Efficient Surrogate Modeling for Subsurface Flow Simulation Using Multi-Fidelity Data with Physical Constraints

Summary In the field of subsurface flow simulation, deep-learning-based surrogate modeling is shown as a promising approach to significantly reduce the computational cost associated with full-physics reservoir simulations. However, the successful construction of highly accurate deep-learning-based models often requires a large number of training simulations, which can be very time-consuming to generate by itself for large-scale systems. The incorporation of physics constraints during the training process was shown to be an effective approach to reduce the training cost and to improve model accuracy. However, it remains challenging to reimplement the physics constraints correctly for modeling training when it comes to reservoir models with complex physics or gridding methods. In this study, we propose a physics-constrained surrogate (PCS) model training approach for production optimization that integrates multifidelity training data, together with a new way of implementing the physics constraints that leverages an existing mature reservoir simulator. The proposed approach starts with model pretraining on a relatively large number of low-cost, low-fidelity training data, followed by model fine-tuning with a smaller number of high-fidelity training samples and the inclusion of physics constraints. The physics constraints are implemented by adding the residuals of discretized governing equations into the loss function. Training with multifidelity data and incorporating physics constraints allows for reduced reliance on high-fidelity data while enhancing physical consistency. Systematic comparison studies were performed for both 2D and 3D cases, and it was shown that the proposed approach can reduce the computational costs associated with training data generation by about 80%, while achieving a similar level of prediction accuracy of the surrogate model. In addition, under a small number of training simulations (i.e., 50 equivalent high-fidelity runs), our proposed PCS model with multifidelity data can reduce the prediction error by 90%, in comparison with the model trained with only high-fidelity data. Finally, the trained surrogate model was applied to a well-control optimization problem. In comparison with the use of full-order simulations, the total computational time can be reduced by 97.7%.

Multi-fidelity surrogate (MFS) modeling technology, which efficiently constructs surrogate models using low-fidelity (LF) and high-fidelity (HF) data, has been studied to enhance the predictive capability of engineering performances. In addition, several neural network (NN) structures for MFS modeling have been introduced, benefiting from recent developments in deep learning research. However, existing multi-fidelity (MF) NNs have been developed assuming identical sets of input variables for LF and HF data, a condition that is often not met in practical engineering systems. Therefore, this study proposes a new structure of composite NN designed for MF data with different input variables. The proposed network structure includes an input mapping network that connects the LF and HF data's input variables. Even when the physical relationship between these variables is unknown, the input mapping network can be concurrently trained during the process of training the whole network model. Customized loss functions and activation variables are suggested in this study to facilitate forward and backward propagation for the proposed NN structures when training MF data with different inputs. The effectiveness of the proposed method, in terms of prediction accuracy, is demonstrated through mathematical examples and practical engineering problems related to tire performances. The results confirm that the proposed method offers better accuracy than existing surrogate models in most problems. Moreover, the proposed method proves advantageous for surrogate modeling of nonlinear or discrete functions, a characteristic feature of NN-based methods.

Design approach for tilt propellers of UAM/eVTOLs for cruise and hover considering aerodynamic and aeroacoustic characteristics via a multi-fidelity model

The growing demand for biopharmaceutical products reflects their effectiveness in medical treatments. However, developing new biopharmaceuticals remains a major bottleneck, often taking up to a decade before market approval. Machine learning (ML) models have the potential to accelerate this process, but their success depends on access to large and diverse data sets for training. Multi-fidelity ML techniques offer a promising solution by integrating abundant, low-cost, and less accurate low-fidelity (LF) data with limited, expensive, and more accurate high-fidelity (HF) data. In this framework, LF data capture global system trends, while HF data refine and align model predictions with the available ground truth. Such integration can substantially reduce development costs and timelines by minimizing the need to acquire HF data, for example, through extensive experimental campaigns. This work reviews developments in surrogate modeling within the biopharmaceutical context, including Gaussian processes, neural networks, and physics-informed approaches. It also provides practical recommendations for identifying appropriate LF and HF data. Existing research has primarily focused on upstream processing and drug discovery, highlighting opportunities to extend these methods to other stages, like downstream processing. While Gaussian processes and neural networks remain the most frequently used models, emerging architectures such as Transformer and diffusion models present promising directions for future research.

The next generation low-cost modular unmanned combat aerial vehicles (UCAVs) provide the opportunity to implement innovative solutions to complex tasks, while also bringing new challenges in design, production, and certification subjects. Solving these problems with tools that provide fast modeling in line with the digital twin concept is possible. In this work, we develop an artificial intelligence (AI) based multifidelity surrogate model to determine performance parameters of innovative modular UCAVs. First, we develop a data generation algorithm that includes a high-fidelity model based on computational fluid dynamics methods and a low-fidelity model based on computational aerodynamic approaches. In the next step, a new transfer learning-based surrogate model is generated using multifidelity data. Thanks to this approach, the developed AI model more accurately predicted the flow conditions that were missing in the high-fidelity data with the data obtained from the low-order model. The performance of the proposed AI-based surrogate model is to be investigated in terms of accuracy, robustness, and computational cost using a generic modular UCAV configuration.

SummaryAccurate prediction of the solubility of chemical substances in solvents remains a challenge. The sparsity of high-quality solubility data is recognized as the biggest hurdle in the development of robust data-driven methods for practical use. Nonetheless, the effects of the quality and quantity of data on aqueous solubility predictions have not yet been scrutinized. In this study, the roles of the size and the quality of data sets on the performances of the solubility prediction models are unraveled, and the concepts of actual and observed performances are introduced. In an effort to curtail the gap between actual and observed performances, a quality-oriented data selection method, which evaluates the quality of data and extracts the most accurate part of it through statistical validation, is designed. Applying this method on the largest publicly available solubility database and using a consensus machine learning approach, a top-performing solubility prediction model is achieved.

A physics-informed diffusion model for high-fidelity flow field reconstruction

Multi-fidelity reinforcement learning with control variates

An accurate and efficient surrogate model plays a significant role in the optimal design of electrical motors. This paper presents an accurate and efficient surrogate modeling method for a flux reversal permanent magnet arc motor (FR-PMAM) based on machine learning algorithm. Specifically, the motor topology and the optimized design of the FR-PMAM are firstly illustrated. Then, the PM magnetic motive force-permeance model is developed to select structural parameters of FR-PMAM. After that, a finite-element analysis (FEA) model of FR-PMAM is calculated to obtain sample data. A machine learning algorithm random forest is introduced into the field of motor optimal design for the first time to evaluate the contribution of each parameter to the design objectives. Based on the sample data, an efficient machine learning algorithm CatBoost is innovatively employed to establish the accurate and efficient surrogate model of the FR-PMAM that can capture the complex function relationship between output objectives and input parameters. Subsequently, an improved genetic algorithm with the elitist reservation strategy is adopted to obtain the optimal combination of the structural parameters of FR-PMAM. Finally, a prototype of the FR-PMAM is manufactured. The FEA and experimental results validate the effectiveness of the investigated surrogate modeling method.

This report documents the development and application of two web-based decision-support tools for pump-and-treat (P&T) groundwater remediation systems: PTOLEMY (Pump-and-Treat Optimized Location Evaluation to Maximize Yields) and OPTIMA (Optimization for Pump-and-Treat Implementation, Management, & Assessment). These tools enhance remedy design and management by leveraging advanced computational methods – specifically deep learning and multi-objective optimization – within a user-friendly platform. By integrating data-driven models with established hydrogeological knowledge, PTOLEMY and OPTIMA enable more efficient evaluation of well placement and operational strategies, helping site managers balance multiple remediation objectives under complex conditions. Both tools are implemented as modules within the SOCRATES (Suite Of Comprehensive Rapid Analysis Tools for Environmental Sites) web platform, which provides data access, visualization, and analytics to support remedy optimization across sites in the U.S. Department of Energy Office of Environmental Management complex. PTOLEMY is a rapid screening module designed to identify promising locations for new extraction wells. It employs a multi-channel three-dimensional convolutional neural network (MC3D-CNN) trained on high-fidelity simulation data to predict the relative performance (in terms of contaminant mass recovery) of potential well sites. Through an interactive web interface, PTOLEMY visualizes the probability of high performance across a site, highlighting areas where an extraction well is likely to yield above-threshold contaminant removal over a multi-year period. PTOLEMY’s map-based displays and exportable results support transparent communication of screening analyses. By focusing attention on the most favorable candidate locations, the tool augments traditional engineering judgment and physics-based modeling, providing a data informed basis for subsequent detailed evaluations. OPTIMA is a multi objective optimization module designed to find wellfield layouts and operating schedules that meet various cleanup goals. It quickly evaluates thousands of candidate setups – combinations of well locations, timing, and rates – and returns a small set of best trade-off options for comparison. At its core, OPTIMA uses a U-Net-based surrogate model – a deep-learning emulator of a groundwater flow and transport simulator – to dramatically accelerate scenario evaluations. Coupling this fast surrogate with the NSGA-II (Non-dominated Sorting Genetic Algorithm II) evolutionary algorithm, OPTIMA explores a wide decision space of well locations and schedules to identify Pareto-optimal solutions that trade off key objectives (e.g., minimizing cleanup time, maximizing contaminant mass removal, and minimizing plume extent). The tool outputs a family of optimal configurations and visualizes their trade-offs (Pareto frontiers of cleanup metrics and maps of optimized well placements). Site managers can use these results to understand the range of viable strategies and to select candidate designs for more detailed verification. OPTIMA is currently under active development and not yet fully released; this guide provides early documentation to support planning and gather user feedback.

This study presents a method that combines two deep learning models—the surrogate model and the bandgap optimization model—to design 1-D Phononic Crystals. The surrogate model is trained to predict the bandgaps of Phononic Crystals, while the bandgap optimization model is used to determine their geometric parameters. The goal is to leverage deep learning’s ability to capture complex input-output relationships and exploit the inherent optimization capabilities of these models. To improve design accuracy and account for manufacturing constraints, a user-defined activation function is incorporated into the optimization model. Various loss functions are introduced to address different design objectives, such as maximizing the bandgap at a lower frequency or maximizing while aligning the center frequency of the bandgap with a specified value. The 1-D Phononic Crystal designed for bandgap maximization at lower frequencies using this method outperformed results predicted by a Genetic Algorithm. Unlike previous studies that often rely on deep learning only as a predictive tool or require external optimizers, our method uses a deep learning model directly as an optimization engine. The integration of customizable loss functions, user-defined physical constraints, and an unsupervised training approach enables versatile and efficient design without the need for labeled optimization datasets. The approach is readily extensible to 2-D and 3-D configurations, offering a versatile solution for advanced Phononic Crystal design.

Multi-fidelity surrogate modeling, by integrating high-fidelity (HF) and low-fidelity (LF) data, provides an efficient approximation framework for complex fluid dynamics problems, particularly those driven by numerical resolution discrepancies. However, under limited computational budgets, efficiently selecting HF samples remains a critical challenge. This study proposes a Nonlinear-Guided Active Learning Multi-Fidelity Surrogate (NG-AL-MFS) modeling method. The proposed framework employs a recursive Co-Kriging model combined with an adaptive sampling strategy to achieve hierarchical data fusion. In this approach, the adaptive sampling strategy introduces a local nonlinearity indicator derived from LF responses to identify complex regions and integrates a distance-based exploration criterion to balance exploitation and exploration during potential HF sampling. Throughout the process, NG-AL-MFS quantitatively extracts local nonlinear features from LF responses to iteratively and adaptively update HF samples, thereby constructing a multi-fidelity surrogate that achieves a superior trade-off between modeling accuracy and computational cost. The proposed framework is validated using three benchmark functions and two fluid engineering applications. Results demonstrate that NG-AL-MFS outperforms existing approaches in terms of prediction accuracy, convergence efficiency, and statistical robustness, offering notable advantages in multivariate nonlinear scenarios. Overall, NG-AL-MFS provides a data-efficient and reliable solution for budget-constrained surrogate modeling in fluid dynamics and other computation-intensive domains.

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

Multi-fidelity graph neural networks for efficient power flow analysis under high-dimensional demand and renewable generation uncertainty

Since the physical structure and mathematical models are more complex, reliability analysis in practical engineering can be expensive and difficult. A two-level multifidelity metamodel method for reliability analysis is introduced. Following the surrogate model in most of the relevant works, low-fidelity data and high-fidelity data are integrated by co-Kriging model. Besides, the co-Kriging model also provide an approximation for initial performance function. Bayesian method is adopted in model solution and a hybrid Markov chain Monte Carlo (MCMC) sampling algorithm is proposed. High-fidelity response of reliability performance function is estimated by the conditional distribution derivation based on Bayesian theory. Failure domain is identified by indicator function in sampling space that consists of samples derived from MCMC. Accordingly, failure probability estimations are obtained using Monte Carlo simulation (MCS). It is demonstrated through an illustrative example that the proposed method is valid and accurate.