AI models, 2) study the spatial heterogeneity of grain size and observation reproducibility based on tens of thousands of data points generated by the AI models, and 3) evaluate the impacts of grain size heterogeneity on key HBGC parameters across sediment-to-reach and hourly-to-yearly scales. In particular, the data package contains 116 folders and 179696 files. The files include 41 videos in .mov format, 64047 photos in .jpg format, 13541 video-derived photos in .png format, 12747 segmentation mask data in .tif format, 12747 segmentation data in .json format, 24771 .csv files that with metadata and grain size for each individual photo as well as water depth and velocity data from CFD and observation, 51791 .txt files of raw AI predicted labels, and 11 flight record data in .srt format. The summary for all metadata and grain size statistics information is included in “Scales_V3_NG.csv” and “Statistics_V3_NG.csv”. The summary for data that pass data quality control (QC) level 0-2 is included in “QCStatistics_V3_NG.csv”. The QC level 0 represents photos whose photo resolution is positive, excluding photos that miss reference scale. The QC level 1 means reference scale circularity uncertainty is less than 5% for smartphone images while representing photo resolution is larger than 0.44 mm/pixel for drone images. The QC level 2 means excluding photos whose grain number is less than 100, a minimum number of grains recommended by classic literature. The summary for each video’s name, length, frame rates, survey area, grain number, survey efficiency, etc. can be found in “QCSummary_V3_NG.csv”. The summary for site name, GPS coordinates, and number of images at each site can be found in “SitesSummary_V3_*.csv” files. Overall computational efficiency summary is reported in Table 4 of accompanying manuscript. Additionally, the nitrate concentration data used in this work was downloaded from an existing dataset published on ESS-DIVE (Boat-Dragged Sensor Hanford Reach.csv; Conner A. et al., 2020). We thank the United States Forest Service, Washington Department of Fish and Wildlife, Washington Department of Natural Resources, Cowiche Canyon Conservatory, Port of Benton, and the Confederated Tribes and Bands of the Yakama Nation for access to field locations where the data were collected. We also thank the Yakama Nation Tribal Council and Yakama Nation Fisheries for working with us to facilitate data collection and optimization of data usage according to their values and worldview.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Functional-type modeling approach and data-driven parameterization of methane emissions in wetlands (Final Technical Science Report)

Our goals are to improve understanding and quantitative representation of the multiple processes that affect methane emissions at a high (patch level, vertically detailed) spatial resolution, and translate this understanding to improved modeling capability of coastal wetland fluxes using the E3SM Land Model (ELM v1) wetland CH4 biogeochemistry module. We propose an experimental approach to identify and parameterize uncertainties in ELM. Understanding of methane emissions can be improved along three conceptual axes: (i) horizontal (ecohydrological patch resolution), (ii) vertical (through the depth of the soil column), and (iii) process level (e.g., resolving microbial pathways, vegetation specific transport pathways). Along each of the three axes, we will characterize, quantify, and model, the key ecological, hydrological, and meteorological controls of methane (CH4) flux heterogeneity in four model coastal wetlands.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Neural network approaches for parameterized optimal control

Here, we consider numerical approaches for deterministic, finite-dimensional optimal control problems whose dynamics depend on unknown or uncertain parameters. We seek to amortize the solution over a set of relevant parameters in an offline stage to enable rapid decision-making and be able to react to changes in the parameter in the online stage. To tackle the curse of dimensionality arising when the state and/or parameter are high-dimensional, we represent the policy using neural networks. We compare two training paradigms: First, our model-based approach leverages the dynamics and definition of the objective function to learn the value function of the parameterized optimal control problem and obtain the policy using a feedback form. Second, we use actor-critic reinforcement learning to approximate the policy in a data-driven way. Using an example involving a two-dimensional convection-diffusion equation, which features high-dimensional state and parameter spaces, we investigate the accuracy and efficiency of both training paradigms. While both paradigms lead to a reasonable approximation of the policy, the model-based approach is more accurate and considerably reduces the number of PDE solves.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Reduced basis approximations of parameterized dynamical partial differential equations via neural networks

Projection-based reduced order models are effective at approximating parameter-dependent differential equations that are parametrically separable. When parametric separability is not satisfied, which occurs in both linear and nonlinear problems, projection-based methods fail to adequately reduce the computational complexity. Devising alternative reduced order models is crucial for obtaining efficient and accurate approximations to expensive high-fidelity models. In this work, we develop a timestepping procedure for dynamical parameter-dependent problems, in which a neural-network is trained to propagate the coefficients of a reduced basis expansion. This results in an online stage with a computational cost independent of the size of the underlying problem. Here, we demonstrate our method on several parabolic partial differential equations, including a problem that is not parametrically separable.

97 MATHEMATICS AND COMPUTING↗