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All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Curvature perturbations from stochastic particle production during inflation

We calculate the curvature power spectrum sourced by spectator fields that are excited repeatedly and non-adiabatically during inflation. In the absence of detailed information of the nature of spectator field interactions, we consider an ensemble of models with intervals between the repeated interactions and interaction strengths drawn from simple probabilistic distributions. We show that the curvature power spectra of each member of the ensemble shows rich structure with many features, and there is a large variability between different realizations of the same ensemble. Such features can be probed by the cosmic microwave background (CMB) and large scale structure observations. They can also have implications for primordial black hole formation and CMB spectral distortions. The geometric random walk behavior of the spectator field allows us to calculate the ensembleaveraged power spectrum of curvature perturbations semi-analytically. For sufficiently large stochastic sourcing, the ensemble averaged power spectrum shows a scale dependence arising from the time spent by modes outside the horizon during the period of particle production, in spite of there being no preferred scale in the underlying model. We find that the magnitude of the ensemble-averaged power spectrum overestimates the typical power spectra in the ensemble because the ensemble distribution of the power spectra is highly non-Gaussian with fat tails.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Graph reinforcement learning for exploring model spaces beyond the standard model

We present a methodology for performing scans of beyond the standard model (BSM) parameter spaces with reinforcement learning. We identify a novel procedure using graph neural networks that is capable of exploring spaces of models without the user specifying a fixed particle content, allowing broad classes of BSM models to be explored—in theory, the technique is applicable to nearly any model space with a prespecified gauge group. We provide a generic procedure by which a suitable graph grammar can be developed for any BSM model that features user-specified symmetry groups and a finite number of different possible particle species, the use of which is applicable to a variety of machine learning tasks over the actions of BSM theories beyond our particular reinforcement learning use case. As a proof of concept, we construct the graph grammar for theories with vectorlike leptons that may or may not be charged under a dark U ( 1 ) group, inspired by portal matter extensions of the sub-GeV vector portal/kinetic mixing simplified dark matter models. We then use this graph grammar to create a reinforcement learning environment tasked with creating models with these vectorlike leptons that are consistent with a list of a variety of precision observables. The reinforcement learning agent succeeds in developing models that can address the observed muon anomalous magnetic moment discrepancy while remaining consistent with flavor violation and electroweak precision observables, including both constructions that have previously been studied as well as new models that have not, to our knowledge, previously been identified. By inspecting the resulting ensembles of models that the agent produces and experimenting with different configurations for our reinforcement learning environment and graph grammar, we also infer various lessons about the development of these environments that can be transferable to reinforcement learning scans of more complicated model spaces and comment on future directions for the development of this technique into a more mature tool. Published by the American Physical Society 2025

Wojcik, George N.↗
NASA NTRS2006

A Coupled GCM-Cloud Resolving Modeling System to Study Precipitation Processes

Recent GEWEX Cloud System Study (GCSS) model comparison projects have indicated that cloud resolving models (CRMs) agree with observations better than traditional single column models in simulating various types of clouds and cloud systems from different geographic locations. Current and future NASA satellite programs can provide cloud, precipitation, aerosol and other data at very fine spatial and temporal scales. It requires a coupled global circulation model (GCM) and cloud-scale model (termed a super-parameterization or multi-scale modeling framework, MMF) to use these satellite data to improve the understanding of the physical processes that are responsible for the variation in global and regional climate and hydrological systems. The use of a GCM will enable global coverage and the use of a CRM will allow for better and more sophisticated physical parameterization. NASA Satellite and field campaign cloud related data sets can provide initial conditions as well as validation for both the MMF and CRMs. Also we have implemented a Land Information System (LIS that includes the CLM and NOAH land surface models into the MMF. The Goddard MMF is based on the 2D Goddard Cumulus Ensemble (GCE) model and the Goddard finite volume general circulation model (fvGCM) This modeling system has been applied and tested its performance for two different climate scenarios, El Nino (1998) and La Nina (1999). The coupled new modeling system produced more realistic propagation and intensity of tropical rainfall systems and intraseasonal oscillations, and diurnal variation of precipitation that are very difficult to forecast using even the state-of-the-art GCMs. In this talk I will present: (1) a brief review on GCE model and its applications on precipitation processes (both Microphysical and land processes) and (2) The Goddard MMF and the Major difference between two existing MMFs (CSU MMF and Goddard MMF) and preliminary results (the comparison with traditional GCMs).

Tao, Wei-Kuo↗
NASA NTRS2013

The Impact of Model and Rainfall Forcing Errors on Characterizing Soil Moisture Uncertainty in Land Surface Modeling

The contribution of rainfall forcing errors relative to model (structural and parameter) uncertainty in the prediction of soil moisture is investigated by integrating the NASA Catchment Land Surface Model (CLSM), forced with hydro-meteorological data, in the Oklahoma region. Rainfall-forcing uncertainty is introduced using a stochastic error model that generates ensemble rainfall fields from satellite rainfall products. The ensemble satellite rain fields are propagated through CLSM to produce soil moisture ensembles. Errors in CLSM are modeled with two different approaches: either by perturbing model parameters (representing model parameter uncertainty) or by adding randomly generated noise (representing model structure and parameter uncertainty) to the model prognostic variables. Our findings highlight that the method currently used in the NASA GEOS-5 Land Data Assimilation System to perturb CLSM variables poorly describes the uncertainty in the predicted soil moisture, even when combined with rainfall model perturbations. On the other hand, by adding model parameter perturbations to rainfall forcing perturbations, a better characterization of uncertainty in soil moisture simulations is observed. Specifically, an analysis of the rank histograms shows that the most consistent ensemble of soil moisture is obtained by combining rainfall and model parameter perturbations. When rainfall forcing and model prognostic perturbations are added, the rank histogram shows a U-shape at the domain average scale, which corresponds to a lack of variability in the forecast ensemble. The more accurate estimation of the soil moisture prediction uncertainty obtained by combining rainfall and parameter perturbations is encouraging for the application of this approach in ensemble data assimilation systems.

Maggioni, V.↗
DOE OSTI2022

Using ensembles and distillation to optimize the deployment of deep learning models for the classification of electronic cancer pathology reports

One of the goals of the Surveillance, Epidemiology, and End Results (SEER) program is to estimate incidence, prevalence, and mortality of all cancers. To that end, cancer registries across the country maintain a massive database of cancer pathology reports which contain rich information to understand cancer trends. However, these reports are stored in the form of unstructured text, and human annotators are required to read and extract relevant information. In this article, we show that existing deep learning models for automating information extraction from cancer pathology reports can be significantly improved by using ensemble model distillation. We found that by training multiple predictive models and transferring their knowledge to a single, low-resource model, we can reduce the number of highly confident wrong predictions. Our results show that our implemented methods could save 1000s of manual annotation hours.

60 APPLIED LIFE SCIENCES↗
NASA NTRS2016

A Model-Model and Data-Model Comparison for the Early Eocene Hydrological Cycle

A range of proxy observations have recently provided constraints on how Earth's hydrological cycle responded to early Eocene climatic changes. However, comparisons of proxy data to general circulation model (GCM) simulated hydrology are limited and inter-model variability remains poorly characterised. In this work, we undertake an intercomparison of GCM-derived precipitation and P - E distributions within the extended EoMIP ensemble (Eocene Modelling Intercomparison Project; Lunt et al., 2012), which includes previously published early Eocene simulations performed using five GCMs differing in boundary conditions, model structure, and precipitation-relevant parameterisation schemes. We show that an intensified hydrological cycle, manifested in enhanced global precipitation and evaporation rates, is simulated for all Eocene simulations relative to the preindustrial conditions. This is primarily due to elevated atmospheric paleo-CO2, resulting in elevated temperatures, although the effects of differences in paleogeography and ice sheets are also important in some models. For a given CO2 level, globally averaged precipitation rates vary widely between models, largely arising from different simulated surface air temperatures. Models with a similar global sensitivity of precipitation rate to temperature (dP=dT ) display different regional precipitation responses for a given temperature change. Regions that are particularly sensitive to model choice include the South Pacific, tropical Africa, and the Peri-Tethys, which may represent targets for future proxy acquisition. A comparison of early and middle Eocene leaf-fossil-derived precipitation estimates with the GCM output illustrates that GCMs generally underestimate precipitation rates at high latitudes, although a possible seasonal bias of the proxies cannot be excluded. Models which warm these regions, either via elevated CO2 or by varying poorly constrained model parameter values, are most successful in simulating a match with geologic data. Further data from low-latitude regions and better constraints on early Eocene CO2 are now required to discriminate between these model simulations given the large error bars on paleoprecipitation estimates. Given the clear differences between simulated precipitation distributions within the ensemble, our results suggest that paleohydrological data offer an independent means by which to evaluate model skill for warm climates.

Boundary conditions↗
DOE OSTI2022

Increasing precipitation whiplash in climate change hotspots

Abstract Throughout the world, the hydrologic cycle is projected to become more variable due to climate change, posing challenges in semi-arid regions with high water resource vulnerability. Precipitation whiplash results from hydrologic variability, and refers to interannual shifts between wet (⩾80th historical percentile) and dry (⩽20th historical percentile) years. Using five model large ensembles, we show that whiplash is projected to increase in frequency (25%–60%) and intensity (30%–100%) by 2100 across several semi-arid regions of the globe, including Western North America and the Mediterranean. These changes can be driven by increases in the frequency of wet years or dry years, or both, depending on the region. Moisture budget calculations in these regions illuminate the physical mechanisms behind increased whiplash. Thermodynamic changes generally dominate, with modulations by dynamics, evaporation, and eddies on regional or global scales. These findings highlight increasingly volatile hydrology in semi-arid regions as the 21st Century progresses.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

A Finite-Time Ensemble Method for Mixed Layer Model Comparison

Here, this work evaluates the fidelity of various upper-ocean turbulence parameterizations subject to realistic monsoon forcing and presents a finite-time ensemble vector (EV) method to better manage the design and numerical principles of these parameterizations. The EV method emphasizes the dynamics of a turbulence closure multimodel ensemble and is applied to evaluate 10 different ocean surface boundary layer (OSBL) parameterizations within a single-column (SC) model against two boundary layer large-eddy simulations (LES). Both LES include realistic surface forcing, but one includes wind-driven shear turbulence only, while the other includes additional Stokes forcing through the wave-average equations that generate Langmuir turbulence. The finite-time EV framework focuses on what constitutes the local behavior of the mixed layer dynamical system and isolates the forcing and ocean state conditions where turbulence parameterizations most disagree. Identifying disagreement provides the potential to evaluate SC models comparatively against the LES. Observations collected during the 2018 monsoon onset in the Bay of Bengal provide a case study to evaluate models under realistic and variable forcing conditions. The case study results highlight two regimes where models disagree 1) during wind-driven deepening of the mixed layer and 2) under strong diurnal forcing.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2001

Quasi-Equilibrium States in the Tropics Simulated by a Cloud-Resolving Model: Specific Features and Budget Analysis - Part 1

A series of long-term integrations using the two-dimensional Goddard Cumulus Ensemble (GCE) model were performed by altering imposed environmental components to produce various quasi-equilibrium thermodynamic states. Model results show that the genesis of a warm/wet quasi-equilibrium state is mainly due to either strong vertical wind shear (from nudging) or large surface fluxes (from strong surface winds), while a cold/dry quasi-equilibrium state is attributed to a remarkably weakened mixed-wind shear (from vertical mixing due to deep convection) along with weak surface winds. In general, latent heat flux and net large-scale temperature forcing, the two dominant physical processes, dominate in the beginning stage of the simulated convective systems, then considerably weaken in the final stage, which leads to quasi-equilibrium states. A higher thermodynamic regime is found to produce a larger rainfall amount, as convective clouds are the leading source of rainfall over stratiform clouds even though the former occupy much less area. Moreover, convective clouds are more likely to occur in the presence of strong surface winds (latent heat flux), while stratiform clouds (especially the well-organized type) are favored in conditions with strong wind shear (large-scale forcing). The convective systems, which consist of distinct cloud types due to the variation in horizontal winds, are also found to propagate differently. Accordingly, convective systems with mixed-wind shear generally propagate in the direction of shear, while the system with strong (multidirectional) wind shear propagates in a more complex way. Based on the results from the temperature (Q1) and moisture (Q2) budgets, cloud-scale eddies are found to act as a hydrodynamic 'vehicle' that cascades the heat and moisture vertically. Several other specific features such as atmospheric stability, CAPE, and mass fluxes are also investigated and found to be significantly different between diverse quasi-equilibrium states. Detailed comparisons between the various states are presented.

Shie, C.-L.↗
DOE OSTI2023

Automated Generation of Microkinetics for Heterogeneously Catalyzed Reactions Considering Correlated Uncertainties**

Abstract The study presents an ab‐initio based framework for the automated construction of microkinetic mechanisms considering correlated uncertainties in all energetic parameters and estimation routines. 2000 unique microkinetic models were generated within the uncertainty space of the BEEF‐vdW functional for the oxidation reactions of representative exhaust gas emissions from stoichiometric combustion engines over Pt(111) and compared to experiments through multiscale modeling. The ensemble of simulations stresses the importance of considering uncertainties. Within this set of first‐principles‐based models, it is possible to identify a microkinetic mechanism that agrees with experimental data. This mechanism can be traced back to a single exchange‐correlation functional, and it suggests that Pt(111) could be the active site for the oxidation of light hydrocarbons. The study provides a universal framework for the automated construction of reaction mechanisms with correlated uncertainty quantification, enabling a DFT‐constrained microkinetic model optimization for other heterogeneously catalyzed systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2022

Are Soybean Models Ready for Climate Change Food Impact Assessments?

An accurate estimation of crop yield under climate change scenarios is essential to quantify our ability to feed a growing population and develop agronomic adaptations to meet future food demand. A coordinated evaluation of yield simulations from process-based eco-physiological models for climate change impact assessment is still missing for soybean, the most widely grown grain legume and the main source of protein in our food chain. In this first soybean multi-model study, we used ten prominent models capable of simulating soybean yield under varying temperature and atmospheric CO 2 concentration [CO 2 ] to quantify the uncertainty in soybean yield simulations in response to these factors. Models were first parametrized with high quality measured data from five contrasting environments. We found considerable variability among models in simulated yield responses to increasing temperature and [CO 2 ]. For example, under a + 3 °C temperature rise in our coolest location in Argentina, some models simulated that yield would reduce as much as 24%, while others simulated yield increases up to 29%. In our warmest location in Brazil, the models simulated a yield reduction ranging from a 38% decrease under + 3 °C temperature rise to no effect on yield. Similarly, when increasing [CO 2 ] from 360 to 540 ppm, the models simulated a yield increase that ranged from 6% to 31%. Model calibration did not reduce variability across models but had an unexpected effect on modifying yield responses to temperature for some of the models. The high uncertainty in model responses indicates the limited applicability of individual models for climate change food projections. However, the ensemble mean of simulations across models was an effective tool to reduce the high uncertainty in soybean yield simulations associated with individual models and their parametrization. Ensemble, ensemble mean yield responses to temperature and [CO 2 ] were similar to those reported from the literature. Our study is the first demonstration of the benefits achieved from using an ensemble of grain legume models for climate change food projections, and highlights that further soybean model development with experiments under elevated [CO 2 ] and temperature is needed to reduce the uncertainty from the individual models.

Agricultural Model Inter-comparison and Improvemen↗
NASA NTRSDate not supplied

Comparison of Multivariate Time Series Prediction Techniques for Emulating Noah-LSM Soil Moisture Outputs

Land surface models are crucial tools for many earth science applications including numerical weather prediction, water resource and crop monitoring, and climatological analysis. Given a set of atmospheric forcings, seasonal data, and static parameters, models like Noah-LSM solve for land surface quantities including skin temperature, sensible heat flux, and soil moisture. While these calculations are theoretically robust, they are often computationally expensive. Since artificial neural networks (ANNs) are universal function approximators, they can learn to emulate the output of a deterministic numerical model given a time series of input forcings, with the learned ANN having substantially shorter execution time. The ANN could efficiently parameterize other models, generate ensembles, and provide first-guess inputs for retrievals. As such, with the goal of developing a model that efficiently mimics the output of Noah-LSM given NLDAS2 forcings on a region covering much of the central US, we examine and compare several neural network architectures for the multi-horizon multivariate time series forecasting problem. Recent literature includes a diverse set of approaches including autoregressive architectures like LSTM and GRU, parametric and non-parametric statistical predictors (ForecastNet and MQRNN), self-attention (LSTM-attention-LSTM), and temporal convovlution (DeepTCN). We implement several of these models for the Noah-LSM prediction task, highlighting the features and challenges for each and providing practical insight on the training process.

Mitchell Dodson↗
DOE OSTI2024

Explosion Detection Using Smartphones: Ensemble Learning with the Smartphone High-Explosive Audio Recordings Dataset and the ESC-50 Dataset

Explosion monitoring is performed by infrasound and seismoacoustic sensor networks that are distributed globally, regionally, and locally. However, these networks are unevenly and sparsely distributed, especially at the local scale, as maintaining and deploying networks is costly. With increasing interest in smaller-yield explosions, the need for more dense networks has increased. To address this issue, we propose using smartphone sensors for explosion detection as they are cost-effective and easy to deploy. Although there are studies using smartphone sensors for explosion detection, the field is still in its infancy and new technologies need to be developed. We applied a machine learning model for explosion detection using smartphone microphones. The data used were from the Smartphone High-explosive Audio Recordings Dataset (SHAReD), a collection of 326 waveforms from 70 high-explosive (HE) events recorded on smartphones, and the ESC-50 dataset, a benchmarking dataset commonly used for environmental sound classification. Two machine learning models were trained and combined into an ensemble model for explosion detection. The resulting ensemble model classified audio signals as either “explosion”, “ambient”, or “other” with true positive rates (recall) greater than 96% for all three categories.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
DOE OSTI2020

Projected End-of-Century Changes in the South American Monsoon in the CESM Large Ensemble

Projected changes in the South American monsoon system by the end of the twenty-first century are analyzed using the Community Earth System Model Large Ensemble (CESM-LENS). The wet season is shorter in LENS when compared to observations, with the mean onset occurring 19 days later and the mean retreat date 21 days earlier in the season. Despite a precipitation bias, the seasonality of rainfall over South America is reproduced in LENS, as well as the main circulation features associated with the development of the South American monsoon. Both the onset and retreat of the wet season over South America are delayed in the future compared to current climate by 3 and 7 days, respectively, with a slightly longer wet season. Central and southeastern Brazil are projected to get wetter as a result of moisture convergence from the strengthening of the South Atlantic low-level jet and a weaker South Atlantic subtropical high. The Amazon is projected to get drier by the end of the century, negatively affecting rain forest productivity. During the wet season, an increase in the frequency and intensity of extreme precipitation events is found over most of South America, and especially over northeastern and southern Brazil and La Plata. Meanwhile, during the dry season an increase in the maximum number of consecutive dry days is found over northeastern Brazil and the northern Amazon.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2006

The Effects of Lightning NO(x) Production during the July 21 EULINOX Storm studied with a 3-D Cloud-scale Chemical Transport Model

The July 21,1998 thunderstonn observed during the European Lightning Nitrogen Oxides Project (EULINOX) project was simulated using the three-dimensional Goddard Cumulus Ensemble (GCE) model. The simulation successfully reproduced a number of observed storm features including the splitting of the original cell into a southern cell which developed supercell characteristics, and a northern cell which became multicellular. Output from the GCE simulation was used to drive an offline cloud-scale chemical transport model which calculates tracer transport and includes a parameterization of lightning NO(x) production which uses observed flash rates as input. Estimates of lightning NO(x) production were deduced by assuming various values of production per intracloud and production per cloud-to-ground flash and comparing the results with in-cloud aircraft observations. The assumption that both types of flashes produce 360 moles of NO per flash on average compared most favorably with column mass and probability distribution functions calculated from observations. This assumed production per flash corresponds to a global annual lightning NOx source of 7 Tg N per yr. Chemical reactions were included in the model to evaluate the impact of lightning NO(x), on ozone. During the storm, the inclusion of lightning NOx in the model results in a small loss of ozone (on average less than 4 ppbv) at all model levels. Simulations of the chemical environment in the 24 hours following the storm show on average a small increase in the net production of ozone at most levels resulting from lightning NO(x), maximizing at approximately 5 ppbv per day at 5.5 km. Between 8 and 10.5 km, lightning NO(x) causes decreased net ozone production.

Ott, Lesley E.↗
NASA NTRS2011

A Model of Reduced Kinetics for Alkane Oxidation Using Constituents and Species for N-Heptane

The reduction of elementary or skeletal oxidation kinetics to a subgroup of tractable reactions for inclusion in turbulent combustion codes has been the subject of numerous studies. The skeletal mechanism is obtained from the elementary mechanism by removing from it reactions that are considered negligible for the intent of the specific study considered. As of now, there are many chemical reduction methodologies. A methodology for deriving a reduced kinetic mechanism for alkane oxidation is described and applied to n-heptane. The model is based on partitioning the species of the skeletal kinetic mechanism into lights, defined as those having a carbon number smaller than 3, and heavies, which are the complement of the species ensemble. For modeling purposes, the heavy species are mathematically decomposed into constituents, which are similar but not identical to groups in the group additivity theory. From analysis of the LLNL (Lawrence Livermore National Laboratory) skeletal mechanism in conjunction with CHEMKIN II, it is shown that a similarity variable can be formed such that the appropriately non-dimensionalized global constituent molar density exhibits a self-similar behavior over a very wide range of equivalence ratios, initial pressures and initial temperatures that is of interest for predicting n-heptane oxidation. Furthermore, the oxygen and water molar densities are shown to display a quasi-linear behavior with respect to the similarity variable. The light species ensemble is partitioned into quasi-steady and unsteady species. The reduced model is based on concepts consistent with those of Large Eddy Simulation (LES) in which functional forms are used to replace the small scales eliminated through filtering of the governing equations; in LES, these small scales are unimportant as far as the overwhelming part of dynamic energy is concerned. Here, the scales thought unimportant for recovering the thermodynamic energy are removed. The concept is tested by using tabular information from the LLNL skeletal mechanism in conjunction with CHEMKIN II utilized as surrogate ideal functions replacing the necessary functional forms. The test reveals that the similarity concept is indeed justified and that the combustion temperature is well predicted, but that the ignition time is over-predicted, a fact traced to neglecting a detailed description of the processes leading to the heavies chemical decomposition. To palliate this deficiency, functional modeling is incorporated into this conceptual reduction in addition to the modeling the evolution of the global constituent molar density, the enthalpy evolution of the heavies, the contribution to the reaction rate of the unsteady lights from other light species and from the heavies, the molar density evolution of oxygen and water, and the mole fractions of the quasisteady light species. The model is compact in that there are only nine species-related progress variables. Results are presented showing the performance of the model for predicting the temperature and species evolution. The model reproduces the ignition time over a wide range of equivalence ratios, initial pressure, and initial temperature.

Harstad, Kenneth G.↗
NASA NTRS2010

Application of Ensemble Detection and Analysis to Modeling Uncertainty in Non Stationary Process

Characterization of non stationary and nonlinear processes is a challenge in many engineering and scientific disciplines. Climate change modeling and projection, retrieving information from Doppler measurements of hydrometeors, and modeling calibration architectures and algorithms in microwave radiometers are example applications that can benefit from improvements in the modeling and analysis of non stationary processes. Analyses of measured signals have traditionally been limited to a single measurement series. Ensemble Detection is a technique whereby mixing calibrated noise produces an ensemble measurement set. The collection of ensemble data sets enables new methods for analyzing random signals and offers powerful new approaches to studying and analyzing non stationary processes. Derived information contained in the dynamic stochastic moments of a process will enable many novel applications.

Racette, Paul↗
DOE OSTI2021

Penalized ensemble Kalman filters for high dimensional non-linear systems

The ensemble Kalman filter (EnKF) is a data assimilation technique that uses an ensemble of models, updated with data, to track the time evolution of a usually non-linear system. It does so by using an empirical approximation to the well-known Kalman filter. However, its performance can suffer when the ensemble size is smaller than the state space, as is often necessary for computationally burdensome models. This scenario means that the empirical estimate of the state covariance is not full rank and possibly quite noisy. To solve this problem in this high dimensional regime, we propose a computationally fast and easy to implement algorithm called the penalized ensemble Kalman filter (PEnKF). Under certain conditions, it can be theoretically proven that the PEnKF will be accurate (the estimation error will converge to zero) despite having fewer ensemble members than state dimensions. Further, as contrasted to localization methods, the proposed approach learns the covariance structure associated with the dynamical system. These theoretical results are supported with simulations of several non-linear and high dimensional systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗