Physics-informed machine learning-aided framework for CASL challenge problem solving—a demonstration and prospects
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Zhao, Xingang↗
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Resolving turbulent magnetohydrodynamics: a hybrid operator-diffusion framework
We present a hybrid machine learning framework that combines physics-informed neural operators (PINOs) with score-based generative diffusion models to simulate the full spatio-temporal evolution of two-dimensional, incompressible, resistive magnetohydrodynamic turbulence across a broad range of Reynolds numbers (Re). The framework leverages the equation-constrained generalization capabilities of PINOs to predict coherent, low-frequency dynamics, while a conditional diffusion model stochastically corrects high-frequency residuals, enabling accurate modeling of fully developed turbulence. Trained on a comprehensive ensemble of high-fidelity simulations with Re ϵ {100, 250, 500, 750, 1000, 3000, 10000}, the approach achieves state-of-the-art accuracy in regimes previously inaccessible to deterministic surrogates. At Re = 1000 and 3000, the model faithfully reconstructs the full spectral energy distributions of both velocity and magnetic fields late into the simulation, capturing non-Gaussian statistics, intermittent structures, and cross-field correlations with high fidelity. At extreme turbulence levels (Re = 10 000), it remains the first surrogate capable of recovering the high-wavenumber evolution of the magnetic field, preserving large-scale morphology and enabling statistically meaningful predictions.
Diffusion-Integrated Neural Operators↗
MACHINE LEARNING-ENABLED PREDICTION OF TRANSIENT INJECTION MAP IN AUTOMOTIVE INJECTORS WITH UNCERTAINTY QUANTIFICATION
Accurate prediction of injection profiles is a critical aspect of linking injector operation with engine performance and emissions. However, highly resolved injector simulations can take one to two weeks of wall-clock time, which is incompatible with engine design cycles with desired turnaround times of less than a day. Hence, it is important to reduce the time-to-solution of the internal flow simulations by several orders of magnitude to make it compatible with engine simulations. This work demonstrates a data-driven approach for tackling the computational overhead of injector simulations, whereby the transient injection profiles are emulated for a side-oriented, single-hole diesel injector using a Bayesian machine-learning framework. First, an interpretable Bayesian learning strategy was employed to understand the effect of design parameters on the total void fraction field. Then, autoencoders are utilized for efficient dimensionality reduction of the flowfields. Gaussian process models are finally used to predict the spatiotemporal void fraction field at the injector exit for unknown operating conditions. The Gaussian process models produce principled uncertainty estimates associated with the emulated flowfields, which provide the engine designer with valuable information of where the data-driven predictions can be trusted in the design space. The Bayesian flowfield predictions are compared with the corresponding predictions from a deep neural network, which has been transfer-learned from static needle simulations from a previous work by the authors. The emulation framework can predict the void fraction field at the exit of the orifice within a few seconds, thus achieving a speed-up factor of up to 38 x 10(6) over the traditional simulation-based approach of generating transient injection maps.
machine learning↗
Influence of Aerosol Embedded in Shallow Cumulus Cloud Fields on the Surface Solar Irradiance
Ubiquitous shallow cumulus clouds are associated with complex variability in surface solar irradiance (SSI). Aerosol embedded in the cloud field typically has a much smaller overall radiative effect, but can significantly perturb the shape of the SSI probability density function (PDF). These perturbations have important implications for several applications that utilize SSI, but are poorly quantified and are the subject of this study. Multiple cases of shallow cumulus cloud fields with embedded aerosol are simulated at the Southern Great Plains Atmospheric Observatory using large eddy simulation (LES). The LES-derived cloud and aerosol fields are then ingested into Monte Carlo three-dimensional (3D) radiative transfer to simulate SSI. We find a variety of perturbations to the SSI PDF that depend on aerosol presence and optical properties. The processes leading to these perturbations include extinction of the direct beam that often increases from the clear-sky region toward cloud edge due to aerosol hygroscopic growth, and scattering of radiation by aerosol into cloud shadows. The ability to predict the SSI PDF in the presence of aerosol is assessed by adding three representative aerosol optical properties into an existing machine learning framework. We show that machine learning accurately predicts the SSI PDF across a wide range of conditions with negligible computational expense. Importance metrics reveal the relatively high influence of aerosol optical properties in making the predictions. These new findings highlight the important role that aerosol plays in SSI variability for highly 3D cloud-aerosol environments and provides a computationally efficient route forward for its simulation.
3D radiative transfer↗
Enabling deeper learning on big data for materials informatics applications
Abstract The application of machine learning (ML) techniques in materials science has attracted significant attention in recent years, due to their impressive ability to efficiently extract data-driven linkages from various input materials representations to their output properties. While the application of traditional ML techniques has become quite ubiquitous, there have been limited applications of more advanced deep learning (DL) techniques, primarily because big materials datasets are relatively rare. Given the demonstrated potential and advantages of DL and the increasing availability of big materials datasets, it is attractive to go for deeper neural networks in a bid to boost model performance, but in reality, it leads to performance degradation due to the vanishing gradient problem. In this paper, we address the question of how to enable deeper learning for cases where big materials data is available. Here, we present a general deep learning framework based on Individual Residual learning (IRNet) composed of very deep neural networks that can work with any vector-based materials representation as input to build accurate property prediction models. We find that the proposed IRNet models can not only successfully alleviate the vanishing gradient problem and enable deeper learning, but also lead to significantly (up to 47%) better model accuracy as compared to plain deep neural networks and traditional ML techniques for a given input materials representation in the presence of big data.
36 MATERIALS SCIENCE↗
Improving deep learning model performance under parametric constraints for materials informatics applications
Abstract Modern machine learning (ML) and deep learning (DL) techniques using high-dimensional data representations have helped accelerate the materials discovery process by efficiently detecting hidden patterns in existing datasets and linking input representations to output properties for a better understanding of the scientific phenomenon. While a deep neural network comprised of fully connected layers has been widely used for materials property prediction, simply creating a deeper model with a large number of layers often faces with vanishing gradient problem, causing a degradation in the performance, thereby limiting usage. In this paper, we study and propose architectural principles to address the question of improving the performance of model training and inference under fixed parametric constraints. Here, we present a general deep-learning framework based on branched residual learning (BRNet) with fully connected layers that can work with any numerical vector-based representation as input to build accurate models to predict materials properties. We perform model training for materials properties using numerical vectors representing different composition-based attributes of the respective materials and compare the performance of the proposed models against traditional ML and existing DL architectures. We find that the proposed models are significantly more accurate than the ML/DL models for all data sizes by using different composition-based attributes as input. Further, branched learning requires fewer parameters and results in faster model training due to better convergence during the training phase than existing neural networks, thereby efficiently building accurate models for predicting materials properties.
36 MATERIALS SCIENCE↗
Scientific machine learning benchmarks
Deep learning has transformed the use of machine learning technologies for the analysis of large experimental datasets. In science, such datasets are typically generated by large-scale experimental facilities, and machine learning focuses on the identification of patterns, trends and anomalies to extract meaningful scientific insights from the data. In upcoming experimental facilities, such as the Extreme Photonics Application Centre (EPAC) in the UK or the international Square Kilometre Array (SKA), the rate of data generation and the scale of data volumes will increasingly require the use of more automated data analysis. Furthermore, at present, identifying the most appropriate machine learning algorithm for the analysis of any given scientific dataset is a challenge due to the potential applicability of many different machine learning frameworks, computer architectures and machine learning models. Historically, for modelling and simulation on high-performance computing systems, these issues have been addressed through benchmarking computer applications, algorithms and architectures. Extending such a benchmarking approach and identifying metrics for the application of machine learning methods to open, curated scientific datasets is a new challenge for both scientists and computer scientists. Here, we introduce the concept of machine learning benchmarks for science and review existing approaches. As an example, we describe the SciMLBench suite of scientific machine learning benchmarks.
42 ENGINEERING↗
Learning nuclear cross sections across the chart of nuclides with graph neural networks
We explore the use of deep learning techniques to learn how nuclear cross sections change as we add or remove protons and neutrons. As a proof of principle, we focus on the neutron-induced reactions in the fast energy regime. Our approach follows a two-stage learning framework. First, we apply representation learning to encode cross section data into a latent space using either variational autoencoders (VAEs) or implicit neural representations (INRs). Then, we train graph neural networks (GNNs) on the resulting embeddings to predict missing values across the nuclear chart by leveraging the topological structure of neighboring isotopes. We demonstrate accurate cross section predictions within a 9 × 9 block of missing nuclei. We also find that the optimal GNN training strategy depends on the type of latent representation used, with VAE embeddings performing best under end-to-end optimization in the original space, while INR embeddings achieve better results when the GNN is trained only in the latent space. Furthermore, using clustering algorithms, we map groups of latent vectors into regions of the nuclear chart and show that VAEs and INRs can discover some of the neutron magic numbers. These findings suggest that deep-learning models based on the representation encoding of cross sections combined with graph neural networks hold significant potential in augmenting nuclear theory models, e.g., by providing reliable estimates of covariances of cross sections, including cross-material covariances.
Machine learning↗
A learning-based time-efficient framework for building energy performance evaluation
Not Available
Bhattacharya, Saptarshi↗
Knowledge-guided graph machine learning for spatially distributed prediction of daily discharge and nitrogen export dynamics
Spatially distributed prediction of streamflow and nitrogen export dynamics is essential for precision management of agricultural watersheds. While temporal deep learning models such as Long Short-Term Memory (LSTM) have shown strong performance at basin scales, their ability to generalize spatially is limited by insufficient representation of spatial dependencies and flow paths, particularly under data-scarce conditions. To address this gap, we propose HydroGraphNet, a knowledge-guided graph machine learning framework that integrates process-based knowledge and explicit spatial learning into temporal modeling. This framework incorporates directed graph topology to encode watershed connectivity and upstream inflows, with mass balance constraints to improve physical consistency. To enhance generalization in sparsely monitored regions, HydroGraphNet is pretrained on synthetic data generated by the SWAT+ (Soil and Water Assessment Tool Plus) model. We evaluated HydroGraphNet in the Upper Sangamon River Basin (44 HUC-12 subwatersheds, 2001–2020) against two LSTM baselines: a lumped basin-level model and a distributed variant. When benchmarked on SWAT+ simulations in pretraining, HydroGraphNet improved test NSEs by 8.9% (discharge) and 13.7% (NO₃–N load) in temporal extrapolation, and by 27.1% and 34.7% in spatial extrapolation, relative to the Lumped LSTM baseline. After fine-tuning with USGS monitoring data, the model achieved mean test NSE (KGE) scores of 0.768 (0.861) for discharge and 0.626 (0.664) for NO₃–N load, substantially outperforming baselines. Attribution analysis further highlighted the importance of upstream inflow representation and graph-based spatial learning in capturing cross-subwatershed dependencies. The model also reproduced seasonal hydrological and biogeochemical patterns consistent with known processes, demonstrating its robustness and process fidelity for spatially distributed prediction. Altogether, HydroGraphNet advances the integration of physical knowledge and spatially explicit learning in hydrological modeling, offering a generalizable framework for distributed modeling to support spatially targeted water quality management in data-scarce watersheds.
54 ENVIRONMENTAL SCIENCES↗
Special Issue: Geostatistics and Machine Learning
Abstract Recent years have seen a steady growth in the number of papers that apply machine learning methods to problems in the earth sciences. Although they have different origins, machine learning and geostatistics share concepts and methods. For example, the kriging formalism can be cast in the machine learning framework of Gaussian process regression. Machine learning, with its focus on algorithms and ability to seek, identify, and exploit hidden structures in big data sets, is providing new tools for exploration and prediction in the earth sciences. Geostatistics, on the other hand, offers interpretable models of spatial (and spatiotemporal) dependence. This special issue on Geostatistics and Machine Learning aims to investigate applications of machine learning methods as well as hybrid approaches combining machine learning and geostatistics which advance our understanding and predictive ability of spatial processes.
58 GEOSCIENCES↗
Time-lapse seismic data inversion for estimating reservoir parameters using deep learning
Geologic carbon sequestration involves the injection of captured carbon dioxide ([Formula: see text]) into subsurface formations for long-term storage. The movement and fate of the injected [Formula: see text] plume is of great concern to regulators because monitoring helps to identify potential leakage zones and determines the possibility of safe long-term storage. To address this concern, we design a deep-learning framework for [Formula: see text] saturation monitoring to determine the geologic controls on the storage of the injected [Formula: see text]. We use different combinations of porosities and permeabilities for a given reservoir to generate saturation and velocity models. We train the deep-learning model with a few time-lapse seismic images and their corresponding changes in saturation values for a particular [Formula: see text] injection site. The deep-learning model learns the mapping from the change in the time-lapse seismic response to the change in [Formula: see text] saturation during the training phase. We then apply the trained model to data sets comprising different time-lapse seismic image slices (corresponding to different time instances) generated using different porosity and permeability distributions that are not part of the training to estimate the [Formula: see text] saturation values along with the plume extent. Our algorithm provides a deep-learning assisted framework for the direct estimation of [Formula: see text] saturation values and plume migration in heterogeneous formations using the time-lapse seismic data. Our method improves the efficiency of time-lapse inversion by streamlining the large number of intermediate steps in the conventional time-lapse inversion workflow. This method also helps to incorporate the geologic uncertainty for a given reservoir by accounting for the statistical distribution of porosity and permeability during the training phase. Tests on different examples verify the effectiveness of our approach.
Geochemistry & Geophysics↗
Machine learning-based surrogate models and transfer learning for derivative free optimization of HT-PEM fuel cells
Widespread adoption of high-temperature polymer electrolyte membrane electrochemical systems, such as fuel cells (HT-PEMFCs), requires models and computational tools for accurate optimization and guiding new materials for enhancing performance and durability. In this contribution, knowledge-based modelling and data-driven modelling are combined using Few-Shot Learning and implementing an Automated Machine Learning framework for the generation of Machine Learning-based surrogate models. Applicability of the resulting model for derivative-free optimization is demonstrated. Additionally, a way of considering extrapolation in the optimization task is presented. Results show that although extrapolation is needed to achieve better solutions during optimization, it can be monitored and managed. As a result, tuning the electrode ionomer binder's properties, such as ionic conductivity, in the fuel cell represents a promising pathway for improving HT-PEMFC performance.
08 HYDROGEN↗
Enabling probabilistic learning on manifolds through double diffusion maps
Here, we present a generative learning framework for probabilistic sampling that extends Probabilistic Learning on Manifolds (PLoM), which is designed to generate statistically consistent realizations of a random vector in a finite-dimensional Euclidean space, informed by a (representative) set of observations. In its original form, PLoM constructs a reduced-order probabilistic model by combining three main components: (a) kernel density estimation to approximate the underlying probability measure, (b) Diffusion Maps to characterize the manifold of the data, and (c) a reduced-order Itô Stochastic Differential Equation (ISDE) to sample from the learned distribution. However, its sampling dynamics are posed in the ambient space and the retained number of reduced coordinates is chosen by projection-reconstruction error. In practice, this often (i) requires more coordinates than the data’s intrinsic dimension to achieve stable sampling and (ii) lacks a smooth, basis-independent lifting back to the data domain; moreover, standard Diffusion Maps emphasize harmonic eigenfunctions and can miss non-harmonic latent structure. We address these limitations by decoupling geometry learning from sampling: a first Diffusion Maps pass identifies non-harmonic coordinates on which we formulate a full-order ISDE directly in the latent space, while Double Diffusion Maps captures multiscale geometric features and Geometric Harmonics (GH) learns a smooth lifting map to the ambient variables that is independent of the particular diffusion basis. This hybrid design preserves the system’s dynamical richness with a compact geometric representation and enables principled out-of-sample inference. The effectiveness and robustness of the proposed method are illustrated through two numerical studies: one based on data generated from two-dimensional Hermite polynomial functions and another based on high-fidelity simulations of a detonation wave in a reactive flow.
Double diffusion maps↗
Time-series machine-learning error models for approximate solutions to parameterized dynamical systems
This work proposes a machine-learning framework for modeling the error incurred by approximate solutions to parameterized dynamical systems. In particular, we extend the machine-learning error models (MLEM) framework proposed in Ref. Freno and Carlberg (2019) to dynamical systems. The proposed Time-Series Machine-Learning Error Modeling (T-MLEM) method constructs a regression model that maps features – which comprise error indicators that are derived from standard a posteriori error-quantification techniques – to a random variable for the approximate-solution error at each time instance. The proposed framework considers a wide range of candidate features, regression methods, and additive noise models. We consider primarily recursive regression techniques developed for time-series modeling, including both classical time-series models (e.g., autoregressive models) and recurrent neural networks (RNNs), but also analyze standard non-recursive regression techniques (e.g., feed-forward neural networks) for comparative purposes. Finally, numerical experiments conducted on multiple benchmark problems illustrate that the long short-term memory (LSTM) neural network, which is a type of RNN, outperforms other methods and yields substantial improvements in error predictions over traditional approaches.
42 ENGINEERING↗
Computational Framework for Machine-Learning-Enabled 13 C Fluxomics
13 C metabolic flux analysis (MFA) has emerged as a powerful tool for synthetic biology. This optimization-based approach suffers long computation time and unstable solutions depending on the initial guess. Here, we develop a machine-learning-based framework for 13 C fluxomics. Specifically, training and test data sets are generated by metabolic network decomposition and flux sampling, in which flux ratios at metabolic nodes and simulated labeling patterns of metabolites are used as training targets and features, respectively. To improve prediction accuracy and simplify the model, automated processes are developed for flux ratio selection based on solvability and feature screening based on importance. We found that predictive performance can be significantly improved using both amino acids and central carbon metabolites in comparison with amino acids alone. Together with measured external fluxes, the predicted flux ratios determine the mass balance system, yielding global flux distributions. This approach is validated by flux estimation using both simulated and experimental data in comparison with canonical 13 C MFA. The approach represents a reliable fluxomics method readily applicable to high-throughput metabolic phenotyping, which highlights the advances of intelligent learning algorithms in synthetic biology, specifically in the Test and Learn stage of the Design-Build-Test-Learn cycle.
13C metabolic flux analysis↗
Operation Optimization using Reinforcement Learning with Integrated Artificial Reasoning Framework
In large and complex systems, operational decision-making requires a systematic analysis with a vast amount of data from both process parameters and component status monitoring. In this paper, we present an integrated artificial reasoning approach for system state transition models that can help operational decision-making with explainable and traceable reasoning. The integrated artificial reasoning framework is a physics-based approach of defining the system structure in a Bayesian network, so we leveraged it in a Markov decision process (MDP) for finding optimal operational solutions. In our proposed framework, the MDP is implemented on a dynamic Bayesian network (DBN), which represents causalities in a system. The multilevel flow modeling was utilized in order to extract these causalities in a more efficient and objective manner. Since multilevel flow modeling is based on the fundamental energy and mass conservation laws, the target system is decomposed into several mass, energy, and information structures, which serve as the basis for a DBN. The MDP consists of the processes of finding a solution for the Bellman equation, which can be derived from the conditional probability equations of the constructed DBN. System operators can capture stochastic system dynamics as multiple subsystem state transitions based on their physical relations and uncertainties coming from the component degradation process or random failures. We analyzed a simplified example system to illustrate finding an optimal operational policy with this approach.
99 GENERAL AND MISCELLANEOUS↗
yProv4ML: Effortless provenance tracking for machine learning systems
The rapid growth in interest in deep learning and foundation models (FMs) in particular, has attracted the attention of a diverse range of researchers thanks to their generalization ability. However, the advent of these techniques has also brought to light the lack of transparency and rigor in the way development is pursued. In particular, the inability to determine the number of epochs and other hyperparameters in advance presents challenges in identifying the best model. To address this challenge, machine learning frameworks such as MLFlow can automate the collection of this type of information. However, these tools capture data using proprietary formats and pose little attention to lineage. This paper proposes yProv4ML, a framework that captures provenance information generated during machine learning processes in PROV-JSON format, with minimal code modification.
Machine learning↗