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Distributed Delay Differential Equation Representations of Cyclic Differential Equations
Compartmental ordinary differential equation (ODE) models are used extensively in mathematical biology. When transit between compartments occurs at a constant rate, the well-known linear chain trick can be used to show that the ODE model is equivalent to an Erlang distributed delay differential equation (DDE). Here, we demonstrate that compartmental models with nonlinear transit rates and possibly delayed arguments are also equivalent to a scalar distributed DDE. To illustrate the utility of these equivalences, we calculate the equilibria of the scalar DDE, and compute the characteristic function---without calculating a determinant. Further, we derive the equivalent scalar DDE for two examples of models in mathematical biology and use the DDE formulation to identify physiological processes that were otherwise hidden by the compartmental structure of the ODE model.
Stochastic representation and conditioning of process-based geological model by deep generative and recognition networks
Accurate and realistic geological modeling is the core of oil and gas development and production. In recent years, process-based methods are developed to produce highly realistic geological models by simulating the physical processes that reproduce the sedimentary events and develop the geometry. However, the complex dynamic processes are extremely expensive to simulate, making process-based models difficult to be conditioned to field data. In this work, we propose a comprehensive generative adversarial network framework as a machine-learning-assisted approach for mimicking the outputs of process-based geological models with fast generation. The main objective of our work is to obtain a continuous parametrization of the highly realistic process-based geological models which enables us to calibrate the models and condition the models to data. Numerical results are presented to illustrate the capability of our proposed methodology.
Training Spiking Neural Networks with Synaptic Plasticity under Integer Representation
Neuromorphic computing is emerging as a promising Beyond Moore computing paradigm that employs event-triggered computation and non-von Neumann hardware. Spike Timing Dependent Plasticity (STDP) is a well-known bio-inspired learning rule that relies on activities of locally connected neurons to adjust the weights of their respective synapses. In this work, we analyze a basic STDP rule and its sensitivity on the different hyperparameters for training spiking neural networks (SNNs) with supervision, customized for a neuromorphic hardware implementation with integer weights. We compare the classification performance on four UCI datasets (iris, wine, breast cancer and digits) that depict varying levels of complexity. We perform a search for optimal set of hyperparameters using both grid search and Bayesian optimization. Through the use of Bayesian optimization, we show the general trends in hyperparameter sensitivity in SNN classification problem. With the best sets of hyperparameters, we achieve accuracies comparable to some of the best performing SNNs on these four datasets. With a highly optimized supervised STDP rule we show that these accuracies can be achieved with just 20 epochs of training.
Distributed Localization with Grid-based Representations on Digital Elevation Models.
Abstract not provided.
Moment Representation of Regularized Lattice Boltzmann Methods on NVIDIA and AMD GPUs
The lattice Boltzmann method is a highly scalable Navier-Stokes solver that has been applied to flow problems in a wide array of domains. However, the method is bandwidth-bound on modern GPU accelerators and has a large memory footprint. In this paper, we present new 2D and 3D GPU implementations of two different regularized lattice Boltzmann methods, which are not only able to achieve an acceleration of ∼ 1.4 × w.r.t. reference lattice Boltzmann implementations but also reduce the memory requirements by up to 35% and 47% in 2D and 3D simulations respectively. These new approaches are evaluated on NVIDIA and AMD GPU architectures.
Efficacy of using a dynamic length representation vs. a fixed-length for neuroarchitecture search
Deep learning neuroarchitecture and hyperparameter search are important in finding the best configuration that maximizes learned model accuracy. However, the number of types of layers, their associated hyperparameters, and the myriad of ways to connect layers poses a significant computational challenge in discovering ideal model configurations. Here, we assess two different approaches for neuroarchitecture search for a LeNet style neural network, one that uses a fixed-length approach where there is a preset number of possible layers that can be toggled on or off via mutation, and a variable-length approach where layers can be freely added or removed via special mutation operators. We found that the variable-length implementation trained better models while discovering unusual layer configurations worth further exploration.
A Deep Multimodal Representation Learning Framework for Accurate Molecular Properties Prediction
Drug discovery is a complex and challenging process, requiring the optimization of candidate compounds to identify those with the potential to become safe and effective drugs. Predicting molecular properties is an indispensable step in the drug discovery pipeline. Traditionally, this process is costly and time-intensive, involving multiple rounds of experiments and clinical trials, rendering it impractical for every candidate compound. Deep learning techniques have emerged as a promising approach to drug discovery to reduce the cost and time required to identify novel drugs. However, prevalent research in deep learning models focused on predicting molecular properties has primarily fixated on single-modal models, which utilize a single modality of data, neglecting the potential benefits of combining different data modalities. To overcome this limitation, we introduce MRL-Mol: a deep \textbf{M}ultimodal \textbf{R}epresentation \textbf{L}earning framework for accurate \textbf{Mol}ecular properties prediction. MRL-Mol harnesses three data modalities: sequence, graph, and image, augmenting the depth of comprehension. Leveraging a large-scale unlabeled dataset~($\sim$1M unique molecules), we pretrain MRL-Mol to extract inter- and intra-modal information. Our study demonstrates the superior performance of MRL-Mol in predicting molecular properties across six benchmark datasets, including both classification and regression tasks. Notably, MRL-Mol outperforms other state-of-the-art molecular properties prediction models. These findings suggest that by combining information from multiple data modalities, MRL-Mol can comprehend molecules better than single-modal deep learning models and identify molecular properties with better accuracy.
CLIP Representation Enhanced Predicate Estimation
This software provides functions to perform visual predicate estimation by leveraging the pre-trained vision-language model CLIP. In addition to training the prediction estimator with a labeled dataset, it also performs performance evaluation and visualization of results.
PRIME: Protein Representation Inference for Mutation Evaluation
Protein language machine learning models built upon existing ESM-2 model developed by Evolutionary Scale (evolutionaryscale.ai) and an in-house protein language model based on the BERT model developed by Google. The code also includes model training scripts and saved checkpoints from our own training using publicly available SARS-CoV-2 protein sequences.
Improved Representation of Horizontal Variability and Turbulence in Mesoscale Simulations of an Extended Cold-Air Pool Event
Abstract Cold-air pools (CAPs), or stable atmospheric boundary layers that form within topographic basins, are associated with poor air quality, hazardous weather, and low wind energy output. Accurate prediction of CAP dynamics presents a challenge for mesoscale forecast models in part because CAPs occur in regions of complex terrain, where traditional turbulence parameterizations may not be appropriate. This study examines the effects of the planetary boundary layer (PBL) scheme and horizontal diffusion treatment on CAP prediction in the Weather Research and Forecasting (WRF) Model. Model runs with a one-dimensional (1D) PBL scheme and Smagorinsky-like horizontal diffusion are compared with runs that use a new three-dimensional (3D) PBL scheme to calculate turbulent fluxes. Simulations are completed in a nested configuration with 3-km/750-m horizontal grid spacing over a 10-day case study in the Columbia River basin, and results are compared with observations from the Second Wind Forecast Improvement Project. Using event-averaged error metrics, potential temperature and wind speed errors are shown to decrease both with increased horizontal grid resolution and with improved treatment of horizontal diffusion over steep terrain. The 3D PBL scheme further reduces errors relative to a standard 1D PBL approach. Error reduction is accentuated during CAP erosion, when turbulent mixing plays a more dominant role in the dynamics. Last, the 3D PBL scheme is shown to reduce near-surface overestimates of turbulence kinetic energy during the CAP event. The sensitivity of turbulence predictions to the master length-scale formulation in the 3D PBL parameterization is also explored. Significance Statement In this article, we demonstrate how a new framework for modeling atmospheric turbulence improves cold pool predictions, using a case study from January 2017 in the Columbia River basin (U.S. Pacific Northwest). Cold pools are regions of cold, stagnant air that form within valleys or basins, and improved forecasts could help to mitigate the risks they pose to air quality, transportation, and wind energy production. For the chosen case study, our tests show a reduction in temperature and wind speed errors by up to a factor of 2–3 relative to standard model options. These results strongly motivate continued development of the framework as well as its application to other complex weather events.
Representation of the Convectively Coupled Kelvin Waves in Modern Reanalysis Products
Abstract This study aims to deepen our understanding of the destabilization mechanisms and the mean-state modulation of the convectively coupled Kelvin waves (CCKWs) while testing simple models for CCKWs. We examine CCKW precipitation, vertical structure, and energetics in four modern reanalyses: the fifth version of ECMWF Reanalysis (ERA5), NASA Modern-Era Retrospective Analysis for Research and Applications, version 2 (MERRA-2), the second version of the NCEP Climate Forecast System Reanalysis (CFSR), and the Japanese 55-year Reanalysis (JRA-55). The CCKW precipitation signal strength in the wavenumber–frequency domain and the geographical distribution of CCKW precipitation variability are reasonably represented in all reanalyses, although they commonly underestimate the amplitude of CCKW precipitation. Despite considerable interreanalysis differences in the vertical structure of temperature and diabatic heating anomalies, the eddy available potential energy (EAPE) generation within the CCKWs is found to be associated with the second baroclinic mode whereas the first baroclinic mode damps CCKW EAPE in three out of four reanalyses. Geographically, strong CCKW activity occurs in the areas of high mean-state sea surface temperature (SST), where the second mode EAPE generation is higher, mainly due to a stronger stratiform heating and a tighter wave–convection coupling. Our results are supportive of the simple models for CCKWs in which CCKWs are destabilized within the second baroclinic mode component.
Steric Sea Level Rise and Relationships with Model Drift and Water Mass Representation in GFDL CM4 and ESM4
Abstract Density-driven steric seawater changes are a leading-order contributor to global mean sea level rise. However, intermodel differences in the magnitude and spatial patterns of steric sea level rise exist at regional scales and often emerge during the spinup and preindustrial control integrations of climate models. Steric sea level results from an eddy-permitting climate model, GFDL CM4, are compared with a lower-resolution counterpart, GFDL-ESM4. The results from both models are examined through basin-scale heat budgets and watermass analysis, and we compare the patterns of ocean heat uptake, redistribution, and sea level differ in ocean-only [i.e., Ocean Model Intercomparison Project (OMIP)] and coupled climate configurations. After correcting for model drift, both GFDL CM4 and GFDL-ESM4 simulate nearly equivalent ocean heat content change and global sea level rise during the historical period. However, the GFDL CM4 model exhibits as much as a 40% increase in surface ocean heat uptake in the Southern Ocean and subsequent increases in horizontal export to other ocean basins after bias correction. The results suggest regional differences in the processes governing Southern Ocean heat export, such as the formation of Antarctic Intermediate Water (AAIW), Subpolar Mode Water (SPMW), and gyre transport between the two models, and that sea level changes in these models cannot be fully bias-corrected. Since the process-level differences between the two models are evident in the preindustrial control simulations of both models, these results suggest that the control simulations are important for identifying and correcting sea level–related model biases.
Vegetation Representation Influences Projected Streamflow Changes in the Colorado River Basin
Vegetation parameters for the Variable Infiltration Capacity (VIC) hydrologic model were recently updated using observations from the Moderate Resolution Imaging Spectroradiometer (MODIS). Previous work showed that these MODIS-based parameters improved VIC evapotranspiration simulations when compared to eddy covariance observations. Due to the importance of evapotranspiration within the Colorado River basin, this study provided a basin-by-basin calibration of VIC soil parameters with updated MODIS-based vegetation parameters to improve streamflow simulations. Interestingly, while both configurations had similar historic streamflow performance, end-of-century hydrologic projections, driven by 29 downscaled global climate models under the RCP8.5 emissions scenario, differed between the two configurations. The calibrated MODIS-based configuration had an ensemble mean that simulated little change in end-of-century annual streamflow volume (+0.4%) at Lees Ferry, Arizona, relative to the historical period (1960–2005). In contrast, the previous VIC configuration, which is used to inform decisions about future water resources in the Colorado River basin, projected an 11.7% decrease in annual streamflow. Both VIC configurations simulated similar amounts of evapotranspiration in the historical period. However, the MODIS-based VIC configuration did not show as much of an increase in evapotranspiration by the end of the century, primarily within the upper basin’s forested areas. Differences in evapotranspiration projections were the result of the MODIS-based vegetation parameters having lower leaf area index values and less forested area compared to previous vegetation estimates used in recent Colorado River basin hydrologic projections. These results highlight the need to accurately characterize vegetation and better constrain climate sensitivities in hydrologic models.
Quantifying the Impact of Vertical Resolution on the Representation of Marine Boundary Layer Physics for Global-Scale Models
Abstract While GCM horizontal resolution has received the majority of scale improvements in recent years, ample evidence suggests that a model’s vertical resolution exerts a strong control on its ability to accurately simulate the physics of the marine boundary layer. Here we show that, regardless of parameter tuning, the ability of a single-column model (SCM) to simulate the subtropical marine boundary layer improves when its vertical resolution is improved. We introduce a novel objective tuning technique to optimize the parameters of an SCM against profiles of temperature and moisture and their turbulent fluxes, horizontal winds, cloud water, and rainwater from large-eddy simulations (LES). We use this method to identify optimal parameters for simulating marine stratocumulus and shallow cumulus. The novel tuning method utilizes an objective performance metric that accounts for the uncertainty in the LES output, including the covariability between model variables. Optimization is performed independently for different vertical grid spacings and value of time step, ranging from coarse scales often used in current global models (120 m, 180 s) to fine scales often used in parameterization development and large-eddy simulations (10 m, 15 s). Uncertainty-weighted disagreement between the SCM and LES decreases by a factor of ∼5 when vertical grid spacing is improved from 120 to 10 m, with time step reductions being of secondary importance. Model performance is shown to converge at a vertical grid spacing of 20 m, with further refinements to 10 m leading to little further improvement. Significance Statement In successive generations of computer models that simulate Earth’s atmosphere, improvements have been mainly accomplished by reducing the horizontal sizes of discretized grid boxes, while the vertical grid spacing has seen comparatively lesser refinements. Here we advocate for additional attention to be paid to the number of vertical layers in these models, especially in the model layers closest to Earth’s surface where climatologically important marine stratocumulus and shallow cumulus clouds reside. Our experiments show that the ability of a one-dimensional model to represent physical processes important to these clouds is strongly dependent on the model’s vertical grid spacing.
A General, Automated Method for Building Structural Tensors of Arbitrary Order for Anisotropic Function Representations
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ZFP: A compressed array representation for numerical computations
HPC trends favor algorithms and implementations that reduce data motion relative to FLOPS. We investigate the use of lossy compressed data arrays in place of traditional IEEE floating point arrays to store the primary data of calculations. Simulation is fundamentally an exercise in controlled approximation, and error introduced by finite-precision arithmetic (or lossy compression) is just one of several sources of error that need to be managed to ensure sufficient accuracy in a computed result. We describe ZFP, a compressed numerical format designed for in-memory storage of multidimensional arrays, and summarize theoretical results that demonstrate that the error of repeated lossy compression can be bounded and controlled. Furthermore, we establish a relationship between grid resolution and compression-induced errors and show that, contrary to conventional floating point, ZFP reduces finite-difference errors with finer grids. We present example calculations that demonstrate data reduction by 4x or more with negligible impact on solution accuracy. Our results further demonstrate several orders-of-magnitude increase in accuracy using ZFP over IEEE floating point and Posits for the same storage budget.
Toward more mechanistic representations of biogeochemical processes in stream and river networks: Implementation and demonstration of a multiscale model : Modeling Archive
This Modeling Archive supports the ORNL-SFA and IDEAS-Waterhsed publication submitted to Environmental Modeling and Software. A recently introduced multiscale model for representing the combined effect of hyporheic exchange flows and small-scale hyporheic-zone biogeochemical processes is extended from the reach scale to river network scales. The ADELS (Advection Dispersion Equation with Lagrangian Subgrid) model uses a one-dimensional advection-dispersion-reaction equation for the channel network and couples that equation at each channel location to a one-dimensional advection-reaction subgrid model representing an ensemble of streamlines that are diverted into the hyporheic zone before returning to the channel. The subgrid model is written in a computationally advantageous Lagrangian form with hyporheic age replacing the hyporheic travel distance. In the paper, we summarized implementation in the integrated surface/subsurface hydrology modeling system Advanced Terrestrial Simulator (ATS).