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Physics-based hybrid machine learning for critical heat flux prediction with uncertainty quantification
Critical heat flux (CHF) is a key quantity in nuclear system modeling due to its impact on heat transfer, safety margins, and reactor performance. This study develops and validates an uncertainty-aware hybrid modeling approach that combines machine learning with physics-based models to predict CHF in cases of dryout. The Biasi and Bowring empirical correlations were paired with three ML uncertainty quantification (UQ) techniques: deep neural network (DNN) ensembles, Bayesian neural networks (BNNs), and deep Gaussian processes (DGPs). A pure ML model without a base model was evaluated for comparison. Model performance was assessed under plentiful (7,350 points) and limited (9 points) training data scenarios using parity, uncertainty distributions, and calibration curves. Results show that the Biasi hybrid DNN ensemble achieved the best overall performance, with a mean absolute relative error of 1.846%, and well-calibrated uncertainty estimates. The BNN-based hybrids showed slightly higher error (2.14%) but superior uncertainty calibration. DGP models underperformed, with over 6% error and poor uncertainty calibration. All hybrid models outperformed pure machine learning configurations, demonstrating resistance against data scarcity. These findings indicate that hybrid modeling significantly improves predictive accuracy, interpretability, and resilience to data scarcity. The integration of uncertainty awareness provides actionable confidence in CHF predictions, which is vital for safety-critical decisions in nuclear applications. This hybrid approach offers a viable pathway for deploying ML models in reactor analysis tools while preserving domain knowledge and physical consistency.
Achieving precise multiparameter measurements with distributed optical fiber sensor using wavelength diversity and deep neural networks
The development of advanced distributed optical fiber sensing systems that are capable of performing accurate and spatially resolved multiparameter measurements is of great interest to a wide range of scientific and industrial applications. Here, in this paper, we propose and experimentally demonstrate a wavelength diversity based advanced distributed optical fiber sensor system to accomplish multiparameter sensing while greatly enhancing measurement accuracy. A suite of deep neural network (DNN) algorithms are developed and verified for data denoising, rapid Brillouin frequency shift estimation, and vibration data event classification. As a proof-of-concept, we demonstrate the effectiveness of the proposed advanced wavelength diversity distributed fiber sensor system assisted by DNN for simultaneous, independent measurements of static strain, temperature, and acoustic vibrations over a 25 km long sensing fiber at 3 m spatial resolution. These results suggest the potential for an intelligent multiparameter monitoring system with enhanced performance in advanced structural health monitoring applications.
Bayesian reduced-order deep learning surrogate model for dynamic systems described by partial differential equations
We propose a reduced-order deep-learning surrogate model for dynamic systems described by time-dependent partial differential equations. This method employs space–time Karhunen–Loève expansions (KLEs) of the state variables and space-dependent KLEs of space-varying parameters to identify the reduced (latent) dimensions. Subsequently, a deep neural network (DNN) is used to map the parameter latent space to the state variable latent space. An approximate Bayesian method is developed for uncertainty quantification (UQ) in the proposed KL-DNN surrogate model. The KL-DNN method is tested for the linear advection–diffusion and nonlinear diffusion equations, and the Bayesian approach for UQ is compared with the deep ensembling (DE) approach, commonly used for quantifying uncertainty in DNN models. It was found that the approximate Bayesian method provides a more informative distribution of the PDE solutions in terms of the coverage of the reference PDE solutions (the percentage of nodes where the reference solution is within the confidence interval predicted by the UQ methods) and log predictive probability. The DE method is found to underestimate uncertainty and introduce bias. For the nonlinear diffusion equation, we compare the KL-DNN method with the Fourier Neural Operator (FNO) method and find that KL-DNN is 10% more accurate and needs less training time than the FNO method.
Explainable multi-fidelity Bayesian neural network for distribution system state estimation
Distribution System State Estimation (DSSE) is frequently constrained by limited real-time measurements, the uncertainties introduced by distributed energy resources, and the presence of bad data. To address them, this paper proposes an enhanced Multi-Fidelity Bayesian Neural Network (MFBNN) DSSE approach. A low-fidelity layer based on a Deep Neural Network (DNN) is first pre-trained on pseudo-measurement data to learn fundamental state features. Subsequently, a high-fidelity Bayesian Neural Network (BNN) layer leverages limited but high-quality real-time measurements to refine these features, thereby achieving accurate DSSE. Additionally, the deep SHapley Additive exPlanation (SHAP) is developed to quantify the influence of measurement data on DSSE through dual perspectives of global feature importance and local nodal contributions, establishing a hierarchical explainability framework for machine learning-based DSSE. Comparative studies conducted on the IEEE 13-bus system and a real-world 2135-node system from Dominion Energy demonstrate that the proposed method excels in estimation accuracy, even under situations of high noise levels, bad data, and missing data. Further comparisons with Weighted Least Squares (WLS) and other machine learning-based DSSE approaches verify that the proposed framework offers higher accuracy, improved interpretability, and enhanced robustness.
Predicting critical heat flux with uncertainty quantification and domain generalization using conditional variational autoencoders and deep neural networks
Deep generative models (DGMs) can generate synthetic data samples that closely resemble the original dataset, addressing data scarcity. In this work, we developed a conditional variational autoencoder (CVAE) to augment critical heat flux (CHF) data used for the 2006 Groeneveld lookup table. To compare with traditional methods, a fine-tuned deep neural network (DNN) regression model was evaluated on the same dataset. Both models achieved small mean absolute relative errors, with the CVAE showing more favorable results. Uncertainty quantification (UQ) was performed using repeated CVAE sampling and DNN ensembling. The DNN ensemble improved performance over the baseline, while the CVAE maintained consistent results with less variability and higher confidence. Both models achieved small errors inside and outside the training domain, with slightly larger errors outside. Altogether, the CVAE performed better than the DNN in predicting CHF and exhibited better uncertainty behavior.
Fast and accurate reduced-order modeling of a MOOSE-based additive manufacturing model with operator learning
One predominant challenge in additive manufacturing (AM) is to achieve specific material properties by manipulating manufacturing process parameters during the runtime. Such manipulation tends to increase the computational load imposed on existing simulation tools employed in AM. The goal of the present work is to construct a fast and accurate reduced-order model (ROM) for an AM model developed within the Multiphysics Object-Oriented Simulation Environment (MOOSE) framework, ultimately reducing the time/cost of AM control and optimization processes. Our adoption of the operator learning (OL) approach enabled us to learn a family of differential equations produced by altering process variables in the laser’s Gaussian point heat source. More specifically, we used the Fourier neural operator (FNO) and deep operator network (DeepONet) to develop ROMs for time-dependent responses. Furthermore, we benchmarked the performance of these OL methods against a conventional deep neural network (DNN)-based ROM. Ultimately, we found that OL methods offer comparable performance and, in terms of accuracy and generalizability, even outperform DNN at predicting scalar model responses. The DNN-based ROM afforded the fastest training time. Furthermore, all the ROMs were faster than the original MOOSE model yet still provided accurate predictions. FNO had a smaller mean prediction error than DeepONet, with a larger variance for time-dependent responses. Unlike DNN, both FNO and DeepONet were able to simulate time series data without the need for dimensionality reduction techniques. Finally, the present work can help facilitate the AM optimization process by enabling faster execution of simulation tools while still preserving evaluation accuracy.
Three-dimensional cooperative inversion of airborne magnetic and gravity gradient data using deep-learning techniques
Using multiple geophysical methods has become a prevailing approach in numerous geophysical applications to investigate subsurface structures and parameters. These multimethod-based exploration strategies have the potential to greatly diminish uncertainties and ambiguities encountered during geophysical data analysis and interpretation. One of the applications is the cooperative inversion of airborne magnetic and gravity gradient data for the interpretation of data obtained in mineral, oil and gas, and geothermal explorations. In this paper, a unified cooperative inversion framework is designed by combining the standard separate inversions with a deep neural network (DNN), which serves as the link between different types of data. A well-trained DNN takes the separately inverted susceptibility and density models as the inputs and provides improved models that will be used as the initial models of deterministic inversions. A two-round iteration strategy is adopted to guarantee the reasonability of the recovered models and overall efficiency of the inversion. In addition, this deep-learning (DL)-based framework demonstrates excellent generalization abilities when tested on models that are entirely distinct from the training data sets. The framework can easily incorporate multiphysics without necessitating any structural changes to the network. Synthetic experiments validate that our DL-based method outperforms conventional separate inversions and cross-gradient-based joint inversion in view of the accuracy of the recovered models and inversion efficiency. Successful application to field data further verifies the effectiveness of our DL-based method.
Newton-Raphson AC Power Flow Convergence Based on Deep Learning Initialization and Homotopy Continuation
Power flow forms the basis of many power system studies. With the increased penetration of renewable energy, grid planners tend to perform multiple power flow simulations under various operating conditions and not just selected snapshots at peak or light load conditions. Getting a converged AC power flow (ACPF) case remains a significant challenge for grid planners especially in large power grid networks. This paper proposes a two-stage approach to improve Newton-Raphson ACPF convergence and was applied to a 6102 bus Electric Reliability Council of Texas (ERCOT) system. The first stage utilizes a deep learning-based initializer with data re-training. Here a deep neural network (DNN) initializer is developed to provide better initial voltage magnitude and angle guesses to aid in power flow convergence. This is because Newton-Raphson ACPF is quite sensitive to the initial conditions and bad initialization could lead to divergence. The DNN initializer includes a data re-training framework that improves the initializer's performance when faced with limited training data. The DNN initializer successfully solved 3,285 cases out of 3,899 non-converging dispatch and performed better than random forest and DC power flow initialization methods. ACPF cases not solved in this first stage are then passed through a hot-starting algorithm based on homotopy continuation with switched shunt control. The hot-starting algorithm successfully converged 416 cases out of the remaining 614 non-converging ACPF dispatch. In conclusion, the combined two-stage approach achieved a 94.9% success rate, by converging a total of 3,701 cases out of the initial 3,899 unsolved cases.
Efficient learning of power grid voltage control strategies via model-based deep reinforcement learning
Here this article proposes a model-based deep reinforcement learning (DRL) method to design emergency control strategies for short-term voltage stability problems in power systems. Recent advances show promising results for model-free DRL-based methods in power systems control problems. But in power systems applications, these model-free methods have certain issues related to training time (clock time) and sample efficiency; both are critical for making state-of-the-art DRL algorithms practically applicable. DRL-agent learns an optimal policy via a trial-and-error method while interacting with the real-world environment. It is also desirable to minimize the direct interaction of the DRL agent with the real-world power grid due to its safety-critical nature. Additionally, the state-of-the-art DRL-based policies are mostly trained using a physics-based grid simulator where dynamic simulation is computationally intensive, lowering the training efficiency. We propose a novel model-based DRL framework where a deep neural network (DNN)-based dynamic surrogate model (SM), instead of a real-world power grid or physics-based simulation, is utilized within the policy learning framework, making the process faster and more sample efficient. However, having stable training in model-based DRL is challenging because of the complex system dynamics of large-scale power systems. We addressed these issues by incorporating imitation learning to have a warm start in policy learning, reward-shaping, and multi-step loss in surrogate model training. Finally, we achieved 97.5% reduction in samples and 87.7% reduction in training time for an application to the IEEE 300-bus test system.
Deep-Learning-derived Boundary Layer Height from Meteorological Data over the SGP, GOAMAZON, CACTI
The planetary boundary-layer (PBL) height (PBLH) is an important parameter for various meteorological and climate studies. This study presents a multi-structure deep neural network (DNN) model, designed to estimate PBLH by integrating morning temperature profiles with surface meteorological observations. The DNN model is developed by leveraging a rich data set of PBLH derived from long-standing radiosonde records and augmented with high-resolution micropulse lidar and Doppler lidar observations. We access the performance of the DNN with an ensemble of 10 members, each featuring distinct hidden layer structures, which collectively yield a robust 27-year PBLH data set over the Southern Great Plains from 1994 to 2020. The influence of various meteorological factors on PBLH is rigorously analyzed through the importance test. Moreover, the DNN model's accuracy is evaluated against radiosonde observations and juxtaposed with conventional remote-sensing methodologies, including Doppler lidar, ceilometer, Raman lidar, and micropulse lidar. The DNN model exhibits reliable performance across diverse conditions and demonstrates lower biases relative to remote-sensing methods. In addition, the DNN model, originally trained over a plain region, demonstrates remarkable adaptability when applied to the heterogeneous terrains and climates encountered during the GoAmazon (tropical rainforest) and CACTI (middle-latitude mountain) campaigns. These findings demonstrate the effectiveness of deep learning models in estimating PBLH, enhancing our understanding of boundary-layer dynamics with implications for enhancing the representation of PBL in weather forecasting and climate modeling.
Deep-learning-derived planetary boundary layer height from conventional meteorological measurements
Abstract. The planetary boundary layer (PBL) height (PBLH) is an important parameter for various meteorological and climate studies. This study presents a multi-structure deep neural network (DNN) model, which can estimate PBLH by integrating the morning temperature profiles and surface meteorological observations. The DNN model is developed by leveraging a rich dataset of PBLH derived from long-standing radiosonde records augmented with high-resolution micro-pulse lidar and Doppler lidar observations. We access the performance of the DNN with an ensemble of 10 members, each featuring distinct hidden-layer structures, which collectively yield a robust 27-year PBLH dataset over the southern Great Plains from 1994 to 2020. The influence of various meteorological factors on PBLH is rigorously analyzed through the importance test. Moreover, the DNN model's accuracy is evaluated against radiosonde observations and juxtaposed with conventional remote sensing methodologies, including Doppler lidar, ceilometer, Raman lidar, and micro-pulse lidar. The DNN model exhibits reliable performance across diverse conditions and demonstrates lower biases relative to remote sensing methods. In addition, the DNN model, originally trained over a plain region, demonstrates remarkable adaptability when applied to the heterogeneous terrains and climates encountered during the GoAmazon (Green Ocean Amazon; tropical rainforest) and CACTI (Cloud, Aerosol, and Complex Terrain Interactions; middle-latitude mountain) campaigns. These findings demonstrate the effectiveness of deep learning models in estimating PBLH, enhancing our understanding of boundary layer processes with implications for improving the representation of PBL in weather forecasting and climate modeling.
An adaptive and stability-promoting layerwise training approach for sparse deep neural network architecture
This work presents a two-stage adaptive framework for progressively developing deep neural network (DNN) architectures that generalize well for a given training data set. In the first stage, a layerwise training approach is adopted where a new layer is added each time and trained independently by freezing parameters in the previous layers. We impose desirable structures on the DNN by employing manifold regularization, sparsity regularization, and physics-informed terms. We introduce a ε – δ – stability-promoting concept as a desirable property for a learning algorithm and show that employing manifold regularization yields a ε – δ stability-promoting algorithm. Further, we also derive the necessary conditions for the trainability of a newly added layer and investigate the training saturation problem. In the second stage of the algorithm (post-processing), a sequence of shallow networks is employed to extract information from the residual produced in the first stage, thereby improving the prediction accuracy. Numerical investigations on prototype regression and classification problems demonstrate that the proposed approach can outperform fully connected DNNs of the same size. Moreover, by equipping the physics-informed neural network (PINN) with the proposed adaptive architecture strategy to solve partial differential equations, we numerically show that adaptive PINNs not only are superior to standard PINNs but also produce interpretable hidden layers with provable stability. As a result, we also apply our architecture design strategy to solve inverse problems governed by elliptic partial differential equations.
Multi-objective surrogate-assisted calibration of CPFEM models using macroscopic response and in situ EBSD measurements of grain reorientation trajectories
Crystal plasticity finite element method (CPFEM) models are widely used to simulate the deformation behaviour of polycrystalline materials, but their calibration is often limited by their high computational cost and the non-convexity of the optimisation landscape. Here, this study develops a multi-objective surrogate-assisted calibration workflow that couples a multi-objective genetic algorithm (MOGA) with an adaptively trained deep neural network (DNN) surrogate model to efficiently identify CPFEM parameters from experimental data. The workflow is demonstrated on three crystal plasticity (CP) formulations of increasing complexity — Voce hardening (VH), two-coefficient latent hardening (LH2), and six-coefficient latent hardening (LH6) — using in situ electron backscatter diffraction (EBSD) measurements of Alloy 617 under uniaxial tensile loading. The CPFEM models are calibrated against the experimentally observed stress–strain response and reorientation trajectories of eight grains, then validated against eight additional trajectories and overall texture evolution. Across the CP formulations, the macroscopic response was reproduced reliably, while differences emerged in the robustness and accuracy of the grain-scale predictions. Including grain reorientation trajectories in the multi-objective calibration improved texture evolution predictions and filtered out physically inconsistent parameter sets that can arise from calibrating against only the stress–strain data. The workflow also demonstrates good transferability of calibrated parameters from a low- to a high-fidelity microstructural model. These results provide practical guidance for integrating in situ microstructural data into CPFEM through efficient, repeatable, and physically meaningful multi-objective calibration.
A hybrid numerical and machine learning framework for evaluating the performance of a 780 cm 2 aqueous organic redox flow battery
Aqueous organic redox flow battery (AORFB) is a promising cost-competitive technology for large-scale energy storage. Among existing work, the dihydroxyphenazine (DHP)-based AORFB has demonstrated high energy density and low capacity degradation in 10 cm2 cells during lab tests. However, its commercial-scale performance in more complex environments remains unknown, posing a barrier for commercialization. To address this gap, this work presents a comprehensive performance evaluation of a 780 cm 2 DHP-based AORFB by combining physics-based numerical model, machine learning (ML)-based surrogate models, and ML-derived sensitivity quantification. Specifically, we first select 12 key battery parameters that include 10 physicochemical quantities and 2 operation quantities, then select 6 performance metrics that include energy efficiency (EE), discharging capacity, charging energy, and power losses due to concentration, activation, and ohmic over-potentials. With such selection, 12800 combinations of the 12 parameters are subsequently generated using the Latin Hypercube Sampling method. These combinations, together with 38 pre-defined State of Charge, are then integrated to a validated AORFB model developed in COMSOL to compute the performance metrics. With both input parameters and performance metrics, 60 deep neural network (DNN) surrogate models are then trained to approximate the relationship between the 10 physicochemical quantities and 6 performance metrics at each flow rate and current density. Sensitivity scores are then calculated based on the DNN models. Two additional sensitivity analysis tools, i.e., MARS, and SHAP, are also used to cross-validate the sensitivity scores from the DNN. The results demonstrate that 1) the standard potential ranks the first in controlling EE and charging energy, 2) the membrane conductivity is most critical for power loss and EE, and 3) specific area and reaction rate control activation power loss.
An investigation on machine learning predictive accuracy improvement and uncertainty reduction using VAE-based data augmentation
The confluence of ultrafast computers with large memory, rapid progress in Machine Learning (ML) algorithms, and the availability of large datasets place multiple engineering fields at the threshold of dramatic progress. However, a unique challenge in nuclear engineering is data scarcity because experimentation on nuclear systems is usually more expensive and time-consuming than most other disciplines. One potential way to resolve the data scarcity issue is deep generative learning, which uses certain ML models to learn the underlying distribution of existing data and generate synthetic samples that resemble the real data. In this way, one can significantly expand the dataset to train more accurate predictive ML models. In this study, our objective is to evaluate the effectiveness of data augmentation using variational autoencoder (VAE)-based deep generative models. We investigated whether the data augmentation leads to improved accuracy in the predictions of a deep neural network (DNN) model trained using the augmented data. Additionally, the DNN prediction uncertainties are quantified using Bayesian Neural Networks (BNN) and conformal prediction (CP) to assess the impact on predictive uncertainty reduction. To test the proposed methodology, we used TRACE simulations of steady-state void fraction data based on the NUPEC Boiling Water Reactor Full-size Fine-mesh Bundle Test (BFBT) benchmark. Here, we found that augmenting the training dataset using VAEs has improved the DNN model’s predictive accuracy, improved the prediction confidence intervals, and reduced the prediction uncertainties.
Resistive Switching of Spinel Li 4 Ti 5 O 12 Lithium-Ion Battery Material for Neuromorphic Computing
The rapid rise of AI has exposed significant limitations in conventional Von Neumann computing architecture, particularly in regard to speed and energy efficiency. To address these challenges, researchers are exploring a brain-inspired neuromorphic architecture that mimics biological neural networks, enabling massive parallel processing with reduced power consumption for complex AI computational demands. Recent interest has focused on utilizing battery electrodes and solid electrolyte materials for their resistive switching properties in developing a neuromorphic architecture. These properties are precisely tuned through local- and bulk-level chemical composition modifications via voltage bias stimuli. In this study, we demonstrate fabricating a three-terminal lithium-ion electrochemical transistor based on lithium titanium oxide (Li 4 Ti 5 O 12 ), a popular lithium-ion battery anode material. We deposited and characterized LTO thin films using RF sputtering, demonstrating a 6 orders of magnitude increase in electronic conductivity upon lithiation, with conductivity plateauing after 20% lithiation. Density functional theory calculations revealed transformation from the insulating to conducting state, supported by experimental characterization through X-Ray Photoelectron Spectroscopy (XPS) and Direct Current (DC) polarization analyses. The fabricated transistor consisted of LTO as the channel layer, gold as source/drain terminals, lithium phosphorus oxynitride (LiPON) as the lithium-ion conductor, and copper as the gate terminal. The device exhibited clear hysteresis in transfer characteristics due to lithium insertion/extraction processes. Long-term potentiation (LTP) and long-term depression (LTD) measurements showed an asymmetric ratio of 1.425 and maximum/minimum conductance ratio of 7.83. When implemented in a deep neural network (DNN) for MNIST handwritten digit recognition, the device achieved 92.03% accuracy over 20 training epochs. Detailed transport mechanism analysis revealed the crucial role of oxygen vacancies and interface effects in device operation. Our preliminary findings establish LTO-based lithium-ion electrochemical transistors as promising candidates for energy-efficient neuromorphic computing applications, offering potential solutions to traditional Von Neumann architecture limitations.
A Medium‐Sized Paleo‐Tsunami Reconstruction by a Deep Neural Network Processing Sedimentary Deposits
Abstract Reconstructing the magnitude and recurrence time of tsunamis, one of the most destructive and unpredictable natural hazards impacting coastal communities, is essential. While major tsunamis are the most studied due to their disastrous impact, small/medium tsunamis (SMTs) are much more frequent and can still significantly impact the coast. Therefore, SMTs potentially provide an extensive archive of information preserved in the geological record. Analyzing the deposits of small/medium paleo‐tsunamis (SMPTs) opens a window into when their direct observation was unavailable. However, deposits of SMPTs are often degraded, traditional sediment deposition inversion models might fail. Recent research has shown that Deep Neural Networks (DNN) can effectively reconstruct the flow conditions of major tsunamis from their deposits. We evaluate the effectiveness of this approach in reconstructing the characteristics of a recent medium size tsunami (2006 Java) and of a medium paleo‐tsunami (1929 Grand Banks). We successfully reconstruct the flow characteristics of the 2006 Java event and show that an inversion of comparable quality is possible for the 1929 Grand Banks tsunami, despite greater uncertainties due to the deposit degradation. Our research shows that Machine Learning has the potential to unseal the meaning of data of thousands SMPTs.