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At least 523 records · Page 29

The future of the El Niño–Southern Oscillation: using large ensembles to illuminate time-varying responses and inter-model differences

Future changes in the El Niño–Southern Oscillation (ENSO) are uncertain, both because future projections differ between climate models and because the large internal variability of ENSO clouds the diagnosis of forced changes in observations and individual climate model simulations. By leveraging 14 single model initial-condition large ensembles (SMILEs), we robustly isolate the time-evolving response of ENSO sea surface temperature (SST) variability to anthropogenic forcing from internal variability in each SMILE. We find nonlinear changes in time in many models and considerable inter-model differences in projected changes in ENSO and the mean-state tropical Pacific zonal SST gradient. We demonstrate a linear relationship between the change in ENSO SST variability and the tropical Pacific zonal SST gradient, although forced changes in the tropical Pacific SST gradient often occur later in the 21st century than changes in ENSO SST variability, which can lead to departures from the linear relationship. Single-forcing SMILEs show a potential contribution of anthropogenic forcing (aerosols and greenhouse gases) to historical changes in ENSO SST variability, while the observed historical strengthening of the tropical Pacific SST gradient sits on the edge of the model spread for those models for which single-forcing SMILEs are available. Our results highlight the value of SMILEs for investigating time-dependent forced responses and inter-model differences in ENSO projections. The nonlinear changes in ENSO SST variability found in many models demonstrate the importance of characterizing this time-dependent behavior, as it implies that ENSO impacts may vary dramatically throughout the 21st century.

54 ENVIRONMENTAL SCIENCES↗

Decoding Liquid Crystal Oligomer Phase Transitions: Toward Molecularly Engineered Shape Changing Materials

This work details an integrated investigation of liquid crystal (LC) oligomers that combines experiments and molecular dynamics simulations to obtain a detailed understanding of the molecular structure of LC oligomers and the mechanism underlying their phase transition temperatures. We synthesized and characterized a series of LC oligomers prepared from different lengths of methylene spacers in the reactive LC monomers and n-alkylamine chain extenders via the aza -Michael addition reaction. In parallel, we performed isothermal–isobaric ( NPT ) ensemble coarse-grained molecular dynamics (CG-MD) simulation of analogue mesogens that are connected to flexible spacers and extenders at varying temperatures, spacer lengths, and extender lengths. This approach allowed the effect of length in the flexible spacer as well as in the chain extender on the nematic–isotropic transition temperature ( T ni ) to be determined. The results showed that increasing the length of the extender decreases T ni for LC oligomers and amplifies the decrease of T ni in LC oligomers when the spacer length is short. We infer that the combination of spacer and extender changes the shape anisotropy of LC oligomers, changing the packing behavior of constituent mesogens, thus affecting their ability to transition from the isotropic to the nematic phase. Here, the detailed molecular structure–property relationships formulated enable prescribing design rules for LC oligomers geared toward molecularly engineered shape changing materials.

36 MATERIALS SCIENCE↗

Scale–Bridging in Three–Dimensional Fracture Networks: Characterizing the Effects of Variable Fracture Apertures on Network–Scale Flow Channelization

Here, we incorporate observations of real fracture aperture variability observed in laboratory experiments into an ensemble of three-dimensional discrete fracture network (DFN) simulations to characterize how variations of this micro-scale feature can influence flow and transport behavior at the network scale. A shear fracture is created within a Marcellus shale sample, and the fracture aperture is measured using a triaxial direct-shear device coupled with real-time X-ray imaging at in-situ stress conditions. We construct an ensemble of fracture networks based on natural fractures in Marcellus shale and project regions of the experimental aperture field onto each fracture in the networks. Our calculations demonstrate that the degree of flow channelization, a network-scale flow field structure, is dramatically increased by local changes in the aperture field that in turn affects flow and transport properties.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Using a surrogate-assisted Bayesian framework to calibrate the runoff-generation scheme in the Energy Exascale Earth System Model (E3SM) v1

Abstract. Runoff is a critical component of the terrestrial water cycle, and Earth system models (ESMs) are essential tools to study its spatiotemporal variability. Runoff schemes in ESMs typically include many parameters so that model calibration is necessary to improve the accuracy of simulated runoff. However, runoff calibration at a global scale is challenging because of the high computational cost and the lack of reliable observational datasets. In this study, we calibrated 11 runoff relevant parameters in the Energy Exascale Earth System Model (E3SM) Land Model (ELM) using a surrogate-assisted Bayesian framework. First, the polynomial chaos expansion machinery with Bayesian compressed sensing is used to construct computationally inexpensive surrogate models for ELM-simulated runoff at 0.5∘ × 0.5∘ for 1991–2010. The error metric between the ELM simulations and the benchmark data is selected to construct the surrogates, which facilitates efficient calibration and avoids the more conventional, but challenging, construction of high-dimensional surrogates for the ELM simulated runoff. Second, the Sobol' index sensitivity analysis is performed using the surrogate models to identify the most sensitive parameters, and our results show that, in most regions, ELM-simulated runoff is strongly sensitive to 3 of the 11 uncertain parameters. Third, a Bayesian method is used to infer the optimal values of the most sensitive parameters using an observation-based global runoff dataset as the benchmark. Our results show that model performance is significantly improved with the inferred parameter values. Although the parametric uncertainty of simulated runoff is reduced after the parameter inference, it remains comparable to the multimodel ensemble uncertainty represented by the global hydrological models in ISMIP2a. Additionally, the annual global runoff trend during the simulation period is not well constrained by the inferred parameter values, suggesting the importance of including parametric uncertainty in future runoff projections.

58 GEOSCIENCES↗

Accurate Modeling of Bromide and Iodide Hydration with Data-Driven Many-Body Potentials

Ion–water interactions play a central role in determining the properties of aqueous systems in a wide range of environments. However, a quantitative understanding of how the hydration properties of ions evolve from small aqueous clusters to bulk solutions and interfaces remains elusive. Here, we introduce the second generation of data-driven many-body energy (MBnrg) potential energy functions (PEFs) representing bromide–water and iodide–water interactions. The MB-nrg PEFs use permutationally invariant polynomials to reproduce two-body and three-body energies calculated at the coupled cluster level of theory, and implicitly represent all higher-body energies using classical many-body polarization. Further, a systematic analysis of the hydration structure of small Br - (H 2 O) n and I - (H 2 O) n clusters demonstrates that the MBnrg PEFs predict interaction energies in quantitative agreement with “gold standard” coupled cluster reference values. Importantly, when used in molecular dynamics simulations carried out in the isothermal-isobaric ensemble for single bromide and iodide ions in liquid water, the MB-nrg PEFs predict extended X-ray absorption fine structure (EXAFS) spectra that accurately reproduce the experimental spectra, which thus allows for characterizing the hydration structure of the two ions with high level of confidence.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The Evolving Distribution of Relative Humidity Conditional Upon Daily Maximum Temperature in a Warming Climate

Abstract The impacts of heat waves in a warming climate depend not only on changing temperatures but also on changing humidity. Using 35 simulations from the Community Earth System Model Large Ensemble (CESM LENS), we investigate the long‐term evolution of the joint distribution of summer relative humidity (RH) and daily maximum temperature ( Tmax ) near four U.S. cities (New York City, Chicago, Phoenix, and New Orleans) under the high‐emissions Representative Concentration Pathway (RCP) 8.5. We estimate the conditional quantiles of RH given Tmax with quantile regression models, using functions of temperature for each city in July for three time periods (1990–2005, 2026–2035, and 2071–2080). Quality‐of‐fit diagnostics indicate that these models accurately estimate conditional quantiles for each city. As expected, each quantile of Tmax increases from 1990–2005 to 2071–2080, while mean RH decreases modestly. Conditional upon a fixed quantile of Tmax , the median and high quantiles of RH decrease, while those of the Heat Index (HI) and dew point both increase. This result suggests that, despite a modest decrease in median relative humidity, heat stress measured by metrics considering both humidity and temperature in a warming climate will increase faster than that measured by temperatures alone would indicate. For a fixed Tmax , the high quantiles of RH (and thus of HI and dew point) increase from 1990–2005 to 2071–2080 in all four cities. This result suggests that the heat stress of a day at a given Tmax will increase in a warming climate due to the increase of RH.

Yuan, Jiacan↗

Spring Regional Sea Surface Temperatures as a Precursor of European Summer Heatwaves

Different spring and early summer North Atlantic sea surface temperature anomalies (SSTAs) have been shown to precede recent European summer heatwaves (EuSHWs). So far, the limited number of observed events associated with several physical mechanisms has prevented a robust identification of SSTAs as precursors. Here, we extend beyond previous studies by combining 100 historical simulations (1850–2005) of the MPI Grand-Ensemble with an explainable neural-network method. We find that the spring tripolar North Atlantic pattern with positive SSTAs in the Subtropical Gyre is a precursor of EuSHWs. In addition, positive SSTAs west of the Iberian Peninsula, and in the North Sea, the Baltic Sea and the Mediterranean Sea relate to distinct early summer soil moisture anomaly patterns and are precursors of western and southeastern EuSHWs, respectively. While the phase of the tripolar North Atlantic pattern indicates whether a EuSHW might emerge, regional SSTAs indicate the spatial characteristics of EuSHWs.

54 ENVIRONMENTAL SCIENCES↗

Uncertainty in El Niño-like warming and California precipitation changes linked by the Interdecadal Pacific Oscillation

Abstract Marked uncertainty in California (CA) precipitation projections challenges their use in adaptation planning in the region already experiencing severe water stress. Under global warming, a westerly jet extension in the North Pacific analogous to the El Niño-like teleconnection has been suggested as a key mechanism for CA winter precipitation changes. However, this teleconnection has not been reconciled with the well-known El Niño-like warming response or the controversial role of internal variability in the precipitation uncertainty. Here we find that internal variability contributes > 70% and > 50% of uncertainty in the CA precipitation changes and the El Niño-like warming, respectively, based on analysis of 318 climate simulations from several multi-model and large ensembles. The Interdecadal Pacific Oscillation plays a key role in each contribution and in connecting the two via the westerly jet extension. This unifying understanding of the role of internal variability in CA precipitation provides critical guidance for reducing and communicating uncertainty to inform adaptation planning.

54 ENVIRONMENTAL SCIENCES↗

Interfacial water asymmetry at ideal electrochemical interfaces

Controlling electrochemical reactivity requires a detailed understanding of the charging behavior and thermodynamics of the electrochemical interface. Experiments can independently probe the overall charge response of the electrochemical double layer by capacitance measurements and the thermodynamics of the inner layer with potential of maximum entropy measurements. Relating these properties by computational modeling of the electrochemical interface has so far been challenging due to the low accuracy of classical molecular dynamics (MD) for capacitance and the limited time and length scales of ab initio MD. Here, we combine large ensembles of long-time-scale classical MD simulations with charge response from electronic density functional theory to predict the potential-dependent capacitance of a family of ideal aqueous electrochemical interfaces with different peak capacitances. We show that while the potential of maximum capacitance varies, this entire family exhibits an electrode charge of maximum capacitance (CMC) between -2.9 and -2.2 μC/cm 2 , regardless of the details in the electronic response. Simulated heating of the same interfaces reveals that the entropy peaks at a charge of maximum entropy (CME) of -5.1 ± 0.6 μC/cm 2 , in agreement with experimental findings for metallic electrodes. The CME and CMC both indicate asymmetric response of interfacial water that is stronger for negatively charged electrodes, while the difference between CME and CMC illustrates the richness in behavior of even the ideal electrochemical interface.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Analytical and EZmock covariance validation for the DESI 2024 results

The estimation of uncertainties in cosmological parameters is an important challenge in Large-Scale-Structure (LSS) analyses. For standard analyses such as Baryon Acoustic Oscillations (BAO) and Full-Shape two approaches are usually considered. First: analytical estimates of the covariance matrix use Gaussian approximations and (nonlinear) clustering measurements to estimate the matrix, which allows a relatively fast and computationally cheap way to generate matrices that adapt to an arbitrary clustering measurement. On the other hand, sample covariances are an empirical estimate of the matrix based on an ensemble of clustering measurements from fast and approximate simulations. While more computationally expensive due to the large amount of simulations and volume required, these allow us to take into account systematics that are impossible to model analytically. In this work we compare these two approaches in order to enable DESI's key analyses. We find that the configuration space analytical estimate performs satisfactorily in BAO analyses and its flexibility in terms of input clustering makes it the fiducial choice for DESI's 2024 BAO analysis. On the contrary, the analytical computation of the covariance matrix in Fourier space does not reproduce the expected measurements in terms of Full-Shape analyses, which motivates the use of a corrected mock covariance for DESI's 2024 Full Shape analysis.

79 ASTRONOMY AND ASTROPHYSICS↗

Establishing model credibility for process-microstructure-property relationships in additive manufacturing using exascale computing

Additive Manufacturing (AM) of alloys holds significant promise as a disruptive technology in various industries, yet its adoption is often hindered by challenges in achieving consistent part quality. These issues are primarily due to the complex process-microstructure-property (PSP) relationships inherent to AM. Computational models can greatly aid in understanding these relationships, but their widespread impact and adoption has been limited by a lack of validated, open-source, and computationally efficient PSP modeling frameworks and hardware limitations. Here, this study leverages the ExaAM software suite and data from the AMBench-2018 series of laser powder bed fusion (LPBF) benchmark experiments to perform a comprehensive model assessment, including verification, validation, sensitivity analysis, and uncertainty quantification. The RADICAL-EnTK workflow manager was used to perform an ensemble of heat transport, solidification, and mechanical response simulations on the exascale computer Frontier, considering uncertainties in critical model inputs such as laser spot size and nucleation parameters, and consisting of 125 explicit grain structure simulations and 7875 crystal plasticity simulations. For a selected location within the Inconel 625 AMBench-2018 test artifact, sensitivity analysis and uncertainty quantification were performed using the predicted distributions of grain structure and mechanical properties. Qualitative agreement was found between the predicted grain size and texture and the observed AMBench-2018 microstructure, the mean predicted yield stress was within 5% of the experimental measurement mean, and the mean predicted engineering stress at 5% strain was within 10% of the experimental measurement mean. The insights gained from development and validation of the ExaAM PSP modeling framework will help guide future directions for enhancing the credibility and reliability of PSP models in AM, thereby accelerating the adoption of AM technologies in various industries.

Additive manufacturing↗

Holocene thinning of Darwin and Hatherton glaciers, Antarctica, and implications for grounding-line retreat in the Ross Sea

Chronologies of glacier deposits in the Transantarctic Mountains provide important constraints on grounding-line retreat during the last deglaciation in the Ross Sea. However, between Beardmore Glacier and Ross Island – a distance of some 600 km – the existing chronologies are generally sparse and far from the modern grounding line, leaving the past dynamics of this vast region largely unconstrained. We present exposure ages of glacial deposits at three locations alongside the Darwin–Hatherton Glacier System – including within 10 km of the modern grounding line – that record several hundred meters of Late Pleistocene to Early Holocene thickening relative to present. As the ice sheet grounding line in the Ross Sea retreated, Hatherton Glacier thinned steadily from about 9 until about 3 ka. Our data are equivocal about the maximum thickness and Mid-Holocene to Early Holocene history at the mouth of Darwin Glacier, allowing for two conflicting deglaciation scenarios: (1) ~500 m of thinning from 9 to 3 ka, similar to Hatherton Glacier, or (2) ~950 m of thinning, with a rapid pulse of ~600 m thinning at around 5 ka. We test these two scenarios using a 1.5-dimensional flowband model, forced by ice thickness changes at the mouth of Darwin Glacier and evaluated by fit to the chronology of deposits at Hatherton Glacier. The constraints from Hatherton Glacier are consistent with the interpretation that the mouth of Darwin Glacier thinned steadily by ~500 m from 9 to 3 ka. Rapid pulses of thinning at the mouth of Darwin Glacier are ruled out by the data at Hatherton Glacier. This contrasts with some of the available records from the mouths of other outlet glaciers in the Transantarctic Mountains, many of which thinned by hundreds of meters over roughly a 1000-year period in the Early Holocene. The deglaciation histories of Darwin and Hatherton glaciers are best matched by a steady decrease in catchment area through the Holocene, suggesting that Byrd and/or Mulock glaciers may have captured roughly half of the catchment area of Darwin and Hatherton glaciers during the last deglaciation. An ensemble of three-dimensional ice sheet model simulations suggest that Darwin and Hatherton glaciers are strongly buttressed by convergent flow with ice from neighboring Byrd and Mulock glaciers, and by lateral drag past Minna Bluff, which could have led to a pattern of retreat distinct from other glaciers throughout the Transantarctic Mountains.

54 ENVIRONMENTAL SCIENCES↗

Tandem particle-slurry batch reactors for solar water splitting (Final Scientific/Technical Report)

Economically, particle slurry reactors are projected to be one of the most promising technologies for solar photoelectrochemical hydrogen production, according to a 2009 techno-economic analysis commissioned by the US DOE and performed by Directed Technologies, Inc. The Fuel Cell Technologies Office’s Multi-Year Research, Development and Demonstration (MYRD&D) goals and targets are to reduce the cost of H 2 produced from renewable sources at the plant gate (i.e. not including delivery, dispensing, or storage) to < $2.00/gge, equivalent to ~$2.00/kg H 2 . Research results from our techno-economic modeling research suggest that this target could be met using particle slurry reactors assuming STH efficiencies in the range of 5 – 10%, materials lifetimes of < 1 year, and nanoparticles that cost up to 20 times more than projected costs of TiO 2 -coated Fe 2 O 3 nanoparticles. Although most large worldwide research efforts directed at solar photoelectrochemical hydrogen production focus on wafer-based designs, the projected lower cost for a particle slurry reactor at these disparate projected STH efficiencies clearly suggests that particle slurry reactors could be a scalable and deployable technology, assuming several challenges are overcome. These major technological challenges include the demonstration of a vertically-stacked-vessel architecture that is capable of operating sustainably while mostly relying on diffusion and natural convection to mix the redox shuttles between the vessels, and the demonstration that photocatalyst particles can operate at an overall 1% STH efficiency or larger when incorporated into this two-vessel design. Our research adds to the understanding of photocatalytic reactors for solar water splitting through numerical modeling results and experimental results. Numerical models were developed to simulate relevant device physics including particle and reactor dimensions which affect optical, transport, and rheological properties, electrocatalytic and photovoltaic properties of particles at various temperatures, and properties of redox shuttles and separators. Moreover, theoretical maximum solar-to-hydrogen efficiencies for ensembles of particles like in photocatalyst reactors were modeled and simulated and shown to equal or exceed those of photoelectrochemical designs under most scenarios. These results help determine constraints on the reactor that will enable more optimal designs for future prototypes. In parallel, experiments were performed to identify the most effective redox shuttles and to empirically validate the numerical models and simulations. Toward the latter, state-of-the-art light-absorbing particles and electrocatalysts were synthesized and characterized physically and photoelectrochemically for water electrolysis and redox chemistry with redox shuttles in the form factor of mesoporous electrodes and free-floating particles. The most promising materials candidates were used in a suspension reactor to evaluate performance toward photocatalytic H 2 production and results from the two measurements were compared. Predominantly, state-of-the-art cocatalyst-modified Rh-doped SrTiO 3 and BiVO 4 particles were further characterized to assess for their ability to perform visible-light-driven H 2 and O 2 evolution, respectively, and results were similar to those reported for the state-of-the-art in the peer-reviewed literature. Outcomes from this work inform the public of the effectiveness and promise of solar photocatalytic water splitting for clean and renewable hydrogen production. This work may also help increase research interest and funding for photocatalysis projects, which will accelerate development of a technology that will benefit the public by generating fuel while emitting few greenhouse gases and pollutants.

08 HYDROGEN↗

Strongly Interacting, Two-Dimensional, Dipolar Spin Ensembles in (111)-Oriented Diamond

Systems of spins with strong dipolar interactions and controlled dimensionality enable new explorations in quantum sensing and simulation. In this work, we investigate the creation of strong dipolar interactions in a two-dimensional ensemble of nitrogen-vacancy (NV) centers generated via plasma-enhanced chemical vapor deposition on (111)-oriented diamond substrates. We find that diamond growth on the (111) plane yields high incorporation of spins, both nitrogen and NV centers, where the density of the latter is tunable via the miscut of the diamond substrate. Our process allows us to form dense, preferentially aligned, 2D NV ensembles with volume-normalized ac sensitivity down to η ac = 810 pT μ m 3 / 2 Hz − 1 / 2 . Furthermore, we show that (111) affords maximally positive dipolar interactions among a 2D NV ensemble, which is crucial for leveraging dipolar-driven entanglement schemes and exploring new interacting spin physics. Published by the American Physical Society 2025

Hughes, Lillian B. (ORCID:0000000210201661)↗

Uncertainty Visualization Challenges in Decision Systems with Ensemble Data & Surrogate Models: Preprint

Uncertainty visualization is a key component in translating important insights from ensemble data into actionable decision-making by visually conveying various aspects of uncertainty within a system. With the recent advent of fast surrogate models for computationally expensive simulations, users can interact with more aspects of data spaces than ever before. However, the integration of ensemble data with surrogate models in a decision-making tool brings up new challenges for uncertainty visualization, namely how to reconcile and communicate the new and different types of uncertainties brought in by surrogates and how to utilize these new data estimates in actionable ways. In this work, we examine these issues as they relate to high-dimensional data visualization, the integration of discrete datasets and the continuous representations of those datasets, and the unique difficulties associated with systems that allow users to iterate between input and output spaces. We assess the role of uncertainty visualization in facilitating intuitive and actionable interaction with ensemble data and surrogate models, and highlight key challenges in this new frontier of computational simulation.

ensemble visualization↗

Quantitative evaluations of subtropical westerly jet simulations over East Asia based on multiple CMIP5 and CMIP6 GCMs

As a salient feature of the Asian monsoon system, the East Asian subtropical westerly jet (EASWJ) exerts significant impacts on weather and climate changes in China and even throughout East Asia. In this paper, we applied a new self-adaptive algorithm to detect the EASWJ, identify its boundaries, and then represent its characteristics by defining three indices: the intensity index, meridional displacement index, and width index. Compared to the reanalysis data, we carried out a comprehensive, objective, and quantitative EASWJ evaluation using historical experiments from multiple global climate models (GCMs) in the Coupled Model Intercomparison Project Phases 5 and 6 (CMIP5 and CMIP6). The results show that the multimodel ensemble mean (MME) of both CMIP5 and CMIP6 can simulate the characteristics of winter EASWJ well. While for the other three seasons, the MME of both phase models underestimate the 200-hPa zonal wind (U200) strength in the jet coverage area and overestimate the U200 outside the jet area, such simulation results weaken the meridional shear of the wind field. The EASWJ simulations from the CMIP5 GCMs had no consistent intensity or location characteristic tendencies, and most CMIP5 GCMs tended to simulate relatively wide-coverage jets. In contrast, most CMIP6 GCMs are inclined to simulate significantly weaker, wider, and more-northward jets. Compared to the predecessors in CMIP5, about half of CMIP6 GCMs significantly minimized the jet intensity bias, but remarkable errors were still observed in their jet location and coverage representations. Furthermore, the comparative analysis performed by classifying models based on their evaluated simulation results suggested that the simulated performance of the meridional temperature gradient was important for capturing the EASWJ characteristics. Further in-depth study of the causes of model differences is warranted to improve simulation results.

54 ENVIRONMENTAL SCIENCES↗

Enhanced accuracy through ensembling of randomly initialized auto-regressive models for dynamical systems

Computational mechanics simulations using traditional finite element methods (FEM) require prohibitively expensive computational resources for real-time engineering applications, design optimization, and digital twin implementations. While machine learning (ML) surrogate models offer significant computational speedups, autoregressive ML models for time-dependent mechanical systems suffer from error accumulation that compromises long-term prediction reliability - a critical concern for engineering applications where accuracy over extended time horizons is essential for safety and performance assessments. Here, we propose a deep ensemble framework specifically designed to address this challenge in computational mechanics applications, where multiple ML surrogate models with random weight initializations are trained in parallel and their predictions aggregated during inference. This approach leverages statistical diversity to maximize information gain from a fixed set of training data and to mitigate error propagation, while maintaining the computational efficiency that makes ML surrogates attractive for engineering practice. We validate the framework on three representative problems spanning critical areas of computational mechanics: stress field evolution in heterogeneous microstructures under complex loading (relevant to advanced materials design and composite analysis), planetary-scale shallow water dynamics (applicable to environmental and geotechnical engineering), and Gray-Scott reaction-diffusion systems (relevant to mass transport and chemical process engineering). Across all test cases, the ensemble approach demonstrates consistent error reduction of 15-33% compared to individual models. The codes for this work are available on GitHub (https://github.com/Graham-Brady-Research-Group/AutoregressiveEnsemble_SpatioTemporal_Evolution).

autoregressive prediction↗