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At least 667 records · Page 37

On the predictability of turbulent fluxes from land: PLUMBER2 MIP experimental description and preliminary results

Accurate representation of the turbulent exchange of carbon, water, and heat between the land surface and the atmosphere is critical for modelling global energy, water, and carbon cycles in both future climate projections and weather forecasts. Evaluation of models' ability to do this is performed in a wide range of simulation environments, often without explicit consideration of the degree of observational constraint or uncertainty and typically without quantification of benchmark performance expectations. We describe a Model Intercomparison Project (MIP) that attempts to resolve these shortcomings, comparing the surface turbulent heat flux predictions of around 20 different land models provided with in situ meteorological forcing evaluated with measured surface fluxes using quality-controlled data from 170 eddy-covariance-based flux tower sites. Predictions from seven out-of-sample empirical models are used to quantify the information available to land models in their forcing data and so the potential for land model performance improvement. Sites with unusual behaviour, complicated processes, poor data quality, or uncommon flux magnitude are more difficult to predict for both mechanistic and empirical models, providing a means of fairer assessment of land model performance. When examining observational uncertainty, model performance does not appear to improve in low-turbulence periods or with energy-balance-corrected flux tower data, and indeed some results raise questions about whether the energy balance correction process itself is appropriate. In all cases the results are broadly consistent, with simple out-of-sample empirical models, including linear regression, comfortably outperforming mechanistic land models. In all but two cases, latent heat flux and net ecosystem exchange of CO 2 are better predicted by land models than sensible heat flux, despite it seeming to have fewer physical controlling processes. Land models that are implemented in Earth system models also appear to perform notably better than stand-alone ecosystem (including demographic) models, at least in terms of the fluxes examined here. The approach we outline enables isolation of the locations and conditions under which model developers can know that a land model can improve, allowing information pathways and discrete parameterisations in models to be identified and targeted for future model development.

54 ENVIRONMENTAL SCIENCES↗

LLM-Based Adaptive Distribution Voltage Regulation Under Frequent Topology Changes: An In-Context MPC Framework

This paper proposes a large language model (LLM) based adaptive inverter control for distribution voltage regulation under frequent topology changes. We leverage the ability of the LLM to perform in-context learning and create a topology-adaptive surrogate model for power flow calculation. The surrogate model is then integrated with a long short-term memory-based load forecaster and a model predictive control (MPC) scheme to achieve the optimal inverter control that adapts to frequent topology changes. Unlike many existing works that assume fixed-topology grids or require the knowledge of all possible topologies when training a model, the proposed in-context MPC method tackles the distribution voltage control problem under various topologies and adapts to unknown topologies with limited data requirement for fine-tuning. The effectiveness of our method is demonstrated on a modified IEEE 123-bus test system.

24 POWER TRANSMISSION AND DISTRIBUTION↗

From RNNs to Foundation Models: An Empirical Study on Commercial Building Energy Consumption

Accurate short-term energy consumption forecasting for commercial buildings is crucial for smart grid operations. While smart meters and deep learning models enable forecasting using past data from multiple buildings, data heterogeneity from diverse buildings can reduce model performance. The impact of increasing dataset heterogeneity in time series forecasting, while keeping size and model constant, is understudied. We tackle this issue using the ComStock dataset, which provides synthetic energy consumption data for U.S. commercial buildings. Two curated subsets, identical in size and region but differing in building type diversity, are used to assess the performance of various time series forecasting models, including finetuned open-source foundation models (FMs). The results show that dataset heterogeneity and model architecture have a greater impact on post-training forecasting performance than the parameter count. Moreover, despite the higher computational cost, finetuned FMs demonstrate competitive performance compared to base models trained from scratch.

commercial buildings↗

Challenges of COVID-19 Case Forecasting in the US, 2020–2021

During the COVID-19 pandemic, forecasting COVID-19 trends to support planning and response was a priority for scientists and decision makers alike. In the United States, COVID-19 forecasting was coordinated by a large group of universities, companies, and government entities led by the Centers for Disease Control and Prevention and the US COVID-19 Forecast Hub ( https://covid19forecasthub.org ). We evaluated approximately 9.7 million forecasts of weekly state-level COVID-19 cases for predictions 1–4 weeks into the future submitted by 24 teams from August 2020 to December 2021. We assessed coverage of central prediction intervals and weighted interval scores (WIS), adjusting for missing forecasts relative to a baseline forecast, and used a Gaussian generalized estimating equation (GEE) model to evaluate differences in skill across epidemic phases that were defined by the effective reproduction number. Overall, we found high variation in skill across individual models, with ensemble-based forecasts outperforming other approaches. Forecast skill relative to the baseline was generally higher for larger jurisdictions (e.g., states compared to counties). Over time, forecasts generally performed worst in periods of rapid changes in reported cases (either in increasing or decreasing epidemic phases) with 95% prediction interval coverage dropping below 50% during the growth phases of the winter 2020, Delta, and Omicron waves. Ideally, case forecasts could serve as a leading indicator of changes in transmission dynamics. However, while most COVID-19 case forecasts outperformed a naïve baseline model, even the most accurate case forecasts were unreliable in key phases. Further research could improve forecasts of leading indicators, like COVID-19 cases, by leveraging additional real-time data, addressing performance across phases, improving the characterization of forecast confidence, and ensuring that forecasts were coherent across spatial scales. In the meantime, it is critical for forecast users to appreciate current limitations and use a broad set of indicators to inform pandemic-related decision making.

59 BASIC BIOLOGICAL SCIENCES↗

Improving tropical cyclone rapid intensification forecasts with satellite measurements of sea surface salinity and calibrated machine learning

Forecasting rapid intensification (RI) of tropical cyclones (TC) is a mission known for large errors. One under-researched factor that affects TC intensification is salinity, which is important for density stratification in certain ocean regions and can affect the surface enthalpy flux under a strengthening hurricane. To investigate the impact and efficacy of using salinity information in state-of-the-art forecasting, we use a statistical model consisting of a variety of machine learning (ML) methods. For salinity data, we use satellite measurements of pre-storm sea surface salinity (SSS) as a proxy for the salinity stratification. We train and test the model on various ocean basins, including the Atlantic, eastern North Pacific and western North Pacific. A calibrator is trained on top of the ML models to correct and enhance probability forecasts. The calibrator significantly improves probability forecasts relative to recent works. The ML model performance is improved with the addition of SSS in the Eastern North Pacific, western North Pacific, and the Caribbean subregion of the North Atlantic, and the overall model performance is better than previous studies. SSS decreases model skill for a model trained on the full Atlantic basin. In the Indian Ocean, SSS is also notably correlated with RI occurrence, but the TC samples are not sufficient to train ML models.

hurricane↗

Data and scripts associated with “Sequential Precipitation Input Tagging (SPIT) to Estimate Water Transit Times and Hydrologic Tracer Dynamics within Water-Tagging Enabled Hydrologic Models” (v3)

This data package is associated with the publication “Sequential Precipitation Input Tagging (SPIT) to Estimate Water Transit Times and Hydrologic Tracer Dynamics within Water-Tagging Enabled Hydrologic Models” submitted to Journal of Advances in Modeling Earth Systems (Butler et al. 2025). This study developed the Sequential Precipitation Input Tagging (SPIT) framework to tag input precipitation and estimate water transit times and hydrologic tracers. SPIT tags all precipitation events at regular intervals over an extended period (monthly tags over seven years) in a hydrologic model from 2016-2022. SPIT is applied at six National Ecological Observatory Network (NEON) sites across the continental United States to calculate transit time distributions (TTD) and derive from these mean transit times (MTT), fractions of young water (Fyw), and hydrologic tracer concentrations in stream water (δ18O) within a water-tagging enabled version of the Weather Research and Forecast (WT-WRF-Hydro) model with national water model (NWM) configurations. We go on to validate WT-WRF-Hydro estimates against Butler et al. (2023), who analyzed the same NEON sites using stable water isotope data to estimate water transit times. This new tracking method provides a detailed picture of water movement and helps improve predictions about water availability in the future. This data package was originally published in January 2025. It was updated May 2025 (v2; new and modified files) and October 2025 (v3; new and modified files). File and folder names were not revised to indicate changes. See the change history section in the readme for more details. This data package contains the data and scripts used to develop the SPIT framework WT-WRF-Hydro (Water Tagging Weather Research and Forecasting Hydrologic) model and is associated with the following GitHub repository: https://github.com/zbutler33/SPIT-Framework. This data package contains five parent folders: (1) “Manipulated_outputs”, (2) “Metadata”, (3) “Observed”, (4) “Outputs”, and (5) “Scripts”. Each of these parent folders contains additional subfolders and files. Please see the FLMD (“v*_Butler_2024_WT_WRF_Hydro_flmd.csv”) for a list of all the files contained in this data package and descriptions for each. See the data dictionary (“v*_Butler_2024_WT_WRF_Hydro_dd.csv”) for definitions and units of all of the tabular (files ending in “.csv” and ".tsv") column headers.

54 ENVIRONMENTAL SCIENCES↗

Data-driven modeling to enhance municipal water demand estimates in response to dynamic climate conditions

Altered precipitation and temperature patterns from a changing climate will affect supply, demand, and overall municipal water system operations throughout the arid western U.S. While supply forecasts leverage hydrological models to connect climate influences with surface water availability, demand forecasts typically estimate water use independent of climate and other externalities. Stemming from an increased focus on seasonal water demand management, we use the Salt Lake City, Utah municipal water system as a test bed to assess model accuracy versus complexity trade-offs between simple climate-independent econometric-based models and complex climate-sensitive data-driven models to average to extreme wet and dry climate conditions—representative of a new climate normal. Here, the climate-independent model displayed low performance during extreme dry conditions with predictions exceeding 90% and 40% of the observed monthly and seasonal volumetric demands, respectively, which we attribute to insufficient model complexity. The climate-sensitive models displayed greater accuracy in all conditions, with an ordinary least squares model demonstrating a measurable reduction in prediction bias (3.4% vs. -27.3%) and RMSE (74.0 lpcd vs. 294 lpcd) compared to the climate-independent model. The climate-sensitive workflow increased model accuracy and characterized climate-demand interactions, demonstrating a novel tool to enhance water system management.

54 ENVIRONMENTAL SCIENCES↗

Automating Rabi & Ramsey Measurements via ML

As quantum computers scale up, the manual process of qubit tune-up becomes increasingly impractical due to its time-consuming and repetitive nature. While existing research has explored some automation techniques, many models remain underutilized for this purpose. This research aims to answer the question: is qubit tune-up able to be automated using the Long Short-Term Memory (LSTM) model? For the purposes of this project, only the rabi and ramsey measurement cycle was automated. These measurements are used to fine-tune a rough qubit frequency by repeating them until the optimal qubit frequency is obtained. The LSTM model uses the qubit frequency at one time step to forecast the qubit frequency at the next time step. A rabi-ramsey simulation was made to fabricate a dataset to train and test the LSTM model. As the model was trained, the error of the model decreased. Although there wasn't enough training data to generate perfect predictions, this shows it is possible to utilize forecasting models in automating the tune-up process.

Roberts, Rachel↗

Automating Rabi & Ramsey Measurements via ML

As quantum computers scale up, the manual process of qubit tune-up becomes increasingly impractical due to its time-consuming and repetitive nature. While existing research has explored some automation techniques, many models remain underutilized for this purpose. This research aims to answer the question: can qubit tune-up be automated using the Long Short-Term Memory (LSTM) model? For the purposes of this project, only the rabi and ramsey measurement cycle was automated. These measurements are used to fine-tune a rough qubit frequency by repeating them until the optimal qubit frequency is obtained. The LSTM model uses the qubit frequency at one time step to forecast the qubit frequency at the next time step. A rabi-ramsey simulation was made to fabricate a dataset to train and test the LSTM model. As the model was trained, the error of the model decreased. Although there wasn t enough training data to generate perfect predictions, this shows it is possible to utilize forecasting models in automating the tune-up process.

Roberts, Rachel↗

Automating Rabi & Ramsey Measurements via Machine Learning

As quantum computers scale up, the manual process of qubit tune-up becomes increasingly impractical due to its time-consuming and repetitive nature. While existing research has explored some automation techniques, many models remain underutilized for this purpose. This research aims to answer the question: can qubit tune-up be automated using the Long Short-Term Memory (LSTM) model? For the purposes of this project, only the rabi and ramsey measurement cycle was automated. These measurements are used to fine-tune a rough qubit frequency by repeating them until the optimal qubit frequency is obtained. The LSTM model uses the qubit frequency at one time step to forecast the qubit frequency at the next time step. A rabi-ramsey simulation was made to fabricate a dataset to train and test the LSTM model. As the model was trained, the error of the model decreased. Although there wasn't enough training data to generate perfect predictions, this shows it is possible to utilize forecasting models in automating the tune-up process.

Roberts, Rachel↗

Validation of RU-WRF, the Custom Atmospheric Mesoscale Model of the Rutgers Center for Ocean Observing Leadership

The Rutgers University Center for Ocean Observing Leadership (RU-COOL) contracted the National Renewable Energy Laboratory (NREL) to evaluate RU-COOL's atmospheric observation and modeling capabilities for characterizing the New Jersey offshore wind resource. The observational network used by RU-COOL consists of mostly public but some private coastal and offshore buoy-based stations. The core wind resource modeling capability of RU-COOL is a custom setup of the Weather Research and Forecasting (WRF) mesoscale model, referred to in this report as RU-WRF. The most unique feature of RU-WRF and not found in other WRF model setups is the use of custom sea surface temperature (SST) product generated by RU-COOL. This custom product was designed to better capture the unique coastal upwelling and strong storm mixing in the Mid-Atlantic Bight, which other typical SST products are not designed to capture. Funding for the development, maintenance, and use of RU-WRF by RU-COOL is provided by the New Jersey Board of Public Utilities, who also funded the validation work presented in this report. In this validation study, NREL was specifically tasked to: 1) Assess the observational network used by RU-COOL to validate RU-WRF and make recommendations for improvement, 2) Assess methods used by RU-COOL to validate RU-WRF and make recommendations for improvement, 3) Examine the inputs to and setup within RU-WRF, compare against available NREL data sets, and make recommendations for improvement.

17 WIND ENERGY↗

Analyzing inference workloads for spatiotemporal modeling

Ensuring power grid resiliency, forecasting climate conditions, and optimization of transportation infrastructure are some of the many application areas where data is collected in both space and time. Spatiotemporal modeling is about modeling those patterns for forecasting future trends and carrying out critical decision-making by leveraging machine learning/deep learning. Once trained offline, field deployment of trained models for near real-time inference could be challenging because performance can vary significantly depending on the environment, available compute resources and tolerance to ambiguity in results. Users deploying spatiotemporal models for solving complex problems can benefit from analytical studies considering a plethora of system adaptations to understand the associated performance-quality trade-offs. To facilitate the co-design of next-generation hardware architectures for field deployment of trained models, it is critical to characterize the workloads of these deep learning (DL) applications during inference and assess their computational patterns at different levels of the execution stack. In this paper, we develop several variants of deep learning applications that use spatiotemporal data from dynamical systems. We study the associated computational patterns for inference workloads at different levels, considering relevant models (Long short-term Memory, Convolutional Neural Network and Spatio-Temporal Graph Convolution Network), DL frameworks (Tensorflow and PyTorch), precision (FP16, FP32, AMP, INT16 and INT8), inference runtime (ONNX and AI Template), post-training quantization (TensorRT) and platforms (Nvidia DGX A100 and Sambanova SN10 RDU). Overall, our findings indicate that although there is potential in mixed-precision models and post-training quantization for spatiotemporal modeling, extracting efficiency from contemporary GPU systems might be challenging. Instead, co-designing custom accelerators by leveraging optimized High Level Synthesis frameworks (such as SODA High-Level Synthesizer for customized FPGA/ASIC targets) can make workload-specific adjustments to enhance the efficiency.

97 MATHEMATICS AND COMPUTING↗

Semi-Analytical Hierarchical Bayesian Inference of Nonlinear Model Structure in Stochastic Dynamics: Applied to Compartmental Models of Infectious Diseases

A Bayesian computational framework for parsimonious inference in stochastic nonlinear dynamical systems is presented. This framework enables the concurrent estimation of system states, time-varying parameters, time-invariant parameters, and the optimal sparsity structure of the model parameters. Because differential equation-based models are often simplified mechanistic or phenomenological representations, robust inference from noisy measurement data requires explicit treatment of model error and uncertainty. Model error and time-varying parameters can be represented as random processes, enabling inference while making minimal assumptions about the underlying sources of discrepancy and variability. Adopting stochastic differential equation representations affords the model significant flexibility, but can also render it susceptible to overfitting during statistical inversion, where the inferred model may track noise rather than the underlying signal. To alleviate the effects of overfitting and to enable the discovery of the optimal sparse representation of the time-invariant parameters, a Bayesian sparse learning algorithm is embedded within the framework. This sparse learning framework adopts an approximate hierarchical Bayesian setting defined by a series of semi-analytical expressions. The model structure inference framework is validated using a stochastic compartmental model for tracking and forecasting active cases of an infectious disease. Compartmental models describe population-level infectious disease dynamics through interactions among population fractions grouped by disease state. Mathematically, such models consist of a system of coupled ordinary differential equations. This example adopts an expressive compartmental model that includes multiple possible interactions between disease states, motivated by early uncertainty surrounding COVID-19 reinfection dynamics and their implications for long-term epidemic forecasting. The sparse learning exercise permits the inference of a priori unknown epidemiological dynamics from simulated public health data, discovering the nested compartmental model that optimizes the trade-off between average data-fit and model complexity. It is shown that inducing sparsity among the model parameters eliminates redundant interactions between compartments, equivalently revealing the optimal coupling structure between differential equations.

97 MATHEMATICS AND COMPUTING↗

Solar Uncertainty Management and Mitigation for Exceptional Reliability in Grid Operations (SUMMER-GO): Project Final Report

The Solar Uncertainty Management and Mitigation for Exceptional Reliability in Grid Operation (SUMMER-GO) project was recently completed through a collaboration among the National Renewable Energy Laboratory, Maxar, the Electric Reliability Council of Texas (ERCOT), the University of Texas at Dallas, the University of California Berkeley, and the University of Colorado Boulder. The project made significant advances in probabilistic solar power forecasting, both through the development of Bayesian model averaging methods for ensemble forecasting and in bringing these and other advancements into practice with Maxar's delivery of operational forecasts to ERCOT. In addition to creating more reliable solar power forecasts, the project developed methods for their utilization in power system operations. These include the development of risk-aware unit commitment and economic dispatch algorithms and methods to reformulate probabilistic forecasts to be used in these power system operational models. Dynamic power system reserve methods were also developed, which have been shown in silico to create economic savings and reliability improvements on an ERCOT-like system as well as financial savings in the ERCOT system through more granular consideration of the uncertainty associated with solar power forecasts. Finally, a situational awareness tool to help grid operators better understand solar power forecast uncertainty in daily operations was developed and extensively vetted.

14 SOLAR ENERGY↗

Short-lead seasonal precipitation forecast in northeastern Brazil using an ensemble of artificial neural networks

This study assesses the deterministic and probabilistic forecasting skill of a 1-month-lead ensemble of Artificial Neural Networks (EANN) based on low-frequency climate oscillation indices. The predictand is the February-April (FMA) rainfall in the Brazilian state of Ceará, which is a prominent subject in climate forecasting studies due to its high seasonal predictability. Additionally, the study proposes combining the EANN with dynamical models into a hybrid multi-model ensemble (MME). The forecast verification is carried out through a leave-one-out cross-validation based on 40 years of data. The EANN forecasting skill is compared with traditional statistical models and the dynamical models that compose Ceará’s operational seasonal forecasting system. A spatial comparison showed that the EANN was among the models with the smallest Root Mean Squared Error (RMSE) and Ranked Probability Score (RPS) in most regions. Moreover, the analysis of the area-aggregated reliability showed that the EANN is better calibrated than the individual dynamical models and has better resolution than Multinomial Logistic Regression for above-normal (AN) and below-normal (BN) categories. It is also shown that combining the EANN and dynamical models into a hybrid MME reduces the overconfidence of the extreme categories observed in a dynamically-based MME, improving the reliability of the forecasting system.

54 ENVIRONMENTAL SCIENCES↗

Saharan Dust Transport Predictability Utilizing a Subseasonal Experiment (SubX) Model

Prediction of Saharan dust customarily requires complex aerosols models and observations. A previous study of the Miami, Florida dust record in conjunction to reanalysis data discovered a possible source of subseasonal predictability using a dust-transport-efficiency (DTE) index. Development of the Subseasonal Forecast Experiment (SubX) has expanded global forecast products; producing multi-model ensemble forecasts out to 45 days. Retrospective forecast data from the Community Climate System Model version 4.0 (CCSM4) is used in direct comparison to National Centers for Environmental Prediction (NCEP) reanalysis to evaluate the CCSM4 subseasonal forecast and DTE index prediction skill of weekly dust variability. Successful prediction of weekly dust transport using the DTE index is variable year-to-year. The DTE most successfully predicts dust when there is high variability in the tropical winds, likely due to a fluctuating subtropical high, and is not dependent on the overall mean flow or total dust mass transported. The CCSM4 SubX retrospective forecast well represents North Atlantic meteorology out to week-3 in both mean flow and variability. Dust transport can be predicted using the DTE index and CCSM4 SubX retrospective forecasts at week-1 leads to the same success as contemporaneous NCEP reanalysis.

54 ENVIRONMENTAL SCIENCES↗

Combining Observations and Models: A Review of the CARDAMOM Framework for Data‐Constrained Terrestrial Ecosystem Modeling

The rapid increase in the volume and variety of terrestrial biosphere observations (i.e., remote sensing data and in situ measurements) offers a unique opportunity to derive ecological insights, refine process‐based models, and improve forecasting for decision support. However, despite their potential, ecological observations have primarily been used to benchmark process‐based models, as many past and current models lack the capability to directly integrate observations and their associated uncertainties for parameterization. In contrast, data assimilation frameworks such as the CARbon DAta MOdel fraMework (CARDAMOM) and its suite of process‐based models, known as the Data Assimilation Linked Ecosystem Carbon Model (DALEC), are specifically designed for model‐data fusion. This review, motivated by a recent CARDAMOM community workshop, examines the development and applications of CARDAMOM, with an emphasis on its role in advancing ecosystem process understanding. CARDAMOM employs a Bayesian approach, using a Markov Chain Monte Carlo algorithm to enable data‐driven calibration of DALEC parameters and initial states (i.e., carbon pool sizes) through observation operators. CARDAMOM's unique ability to retrieve localized model process parameters from diverse datasets—ranging from in situ measurements to global satellite observations—makes it a highly flexible tool for analyzing spatially variable ecosystem responses to environmental change. However, assimilating these data also presents challenges, including data quality issues that propagate into model skill, as well as trade‐offs between model complexity, parameter equifinality, and predictive performance. We discuss potential solutions to these challenges, such as reducing parameter equifinality by incorporating new observations. This review also offers community recommendations for incorporating emerging datasets, integrating machine learning techniques, strengthening collaboration with remote sensing, field, and modeling communities, and expanding CARDAMOM's relevance for localized ecosystem monitoring and decision‐making. CARDAMOM enables a deep, mechanistic understanding of terrestrial ecosystem dynamics that cannot be achieved through empirical analyses of observational datasets or weakly constrained models alone.

Bayesian inference↗

A Deep Learning Modeling Framework to Capture Mixing Patterns in Reactive-Transport Systems

Prediction and control of chemical mixing are vital for many scientific areas such as subsurface reactive transport, climate modeling, combustion, epidemiology, and pharmacology. Due to the complex nature of mixing in heterogeneous and anisotropic media, the mathematical models related to this phenomenon are not analytically tractable. Numerical simulations often provide a viable route to predict chemical mixing accurately. However, contemporary modeling approaches for mixing cannot utilize available spatial-temporal data to improve the accuracy of the future prediction and can be compute-intensive, especially when the spatial domain is large and for long-term temporal predictions. To address this knowledge gap, in this work we will present in this paper a deep learning (DL) modeling framework applied to predict the progress of chemical mixing under fast bimolecular reactions. This framework uses convolutional neural networks (CNN) for capturing spatial patterns and long short-term memory (LSTM) networks for forecasting temporal variations in mixing. By careful design of the framework—placement of non-negative constraint on the weights of the CNN and the selection of activation function, the framework ensures non-negativity of the chemical species at all spatial points and for all times. Our DL-based framework is fast, accurate, and requires minimal data for training. The time needed to obtain a forecast using the model is a fraction (≈ O(-6)) of the time needed to obtain the result using a high-fidelity simulation. To achieve an error of 10% (measured using the infinity norm) for capturing local-scale mixing features such as interfacial mixing, only 24% to 32% of the sequence data for model training is required. To achieve the same level of accuracy for capturing global-scale mixing features, the sequence data required for model training is 64% to 70% of the total spatial-temporal data. Hence, the proposed approach—a fast and accurate way to forecast long-time spatial-temporal mixing patterns in heterogeneous and anisotropic media—will be a valuable tool for modeling reactive-transport in a wide range of applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗