Coarse Simulation Research Articles

Spatially Local Surrogate Modeling of Subgrid-Scale Effects in Idealized Atmospheric Flows: A Deep Learned Approach Using High-Resolution Simulation Data

Abstract We introduce a machine learned surrogate model from high-resolution simulation data to capture the subgrid-scale effects in dry, stratified atmospheric flows. We use deep neural networks (NNs) to model the spatially local state differences between a coarse-resolution simulation and a high-resolution simulation. The setup enables the capture of both dissipative and antidissipative effects in the state differences. The NN model is able to accurately capture the state differences in offline tests outside the training regime. In online tests intended for production use, the NN-coupled coarse simulation has higher accuracy over a significant period of time compared to the coarse-resolution simulation without any correction. We provide evidence of the capability of the NN model to accurately capture high-gradient regions in the flow field. With the accumulation of the errors, the NN-coupled simulation becomes computationally unstable after approximately 90 coarse simulation time steps. Insights gained from these surrogate models further pave the way for formulating stable, complex, physics-based spatially local NN models which are driven by traditional subgrid-scale turbulence closure models. Significance Statement Flows in the atmosphere are highly chaotic and turbulent, comprising flow structures of broad scales. For effective computational modeling of atmospheric flows, the effects of the small- and large-scale structures need to be captured by the simulations. Capturing the small-scale structures requires fine-resolution simulations. Even with the current state-of-the-art supercomputers, it can be prohibitively expensive to simulate these flows when computed for the entire earth over climate time scales. Thus, it is necessary to focus on the larger-scale structures using a coarse-resolution simulation while capturing the effects of the smaller-scale structures using some parameterization (approximation) scheme and incorporating it into the coarse-resolution simulation. We use machine learning to model the effects of the small-scale structures (subgrid-scale effects) in atmospheric flows. Data from a fine-resolution simulation is used to compute the missing subgrid-scale effects in coarse-resolution simulations. We then use machine learning models to approximate these differences between the coarse- and fine-resolution simulations. We see improved accuracy for the coarse-resolution simulations when corrected using these machine learned models.

Super-Resolution Cloth Animation with Spatial and Temporal Coherence

Creating super-resolution cloth animations, which refine coarse cloth meshes with fine wrinkle details, faces challenges in preserving spatial consistency and temporal coherence across frames. In this paper, we introduce a general framework to address these issues, leveraging two core modules. The first module interleaves a simulator and a corrector. The simulator handles cloth dynamics, while the corrector rectifies differences in low-frequency features across various resolutions. This interleaving ensures prompt correction of spatial errors from the coarse simulation, effectively preventing their temporal propagation. The second module performs mesh-based super-resolution for detailed wrinkle enhancements. We decompose garment meshes into overlapping patches for adaptability to various styles and geometric continuity. Our method achieves an 8× improvement in resolution for cloth animations. We showcase the effectiveness of our method through diverse animation examples, including simple cloth pieces and intricate garments.

Convolutional neural networks for compressible turbulent flow reconstruction

This paper investigates deep learning methods in the framework of convolutional neural networks for reconstructing compressible turbulent flow fields. The aim is to develop methods capable of up-scaling coarse turbulent data into fine-resolution images. The method is based on a parallel computational framework that accepts five image sets of various resolutions, trained to correspond to the respective fine resolution. The network architecture mainly consists of convolutional layers, constructing an encoder/decoder network. Based on the U-Net scheme, three different implementations are presented, with residual and skip connections. The methods are implemented in a supersonic shock-boundary-layer interaction problem. The results suggest that simple networks perform better when trained on limited data, and this can be a practical and fast solution when dealing with turbulent flow data, where the computational burden is most of the time difficult to decrease. In such a way, a coarse simulation grid can be upscaled to a fine grid.

The DESI One-Percent Survey: Constructing Galaxy–Halo Connections for ELGs and LRGs Using Auto and Cross Correlations

In the current Dark Energy Spectroscopic Instrument (DESI) survey, emission line galaxies (ELGs) and luminous red galaxies (LRGs) are essential for mapping the dark matter distribution at z ∼ 1. We measure the auto and cross correlation functions of ELGs and LRGs at 0.8 < z ≤ 1.0 from the DESI One-Percent survey. Following Gao et al., we construct the galaxy–halo connections for ELGs and LRGs simultaneously. With the stellar–halo mass relation for the whole galaxy population (i.e., normal galaxies), LRGs can be selected directly by stellar mass, while ELGs can also be selected randomly based on the observed number density of each stellar mass, once the probability P sat of a satellite galaxy becoming an ELG is determined. We demonstrate that the observed small scale clustering prefers a halo mass-dependent P sat model rather than a constant. With this model, we can well reproduce the auto correlations of LRGs and the cross correlations between LRGs and ELGs at r p > 0.1 Mpc h −1. We can also reproduce the auto correlations of ELGs at r p > 0.3 Mpc h −1 (s > 1 Mpc h −1) in real (redshift) space. Although our model has only seven parameters, we show that it can be extended to higher redshifts and reproduces the observed auto correlations of ELGs in the whole range of 0.8 < z ≤ 1.6, which enables us to generate a lightcone ELG mock for DESI. With the above model, we further derive halo occupation distributions for ELGs, which can be used to produce ELG mocks in coarse simulations without resolving subhalos.

Toward accelerated data-driven Rayleigh-Bénard convection simulations.

A hybrid data-driven/finite volume method for 2D and 3D thermal convective flows is introduced. The approach relies on a single-step loss, convolutional neural network that is active only in the near-wall region of the flow. We demonstrate that the method significantly reduces errors in the prediction of the heat flux over the long-time horizon and increases pointwise accuracy in coarse simulations, when compared to direct computations on the same grids with and without a traditional subgrid model. We trace the success of our machine learning model to the choice of the training procedure, incorporating both the temporal flow development and distributional bias.

A Compact Model for Ferroelectric Capacitors Based on Multidomain Phase-Field Framework

A generalized and fast multidomain phase-field-based compact model for the metal-ferroelectric-metal (MFM) capacitor is presented. Time-dependent Landau–Ginzburg (TDGL) and Poisson’s equations are solved self-consistently to model the polarization dynamics. Additionally, physics-based empirical relationships for voltage-dependent kinetic and gradient energy coefficients are formulated. It is also demonstrated how gradient energy coefficient needs to be modified to accurately capture the physics of the device when a coarse simulation grid is used for fast computation. The developed model is 30 000 times faster than our prior multidomain phase-field model with no degradation in accuracy. Moreover, a further computational speedup has been achieved by decreasing the number of Poisson solver nodes with a slight compromise of accuracy. The model shows a good agreement with the experimental results of both transient characteristics and minor hysteresis loops. The proposed model has the potential to facilitate fast and accurate simulations of large-scale circuits containing ferroelectric capacitors.

A Batched Bayesian Optimization Approach for Analog Circuit Synthesis via Multi-Fidelity Modeling

Device sizing is a challenging problem for analog circuit design. Traditional methods depend on domain knowledge and intensive simulations to search for feasible parameters. Recent studies apply the Bayesian optimization (BO) and a Gaussian process (GP) model in analog circuit synthesis to improve efficiency. The BO framework automatically selects the parameter candidates by inferring the surrogate GP model. However, naive BO employs a sequential updating strategy which is inefficient in a multicore environment. Besides, the widely used GP model requires costly high fidelity data, which are obtained from fine simulations. In this article, we propose a constrained batch BO approach with a multifidelity (MF) model to solve the above difficulties. The batch BO exploits parallel computing and selects promising parameters by multiple acquisition function ensemble. In addition, the MF GP model adapts the low fidelity data obtained from coarse simulations. Specifically, the proposed method incorporates information gain in a weighted clustering algorithm to refine the parameter candidates. As a result, the proposed method maintains the candidates’ quality and diversity, which speeds up the optimization convergence. In the experiments, we demonstrate the efficiency of the proposed approach on three real-world circuits. The results show that our approach reduces the simulation costs by at least 54.6% compared to the state-of-the-art baselines.

Modulation of the Eastern Equatorial Pacific Seasonal Cycle by Tropical Instability Waves

AbstractFeedbacks from tropical instability waves (TIWs) on the seasonal cycle of the eastern Pacific Ocean are studied using two eddy‐rich ocean simulations, with and without TIWs. By warming the equatorial waters by up to 0.4°C through nonlinear advection in boreal summer and fall, TIWs reduce the amplitude of the seasonal cycle in upper ocean temperatures. In addition, TIWs stabilize the upper part of the Equatorial Undercurrent (EUC) through enhanced barotropic energy conversion, leading to a year‐round weakening by −0.15 m s−1 and preventing an unrealistic re‐intensification in boreal fall usually found in non‐eddy resolving models. A coarser simulation at 1‐degree horizontal resolution fails to reproduce the TIW‐induced nonlinear warming of equatorial waters, but succeeds in inhibiting the EUC re‐intensification. This suggests a threshold effect in TIW strength, associated with the model's ability to simulate eddies, which may be responsible for long‐standing biases displayed by global climate models in this region.

Progressive Simulation for Cloth Quasistatics

The trade-off between speed and fidelity in cloth simulation is a fundamental computational problem in computer graphics and computational design. Coarse cloth models provide the interactive performance required by designers, but they can not be simulated at higher resolutions ("up-resed") without introducing simulation artifacts and/or unpredicted outcomes, such as different folds, wrinkles and drapes. But how can a coarse simulation predict the result of an unconstrained, high-resolution simulation that has not yet been run? We propose Progressive Cloth Simulation (PCS), a new forward simulation method for efficient preview of cloth quasistatics on exceedingly coarse triangle meshes with consistent and progressive improvement over a hierarchy of increasingly higher-resolution models. PCS provides an efficient coarse previewing simulation method that predicts the coarse-scale folds and wrinkles that will be generated by a corresponding converged, high-fidelity C-IPC simulation of the cloth drape's equilibrium. For each preview PCS can generate an increasing-resolution sequence of consistent models that progress towards this converged solution. This successive improvement can then be interrupted at any point, for example, whenever design parameters are updated. PCS then ensures feasibility at all resolutions, so that predicted solutions remain intersection-free and capture the complex folding and buckling behaviors of frictionally contacting cloth.

Multifidelity multiobjective optimization for wake-steering strategies

Abstract. Wake steering is an emerging wind power plant control strategy where upstream turbines are intentionally yawed out of perpendicular alignment with the incoming wind, thereby “steering” wakes away from downstream turbines. However, trade-offs between the gains in power production and fatigue loads induced by this control strategy are the subject of continuing investigation. In this study, we present a multifidelity multiobjective optimization approach for exploring the Pareto front of trade-offs between power and loading during wake steering. A large eddy simulation is used as the high-fidelity model, where an actuator line representation is used to model wind turbine blades and a rainflow-counting algorithm is used to compute damage equivalent loads. A coarser simulation with a simpler loads model is employed as a supplementary low-fidelity model. Multifidelity Bayesian optimization is performed to iteratively learn both a surrogate of the low-fidelity model and an additive discrepancy function, which maps the low-fidelity model to the high-fidelity model. Each optimization uses the expected hypervolume improvement acquisition function, weighted by the total cost of a proposed model evaluation in the multifidelity case. The multifidelity approach is able to capture the logit function shape of the Pareto frontier at a computational cost only 30 % that of the single-fidelity approach. Additionally, we provide physical insights into the vortical structures in the wake that contribute to the Pareto front shape.

Exponential integration for efficient and accurate multibody simulation with stiff viscoelastic contacts

The simulation of multibody systems with frictional contacts is a fundamental tool for many fields, such as robotics, computer graphics, and mechanics. Hard frictional contacts are particularly troublesome to simulate because they make differential equations stiff, calling for computationally demanding implicit integration schemes. We suggest to tackle this issue by using exponential integrators, a long-standing class of integration schemes (first introduced in the 1960s) that in recent years has enjoyed a resurgence of interest. This scheme can be applied to multibody systems subject to stiff viscoelastic contacts, leading to integration errors similar to implicit Euler, but at much lower computational costs (between 2 to 100 times faster). In our tests with quadruped and biped robots, our method demonstrated a stable behavior with large time steps (10 ms) and stiff contacts (\(10^{5}\) N/m). Its excellent properties, especially for fast and coarse simulations, make it a valuable candidate for many applications in robotics, such as simulation, model predictive control, reinforcement learning, and controller design.

An artificial intelligence method for improving upscaling in complex reservoirs

The upscaling of geological properties is a fundamental requirement to construct a suitable simulation model since the geological model typically contains millions of cells, which makes it computationally difficult to simulate it on such a scale. The process consists of a scale transfer that adapts the petrophysical properties of a high-resolution grid to a coarser grid. Nevertheless, this is not a trivial operation, especially for absolute permeability, which is a non-additive property. One of the most reliable methods is to perform a flow simulation on fine-scale cells that correspond to the coarse block and derive the single permeability value that reflects the same flow value. Still, this is a very time-consuming method and depends on the imposed boundary conditions. This work aims to take advantage of recent advances in artificial intelligence to produce results with similar or better quality of flow-based methods, and more adaptive. It handles models with multiple geological realizations by employing machine learning to capture patterns from a subset of scenarios and use it to generalize for all others. The methodology is divided into two stages — local and global. In the first one, a deep neural network is trained with a fraction of geological realizations using the flow-based results as a reference. In the second stage, clustering analysis is employed along with a neural network optimization to learn an adjustment procedure for the coarse simulation model concerning the cumulative field production predicted by the fine model simulation. Afterward, the trained network performs the upscaling of remaining realizations, but more efficiently in terms of computational time and providing better output in terms of production and injection. The method was applied to a benchmark model and the experimental results demonstrate that the local technique was capable of reproducing very similar values to the flow-based upscaling using only one scenario in training and at the global stage the coarse model was improved even further matching the field oil production forecast of the fine model. Different scenarios were used for training and testing and the results were consistent showing no bias towards a specific configuration and capability of generalization to different scenarios. Ultimately, the proposed artificial intelligence approach performed an accurate upscaling, surpassing the reference approach with forecast production similar to the fine model, and also fast to compute when considering multiple geological realizations, since it reduces the required numerical simulations to a fraction of the total.

Resolved and subgrid-scale crossing trajectory effects in Eulerian large eddy simulations of size-dependent droplet transport

We study the dispersion characteristics of slightly buoyant droplets in a turbulent jet using large eddy simulations (LES). The droplet number density fields are represented using an Eulerian approach, with the dispersed phase modelled using the Fast-Eulerian method (Ferry &amp; Balachandar, Intl J. Multiphase Flow, vol. 27, issue 7, pp. 1199–1226, 2001) that includes the droplet rise velocity. Radial concentration profiles and turbulent concentration fluxes for droplets of different sizes are analysed to quantify the ‘trajectory crossing effect’, when relative motions between particles and turbulent eddies tend to reduce turbulent diffusion. For finer LES grid resolutions, the model captures the differential, size-based dispersion characteristics of the droplets with the transverse dispersion of the larger droplet sizes suppressed, since trajectory crossing effects are explicitly resolved in LES. We examine a similarity solution model for the size-dependent radial concentration profiles based on a modified Schmidt number derived from the theory of turbulent diffusion of particles in the atmosphere proposed by Csanady (J. Atmos. Sci., vol. 20, pp. 201–208, 1963). The results are validated with the high resolution LES data and show good agreement. Then the size-dependent Schmidt number model is reformulated as a model for unresolved subgrid-scale trajectory crossing effects and used to calculate the subgrid concentration flux in a coarse LES of a turbulent jet, with slightly buoyant droplets injected at the centreline in the self-similar region of the jet. The results are compared to a simulation with higher grid resolution and a coarse simulation with a constant Schmidt number subgrid-scale model. We find that the subgrid model enhances the prediction accuracy of the concentration profiles and turbulent concentration flux for the coarse LES.

Evaluation of Asian summer precipitation in different configurations of a high-resolution general circulation model in a range of decision-relevant spatial scales

Abstract. High-resolution general circulation models (GCMs) can provide new insights into the simulated distribution of global precipitation. We evaluate how summer precipitation is represented over Asia in global simulations with a grid length of 14 km. Three simulations were performed: one with a convection parametrization, one with convection represented explicitly by the model's dynamics, and a hybrid simulation with only shallow and mid-level convection parametrized. We evaluate the mean simulated precipitation and the diurnal cycle of the amount, frequency, and intensity of the precipitation against satellite observations of precipitation from the Climate Prediction Center morphing method (CMORPH). We also compare the high-resolution simulations with coarser simulations that use parametrized convection. The simulated and observed precipitation is averaged over spatial scales defined by the hydrological catchment basins; these provide a natural spatial scale for performing decision-relevant analysis that is tied to the underlying regional physical geography. By selecting basins of different sizes, we evaluate the simulations as a function of the spatial scale. A new BAsin-Scale Model Assessment ToolkIt (BASMATI) is described, which facilitates this analysis. We find that there are strong wet biases (locally up to 72 mm d−1 at small spatial scales) in the mean precipitation over mountainous regions such as the Himalayas. The explicit convection simulation worsens existing wet and dry biases compared to the parametrized convection simulation. When the analysis is performed at different basin scales, the precipitation bias decreases as the spatial scales increase for all the simulations; the lowest-resolution simulation has the smallest root mean squared error compared to CMORPH. In the simulations, a positive mean precipitation bias over China is primarily found to be due to too frequent precipitation for the parametrized convection simulation and too intense precipitation for the explicit convection simulation. The simulated diurnal cycle of precipitation is strongly affected by the representation of convection: parametrized convection produces a peak in precipitation too close to midday over land, whereas explicit convection produces a peak that is closer to the late afternoon peak seen in observations. At increasing spatial scale, the representation of the diurnal cycle in the explicit and hybrid convection simulations improves when compared to CMORPH; this is not true for any of the parametrized simulations. Some of the strengths and weaknesses of simulated precipitation in a high-resolution GCM are found: the diurnal cycle is improved at all spatial scales with convection parametrization disabled, the interaction of the flow with orography exacerbates existing biases for mean precipitation in the high-resolution simulations, and parametrized simulations produce similar diurnal cycles regardless of their resolution. The need for tuning the high-resolution simulations is made clear. Our approach for evaluating simulated precipitation across a range of scales is widely applicable to other GCMs.

Soft-Tissue Simulation for Computational Planning of Orthognathic Surgery.

Simulation technologies offer interesting opportunities for computer planning of orthognathic surgery. However, the methods used to date require tedious set up of simulation meshes based on patient imaging data, and they rely on complex simulation models that require long computations. In this work, we propose a modeling and simulation methodology that addresses model set up and runtime simulation in a holistic manner. We pay special attention to modeling the coupling of rigid-bone and soft-tissue components of the facial model, such that the resulting model is computationally simple yet accurate. The proposed simulation methodology has been evaluated on a cohort of 10 patients of orthognathic surgery, comparing quantitatively simulation results to post-operative scans. The results suggest that the proposed simulation methods admit the use of coarse simulation meshes, with planning computation times of less than 10 seconds in most cases, and with clinically viable accuracy.

Sequential Design of Multi-Fidelity Computer Experiments: Maximizing the Rate of Stepwise Uncertainty Reduction

This article deals with the sequential design of experiments for (deterministic or stochastic) multi-fidelity numerical simulators, that is, simulators that offer control over the accuracy of simulation of the physical phenomenon or system under study. Accurate simulations usually entail a high computational effort, while coarse simulations are obtained at a lower cost. The cost can be measured, for example, by the run time of the simulator or the financial cost of the computing resources. In this setting, simulation results obtained at several levels of fidelity can be combined in order to estimate quantities of interest (the optimal value of the output, the probability that the output exceeds a given threshold, etc.) in an efficient manner. We propose a new Bayesian sequential strategy called maximal rate of stepwise uncertainty reduction (MR-SUR), that selects additional simulations to be performed by maximizing the ratio between the expected reduction of uncertainty and the cost of simulation. This generic strategy unifies several existing methods, and provides a principled approach to develop new ones. We assess its performance on several examples, including a computationally intensive problem of fire safety analysis where the quantity of interest is the probability of exceeding a tenability threshold during a building fire.

Engineering the Nanoscaled Morphologies of Linear DNA Homopolymers.

Supramolecular polymers have unique characteristics such as self-healing and easy processing. However, the scope of their structures is limited to mostly either flexible, random coils or rigid, straight chains. By broadening this scope, novel properties, functions, and applications can be explored. Here, DNA is used as a model system to engineer innovative, nanoscaled morphologies of supramolecular polymers. Each polymer chain consists of multiple copies of the same short (38-46 nucleotides long) DNA strand. The component DNA strands first dimerize into homo-dimers, which then further assemble into long polymer chains. By subtly tuning the design, a range of polymer morphologies are obtained; including straight chains, spirals, and closed rings with finite sizes. Such structures are confirmed by AFM imaging and predicted by molecular coarse simulation.

Increasing Resolution and Resolving Convection Improve the Simulation of Cloud‐Radiative Effects Over the North Atlantic

AbstractClouds interact with atmospheric radiation and substantially modify the Earth's energy budget. Cloud formation processes occur over a vast range of spatial and temporal scales, which make their thorough numerical representation challenging. Therefore, the impact of parameter choices for simulations of cloud‐radiative effects is assessed in the current study. Numerical experiments are carried out using the ICOsahedral Nonhydrostatic (ICON) model with varying grid spacings between 2.5 and 80 km and with different subgrid‐scale parameterization approaches. Simulations are performed over the North Atlantic with either one‐moment or two‐moment microphysics and with convection being parameterized or explicitly resolved by grid‐scale dynamics. Simulated cloud‐radiative effects are compared to products derived from Meteosat measurements. Furthermore, a sophisticated cloud classification algorithm is applied to understand the differences and dependencies of simulated and observed cloud‐radiative effects. The cloud classification algorithm developed for the satellite observations is also applied to the simulation output based on synthetic infrared brightness temperatures, a novel approach that is not impacted by changing insolation and guarantees a consistent and fair comparison. It is found that flux biases originate equally from clear‐sky and cloudy parts of the radiation field. Simulated cloud amounts and cloud‐radiative effects are dominated by marine, shallow clouds, and their behavior is highly resolution dependent. Bias compensation between shortwave and longwave flux biases, seen in the coarser simulations, is significantly diminished for higher resolutions. Based on the analysis results, it is argued that cloud‐microphysical and cloud‐radiative properties have to be adjusted to further improve agreement with observed cloud‐radiative effects.

Stochastic representation of mesoscale eddy effects in coarse-resolution barotropic models

A stochastic representation based on a physical transport principle is proposed to account for mesoscale eddy effects on the evolution of the large-scale flow. This framework arises from a decomposition of the Lagrangian velocity into a smooth (in time) component and a highly oscillating term. One important characteristic of this random model is that it conserves the energy of any transported scalar. Such an energy-preserving representation is tested for the coarse simulation of a barotropic circulation in a shallow ocean basin, driven by a symmetric double-gyres wind forcing. The empirical spatial correlation of the random small-scale velocity is estimated from data of an eddy-resolving simulation. After reaching a turbulent equilibrium state, a statistical analysis of tracers shows that the proposed random model enables us to reproduce accurately, on a coarse mesh, the local structures of the first four statistical moments (mean, variance, skewness and kurtosis) of the high-resolution eddy-resolved data.

MoBPS - Modular Breeding Program Simulator.

The R-package MoBPS provides a computationally efficient and flexible framework to simulate complex breeding programs and compare their economic and genetic impact. Simulations are performed on the base of individuals. MoBPS utilizes a highly efficient implementation with bit-wise data storage and matrix multiplications from the associated R-package miraculix allowing to handle large scale populations. Individual haplotypes are not stored but instead automatically derived based on points of recombination and mutations. The modular structure of MoBPS allows to combine rather coarse simulations, as needed to generate founder populations, with a very detailed modeling of todays’ complex breeding programs, making use of all available biotechnologies. MoBPS provides pre-implemented functions for common breeding practices such as optimum genetic contributions and single-step GBLUP but also allows the user to replace certain steps with personalized and/or self-written solutions.