Data-Driven RANS closure with Model Derived Turbulence Variables

Data-driven turbulence models have been created for a k-ε RANS model based on PIV data in a jet in crossflow. In the simpler of two implementations, the nominal value of the model coefficient Cµ was replaced with an optimized value calibrated to the PIV results. Despite being based on only four flow cases of a canonical configuration, the optimized model demonstrated superior performance over 48 flow cases of increasing complexity. A second, more sophisticated data-driven model has been created by mapping a spatially variable Cµ to flow state variables using machine learning of experimentally measured flow field properties of the turbulence. This second model has been implemented in a production RANS code but requires further improvements before it can return results deviating from either the nominal or calibrated Cµ models.

In recent years, the synergy between artificial intelligence and turbulence big data has given rise to a new data-driven paradigm in turbulence research. Data-driven turbulence modeling has emerged as one of the forefront directions in fluid mechanics. Most existing studies focus on feature construction, selection, and the development of modeling frameworks, often overlooking the practical deployment and application of trained models. This paper examines the entire process from model construction to real-world deployment, using data-driven turbulence modeling for high Reynolds number flows over complex three-dimensional configurations as a case study. Key stages include data generation, input-output feature construction, model training, model compilation and optimization, deployment, and validation. We successfully implemented the entire workflow in a heterogeneous supercomputing environment and, through mixed programming techniques, integrated the resulting turbulence model into the Platform for Hybrid Engineering Simulation of Flows (PHengLEI) open-source software framework. This allowed for mixed-precision simulations, with the main equations solved in double precision and the turbulence model in half precision. The new computational framework was validated through large-scale parallel numerical simulations on grids with tens of millions of elements for three-dimensional complex configurations. The results highlight the efficiency of our model deployment, with overall computational efficiency improving by 13.35% and the turbulence model’s solution speed increasing by approximately 3.9 times. The accuracy of the computations was also confirmed, with the average relative error in the lift and drag coefficients calculated by the data-driven turbulence model within 3%. Across various computing nodes, the relative error in the computed aerodynamic coefficients remained within 1%, demonstrating the framework’s scalability. Notably, our contributions have been incorporated as a case study in the latest PHengLEI open-source project5 5 https://forge.osredm.com/PHengLEI/PHengLEI-TestCases/tree/master/Y02_ThreeD_M6_Unstruct_Branch_Ascend. .

We have modeled turbulence for a century, and this entire journey has been guided by data and empiricism. Today we have more access to information, and at scale. The peculiar nature and demands of the turbulence modeling challenge, however, mean that one cannot completely bypass mechanistic modeling; data-driven elements must be cast as *consistent and constrained augmentations* of established RANS/LES frameworks. A brief survey will be provided on the progress over the past decade in embedding learned model augmentations. Particular emphasis will be paid to the balance between parsimony and constraint: Use of small set of physically-inspired, locally non-dimensional, bounded features that promote a near one-to-one map from features to an identifiable augmentation, and keeping training and prediction environments consistent by learning to work with operational variables. Pitfalls are subtle, not dramatic—apparent success on curated benchmarks masks brittleness at the point of use. Candid challenges remain: predictive capabilities across geometries and flow regimes, encapsulating nonlocality, identifiability from finite data, and numerical robustness. The thesis is that generality must be earned—by constraining what the particular modeling scenario (rather than purely physical considerations) demands, limiting capacity to what the data can identify, and aligning training with how we actually compute, and what we seek to predict—so data-driven closures become dependable, auditable components of mission-critical CFD. Success in this endeavor also demands principled design of experiments for information-efficient and active data acquisition, and rigorous uncertainty quantification to certify predictions and define operating envelopes.

Occupant-centric control (OCC) of building systems, which improves energy performance and thermal comfort by considering occupants’ presence, preferences, and activity, has drawn substantial research interest over the past decade. However, most existing studies have focused on evaluating overall performance during a relatively long period, overlooking control robustness during transients.Corner cases in autonomous driving refer to a bug or problem that occurs under unseen, unusual, and perhaps dangerous circumstances. For OCC in buildings, corner cases can be triggered by extreme values or rare patterns of disturbances that are not covered by historical data used to design the controllers. The backbone of many OCC applications is the predictive model, and the root of potential corner cases is that data-driven models sometimes cannot extrapolate well to support decision-making. As the predictive model cannot accurately comprehend the situation or predict what will happen, corner cases could lead to suboptimal or even wrong control actions.Unlike other data-rich domains, building data typically only covers limited operating conditions and therefore is sparse in the feature space. For example, a model for building control trained with data associated with a normal cooling setpoint of 24°C may be unreliable for such higher setpoints as 27 °C. Considering the difficulty in extensive data collection, methods such as physics-informed neural networks have emerged to enhance the extrapolation capability of data-driven models by incorporating physics-based prior knowledge or exerting physical constraints. Yet, despite the claimed merits such as more data-efficient learning and physics-consistent prediction over long horizons, whether and how physics-informed models can help handle the corner cases and improve control robustness remain unknown.To address this knowledge gap, we designed a simulation framework that applies OCC in a multi-zone office building. Corner cases were identified using historical data from a real-world campus building. A group of data-driven predictive models will be developed with different levels of physics integration and tested in OCC simulations. Combining actual and synthetic data, the peer models will be comprehensively examined concerning their predictive capability and control performance. Special attention will be paid to the decision-making process in the corner cases. The experimental results will inform the required level of physics in predictive models to ensure control robustness, leading to two contributions: future development of physics-informed models can be guided in an application-oriented manner, and the actual applications of occupant-centric control can be promoted.

Transient growth and resolvent analyses are routinely used to assess nonasymptotic properties of fluid flows. In particular, resolvent analysis can be interpreted as a special case of viewing flow dynamics as an open system in which free-stream turbulence, surface roughness, and other irregularities provide sources of input forcing. We offer a comprehensive summary of the tools that can be employed to probe the dynamics of fluctuations around a laminar or turbulent base flow in the presence of such stochastic or deterministic input forcing and describe how input–output techniques enhance resolvent analysis. Specifically, physical insights that may remain hidden in the resolvent analysis are gained by detailed examination of input–output responses between spatially localized body forces and selected linear combinations of state variables. This differentiating feature plays a key role in quantifying the importance of different mechanisms for bypass transition in wall-bounded shear flows and in explaining how turbulent jets generate noise. We highlight the utility of a stochastic framework, with white or colored inputs, in addressing a variety of open challenges including transition in complex fluids, flow control, and physics-aware data-driven turbulence modeling. Applications with temporally or spatially periodic base flows are discussed and future research directions are outlined.

 Hydrological modeling is essential for understanding water balance dynamics, yet physical models often face limitations such as computational inefficiency, insufficient representation of complex processes, and challenges in integrating diverse data sources. To address these limitations, data-driven models offer enhanced predictive capabilities, scalability, and real-time analysis potential. In this study, a Long Short-Term Memory (LSTM) model was developed to simulate the water balance using open-source ERA-5 reanalysis data, trained with outputs from the Noah-MP land surface model conducted over Thailand as a case study. The trained LSTM model was subsequently transferred to other basins with varying land use, topography, and climatic conditions, enabling an evaluation of its adaptability across diverse environments. Seasonal performance was assessed to understand the model's sensitivity to climatic variability. To enhance the accuracy of water balance predictions, satellite datasets, including GRACE-derived terrestrial water storage, GLEAM-derived evapotranspiration, and SMAP-derived surface soil moisture, were assimilated into the data-driven model, improving its representation of hydrological processes. Model performance was assessed using observations, yielding notable results: correlation coefficients (R) of 0.98, 0.89, 0.99, and 0.99; and RMSE values of 16.77, 8, 5.2, and 0.01 for runoff, evaporation, groundwater, and soil moisture, respectively. This study highlights the potential of combining data-driven approaches and satellite data assimilation to improve water balance modeling,  providing accurate hydrological predictions across regions with diverse landscapes and climatic regimes.

This paper introduces a physics-guided learning (PGL) to predict flowing bottomhole pressure (FBHP) in shale oil wells undergoing gas-lift operations, overcoming the limitations of data-driven models. We analyze reservoirs, wells, and operational data from 21 Permian Basin shale wells. Several PVT and pipe-flow correlations are investigated to determine the calculation of the flowing bottomhole pressure. Then, FBHP is constrained by both the domain-knowledge item and the single-phase gas and liquid flow physics-based models, with their elevation and friction terms embedded as differentiable operators in the neural network's loss. The PGL is designed to map depth and well inputs, such as diameter, liquid/gas rates, and wellhead pressure, to FBHP. Training combined physics loss, domain knowledge, and gauge data penalties. Hyperparameters such as layers, neurons, activation functions, and learning rates were tuned using genetic algorithms, with 5-fold cross-validation to ensure generalization. The model's performance is benchmarked against empirical and data-driven models for blind wells. The analysis of operational, production, and reservoir parameters shows that hydrocarbon fluid properties, well depth, operating valve depth, wellhead and bottomhole temperatures, wellhead pressure, and liquid and gas rates are key factors influencing FBHP during gas-lift operations. The qualitative relationships are then embedded into the artificial neural network. The PGL hyperparameters are optimized, including the number of layers, the number of neurons, the activation function, and the optimizer. The comparison between PGL and data-driven ANN models showed that PGL outperformed conventional deep learning models in terms of accuracy and stability. Embedded physics acts as a powerful regularizer, preventing overfitting and ensuring the model's reliability, especially in long-term predictions where purely data-based models may fail. The model successfully captures the complex transient dynamics of the wellbore, yielding physically plausible results even with sparse field data. This reliable predictive capability enables continuous optimization of gas injection rates to maintain an ideal reservoir drawdown, a key factor in maximizing the well's ultimate oil recovery. The proposed PGL explicitly embeds the governing equations of well-established flow correlations and qualitative relationships. Unlike other hybrid models that infer physics implicitly from data patterns, our approach mathematically enforces proven engineering principles during training. This creates a tailored "grey-box" model that is more accurate and physically consistent for the specific challenge of dynamic gas-lift operations, providing practicing engineers with a more robust and reliable tool to optimize production and enhance oil recovery.

Do all roads lead to Rome? A comparison of knowledge-based, data-driven, and physics-based surrogate models for performance-based early design

This paper describes a novel and fast placement algorithm for FPGA design space (e.g., area, power or reliability) exploration. The proposed algorithm generates the placement based on the topological similarity between two configurations (netlists) in the design space. Thus, it utilizes the sharing of reusable information during the design space exploration and avoids the time-consuming placement computation like VPR. Tested on logic-level and algorithm-level design space exploration cases, our similarity-based placement accurately depicts the “shape” of a design space and pinpoints the designs which are of most interest to IC designers. Moreover, a turbo version of circuit similarity-based placement performs an average of 30x (up to 100x) faster than VPR's while still achieving comparable placement results.

Data-driven turbulence modeling has been considered an effective method for improving the prediction accuracy of Reynolds-averaged Navier–Stokes equations. Related studies aimed to solve the discrepancy of traditional turbulence modeling by acquiring specific patterns from high-fidelity data through machine learning methods, such as artificial neural networks. The present study focuses on the unsmoothness and prediction error problems from the aspect of feature selection and processing. The selection criteria for the input features are summarized, and an effective input set is constructed. The effect of the computation grid on the smoothness is studied. A modified feature decomposition method for the spatial orientation feature of the Reynolds stress is proposed. The improved machine learning framework is then applied to the periodic hill database with notably varying geometries. The results of the modified method show significant enhancement in the prediction accuracy and smoothness, including the shape and size of separation areas and the friction and pressure distributions on the wall, which confirms the validity of the approach.

Reynolds-Averaged Navier-Stoke (RANS) models offer an alternative avenue in predicting flow characteristics when the corresponding experiments are difficult to achieve due to geometry complexity, limited budget, or knowledge. RANS models require the knowledge of subgrid scale physics to solve conservation equations for mass, energy, and momentum. Mechanistic turbulence models, such as k-ε, are generally evaluated and calibrated for specific flow conditions with various degrees of uncertainty. These models have limited capability to assimilate a substantial amount of data due to model form constraints. Meanwhile, deep learning (DL) has been proven to be universal approximators with the potential to assimilate available, relevant, and adequately evaluated data. Moreover, deep neural networks (DNNs) can create surrogate models without knowing function forms. Such a data-driven approach can be used in updating fluid models based on observations as opposed to hard-wiring models with precalibrated correlations. The paper presents progress in applying DNNs to model Reynolds stress using two machine learning (ML) frameworks. A novel flow feature coverage mapping is proposed to quantify the physics coverage of DL-based closures. It can be used to examine the sufficiency of training data and input flow features for data-driven turbulence models. The case of a backward-facing step is formulated to demonstrate that not only can DNNs discover underlying correlation behind fluid data but also they can be implemented in RANS to predict flow characteristics without numerical stability issues. The presented research is a crucial stepping-stone toward the data-driven turbulence modeling, which potentially benefits the design of data-driven experiments that can be used to validate fluid models with ML-based fluid closures.

Exploration with a generative formalism must necessarily account for the nature of interaction between humans and the design space explorer. Established accounts of design interaction are made complicated by two propositions in Woodbury and Burrow's Keynote on design space exploration. First, the emphasis on the primacy of the design space as an ordered collection of partial designs (version, alternatives, extensions). Few studies exist in the design interaction literature on working with multiple threads simultaneously. Second, the need to situate, aid, and amplify human design intentions using computational tools. Although specific research and practice tools on amplification (sketching, generation, variation) have had success, there is a lack of generic, flexible, interoperable, and extensible representation to support amplification. This paper addresses the above, working with design threads and computer-assisted design amplification through a theoretical model of dialogue based on Grice's model of rational conversation. Using the concept of mixed initiative, the paper presents a visual notation for representing dialogue between designer and design space formalism through abstract examples of exploration tasks and dialogue integration.

All computing platforms, from mobile to supercomputers, are becoming more and more heterogeneous and massively parallel. While they can provide higher power efficiency and computation throughput, effective and confident use of these systems always requires knowledge about low-level programming. The average time necessary to develop and optimize a design on heterogeneous platforms is higher and higher compared to typical homogeneous systems. Dataflow models of computation (MoC) are quickly becoming the common practice in heterogeneous systems development. In domains such as signal processing and multimedia communication, dataflow MoCs have become accepted as standard. However, the shift from a sequential and architecture-specific MoC to a dataflow MoC still uncovers several programming and development challenges. The Cal Actor Language (CAL) is a recently-specified dataflow and actor-based language capable of concisely expressing complex and general purpose parallel applications. However, design tools supporting this language are generally not adequate to fully exploit its features and expressiveness power. In fact, they generally restrict its MoC in order to reduce the design space exploration (DSE) effort. The objective of this thesis is to provide a DSE methodology where all the features of CAL and dynamic dataflow MoCs can be exploited in a more general and effective manner. This dissertation illustrates a novel profiling, analysis and performance estimation methodology for the DSE of dynamic dataflow programs. The main research contributions of this thesis are: the formalization of a graph-based representation of the program execution called an execution trace graph (ETG); the formalization of a systematic methodology for profiling generic dynamic dataflow programs through their code interpretation; the formalization of a complete DSE methodology for dynamic dataflow programs in order to efficiently identify close-to-optimal design points according to various and tailored performance merit functions. In particular, the following design space optimization problems for dynamic dataflow programs are addressed: the analysis of the hotspots and the algorithmic bottlenecks of a parallel program; the bounding and optimization of the buffer size configuration for complex designs; the dynamic power dissipation minimization of programs implemented in multi-clock domain architecture. Furthermore, theoretical concepts like the design space critical path and the potential speedup of a dataflow application have been defined and revisited, respectively. The thesis also presents a DSE framework developed in order to demonstrate the effectiveness of this design methodology.

Successful recovery of hydrocarbons from the reservoirs, notably shale, is attributed to realizing the key fundamentals of reservoir rock properties. Having adequate and sufficient information regarding the variable lithology and mineralogy is crucial in order to identify the "right" pay-zone intervals for shale gas production. Also, contribution of mechanical properties (Principal stress profiles) of shale to hydraulic fracturing strategies is a well understood concept. It may also contribute to better, more accurate simulation models of production from shale gas reservoirs. In this study, synthetic geomechanical logs (Including following properties: Poisson's Ratio, Total Minimum Horizontal Stress, Bulk and Shear Modulus, etc.) are developed for more than 50 Marcellus Shale wells. Using Artificial Intelligence and Data Mining (AI&DM), data-driven models are developed that are capable of generating synthetic geomechanical logs from conventional logs such as Gamma Ray and Density Porosity. The data-driven models are validated using wells with actual geomechanical logs that have been removed from the database to serve as blind validation wells. In addition, having access to necessary data to building a geomechanical distribution (Map and Volume) model can assist in understanding the rock mechanical behavior and consequently creating effective hydraulic fractures which is considered to be an essential step in economically development of Shale assets. Moreover, running geomechanical logs on a subset of wells, but having the luxury of generating logs of similar quality for all the existing wells in a Shale asset can prove to be a sound reservoir management tool for better reservoir characterization, modeling and efficient production of Marcellus Shale reservoir.

Abstract. A comprehensive data driven modeling experiment is presented in a two-part paper. In this first part, an extensive data-driven modeling experiment is proposed. The most important concerns regarding the way data driven modeling (DDM) techniques and data were handled, compared, and evaluated, and the basis on which findings and conclusions were drawn are discussed. A concise review of key articles that presented comparisons among various DDM techniques is presented. Six DDM techniques, namely, neural networks, genetic programming, evolutionary polynomial regression, support vector machines, M5 model trees, and K-nearest neighbors are proposed and explained. Multiple linear regression and naïve models are also suggested as baseline for comparison with the various techniques. Five datasets from Canada and Europe representing evapotranspiration, upper and lower layer soil moisture content, and rainfall-runoff process are described and proposed, in the second paper, for the modeling experiment. Twelve different realizations (groups) from each dataset are created by a procedure involving random sampling. Each group contains three subsets; training, cross-validation, and testing. Each modeling technique is proposed to be applied to each of the 12 groups of each dataset. This way, both prediction accuracy and uncertainty of the modeling techniques can be evaluated. The description of the datasets, the implementation of the modeling techniques, results and analysis, and the findings of the modeling experiment are deferred to the second part of this paper.