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Data Summarization and Inference at Scale
This is the final report for the DOE ASCR grant SC-0022260, Data Summarization and Inference at Scale, PI: Alex Pothen, Purdue University. The goal of the project was to solve data-intensive and compute-intensive problems in the physical sciences, engineering, information science, data science, etc. by designing and implementing new algorithms that could work with a subset of the data. The four subgoals were: (a) The solution of problems where the data is too large to be stored in the memory of a computer. In this streaming model of computation, the data arrives as a stream of elements to the computer, each element is processed as it arrives, and a decision is made to discard the data or to store it; only a small subset of the data proportional to the size of the output solution is stored, and when all the data has been streamed, a solution to the problem is computed from the stored subset. (b) The use of machine learning methods to compute solutions to data-intensive problems. The use of GPUs is critical to obtain high performance on machine learning tasks, but their memory sizes are smaller relative to that of CPUs. For large-scale problems, the data is sampled many times, and small samples are used with repetition, for robustness, to compute solutions to inference tasks. This sampling reduces the memory required to solve the problem, but attention is needed to avoid slow convergence to the solutions, and reduced accuracy of inference. We propose submodular optimization, Large Language Models, and physics-informed neural networks to enable GPU computations here. (c) Modeling and visualization of high-dimensional data using interpretable features. Clinical proteomic data sets from immunology for the detection of cancer and other diseases are temporal and high-dimensional, and algorithms for visualizing these data sets using clinically interpretable features are lacking. We propose methods that compute distances based on the optimal transportation problem and graph edit distances to address this problem. We also propose the use of optimal transport-based distances, spatial statistics, and network structure to classify image data sets, We apply these algorithms to electron micrographs of the peripheral nervous system in the digestive tract. (d) The design of data-intensive algorithms on emerging architectures, specifically, noisy, intermediate-scale quantum (NISQ) devices. Quantum computers offer the possibility of exploring large solution spaces due to the principle of superposition, but current quantum computers are limited by few qubits, short coherence times due to noise, poor interconections among the qubits, etc. We propose the use of the divide and conquer paradigm to solve large-scale problems, wherein collections of small subproblems are solved on the quantum devices, and the solutions to the subproblems are integrated into a solution for the original problem on a classical computer.
Physics-Guided Deep Learning for Complex System Health Management and Decision Making
The landscape of complex engineered systems is rapidly evolving, from smart manufacturing facilities to next-generation transportation vehicles. As these systems become increasingly sophisticated and interconnected, the need for advanced health management systems grows ever more critical. These systems must go beyond simple monitoring, actively predicting potential failures before they occur. This paradigm shift from fixed maintenance schedules to condition-based predictions is key to optimizing system performance, enhancing safety, and paving the way for autonomous decision-making across various industries. Whether in industrial processes, energy systems, or advanced transportation, the ability to anticipate and prevent failures is becoming a cornerstone of operational excellence. To accurately predict the future health of any complex system, knowledge of its current health state and future operational conditions is essential. Recent advancements in data-driven algorithms have generated growing interest in artificial intelligence for industrial applications. However, the limitations of pure data-driven methods, particularly in industries where data acquisition is costly and limited, have become apparent. This has led to a focus on blending physics with data-driven algorithms, mitigating the drawbacks of both approaches while emphasizing their respective advantages. This research proposes a novel framework for integrating physics-based performance models with deep learning algorithms for the prognostics of complex safety-critical systems. In this approach, physics-based models serve as a blueprint, capturing fundamental system behaviors, while deep learning algorithms, leveraging real-world sensor data, fill in gaps and identify subtle patterns indicative of potential problems. This hybrid methodology, utilizing techniques such as Physics-Informed Neural Networks (PINNs), offers a powerful solution for predicting system health. By fusing domain knowledge with data-driven insights, this approach promises more accurate, adaptable, and reliable models for health prediction. The resulting framework is versatile, applicable across various sectors including aerospace, manufacturing, and energy systems, ultimately contributing to safer, more efficient operations in our increasingly complex technological landscape.
Precise Modeling of a Complex Solenoidal Magnetic Field Using a Combination of Analytic Functions and a PINN
We demonstrate an iterative approach to modeling a sparsely measured magnetic field in a large-bore solenoid. This approach uses a hybrid of traditional and machine learning techniques. The traditional technique is a linear least-squares fit using a series solution to Laplace's equation, while the machine learning technique involves the training of a physics-informed neural network (PINN) on the least-squares fit residuals. We use a newly defined activation function "DELTAsnake," a modification to the snake activation function proposed by Ziyin et al. that allows for stronger curvature and non-monotonicity. The combined model approximately obeys Maxwell's equations to a level sufficient for producing high quality physics simulations and analysis. Our approach is applied to a highly realistic calculation of the expected magnetic field in the Mu2e experiment's Detector Solenoid which includes a simple model for the expected statistical measurement uncertainties. Using ten toy measurement simulations, we demonstrate the capabilities of our model in comparison to the least-squares method alone; the least-squares method alone results in a reduced chi-squared statistic of ${2.15 \pm 0.01}$, while our approach improves the reduced chi-square to ${1.034 \pm 0.005}$. Furthermore, for an average toy simulation, we show that the range of the RMS of the three field component residuals reduces from ${0.07-0.37}$ Gauss to ${0.05-0.07}$ Gauss. We find that this novel method is robust against a realistic systematic uncertainty deriving from Hall probe calibration bias and can be used to significantly reduce the number of measurements required to achieve an accurate model.
A Comparative Study of Physics‐Informed and Data‐Driven Neural Networks for Compound Flood Simulation at River‐Ocean Interfaces: A Case Study of Hurricane Irene
Simulating compound flooding (CF) at the river-ocean interface within large-scale Earth System Models (ESMs) presents significant challenges due to complex interactions between river discharge, storm surge, and tides. This study assesses the comparative advantages of physics-informed and data-driven machine learning (ML) approaches for enhancing local ESM performance. We systematically compare data-driven neural network models (i.e., CNNs, U-Net, Long Short-Term Memory (LSTM), Gated Recurrent Unit), and physics-informed neural network (PINN) models, including vanilla PINN and a finite-difference-based PINN (FD-PINN). Specifically, FD-PINN is introduced to enhance computational efficiency, accelerating vanilla PINNs by ∼6.5 times while improving accuracy. To enhance data-driven model training, a new data-generation approach is developed to sample historical fluvial and coastal flood events, which ensures a robust data set for extreme event prediction. The models are evaluated using a realistic one-dimensional river domain extracted from an ESM's river mesh and the Hurricane Irene event as an independent test case. Results show that FD-PINN achieves accurate predictions with significantly reduced computational costs relative to vanilla PINNs. Among data-driven models, the best overall performance is achieved by a CNN-LSTM hybrid, which balances accuracy and efficiency. While a fully connected CNN (CNN-FC) provides the best accuracy, it incurs high computational cost. Architectures lacking strong temporal modeling tend to underperform on unseen events. These findings highlight the importance of sequence-aware designs for robust generalization. This study reveals the trade-offs between physics-informed and data-driven models and proposes an adaptive hybrid framework for integrating ML into ESMs to enhance local flood simulations.
Physics-informed machine learning analysis for nanoscale grain mapping by synchrotron Laue microdiffraction
Understanding the grain morphology, orientation distribution and crystal structure of nanocrystals is essential for optimizing the mechanical and physical properties of functional materials. Synchrotron X-ray Laue microdiffraction is a powerful technique for characterizing crystal structures and orientation mapping using focused X-rays. However, when the grain sizes are smaller than the beam size, mixed peaks in the Laue pattern from neighboring grains limit the resolution of grain morphology mapping. We propose a physics-informed machine learning (PIML) approach that combines a convolutional neural network feature extractor with a physics-informed filtering algorithm to overcome the spatial resolution limits of X-rays, achieving nanoscale resolution for grain mapping. Our PIML method successfully resolves the grain size, orientation distribution and morphology of Au nanocrystals through synchrotron microdiffraction scans, showing good agreement with electron backscatter diffraction results. This PIML-assisted synchrotron microdiffraction analysis can be generalized to other diffraction-based probes, enabling the characterization of nanosized structures with micrometre-sized probes.
Physics-informed latent neural operator for real-time predictions of time-dependent parametric PDEs
Deep operator network (DeepONet) has shown significant promise as surrogate models for systems governed by partial differential equations (PDEs), enabling accurate mappings between infinite-dimensional function spaces. However, when applied to systems with high-dimensional input-output mappings arising from large numbers of spatial and temporal collocation points, these models often require heavily overparameterized networks, leading to long training times. Latent DeepONet addresses some of these challenges by introducing a two-step approach: first learning a reduced latent space using a separate model, followed by operator learning within this latent space. While efficient, this method is inherently data-driven and lacks mechanisms for incorporating physical laws, limiting its robustness and generalizability in data-scarce settings. Here, in this work, we propose PI-Latent-NO, a physics-informed latent neural operator framework that integrates governing physics directly into the learning process. Our architecture features two coupled DeepONets trained end-to-end: a Latent-DeepONet that learns a low-dimensional representation of the solution, and a Reconstruction-DeepONet that maps this latent representation back to the physical space. By embedding PDE constraints into the training via automatic differentiation, our method eliminates the need for labeled training data and ensures physics-consistent predictions. The proposed framework is both memory and compute-efficient, exhibiting near-constant scaling with problem size and demonstrating significant speedups over traditional physics-informed operator models. We validate our approach on a range of parametric PDEs, showcasing its accuracy, scalability, and suitability for real-time prediction in complex physical systems.
PowerModelsGAT-AI: Physics-Informed Graph Attention for Multi-System Power Flow With Continual Learning
Solving the alternating current power flow equations in real time is essential for secure grid operation, yet classical Newton–Raphson solvers can be slow under stressed conditions. Existing graph neural networks for power flow are typically trained on a single system and often degrade on different systems. We present PowerModelsGAT-AI, a physics-informed graph attention network that predicts bus voltages and generator injections. The model uses bus-type-aware masking to handle different bus types and balances multiple loss terms, including a power-mismatch penalty, using learned weights. We evaluate the model on 14 benchmark systems (4 to 6,470 buses) and train a unified model on 13 of these under contingency conditions with up to two branch outages, achieving an average normalized mean absolute error of 0.89% for voltage magnitudes and R 2 >0.99 for voltage angles. We also show continual learning: when adapting a base model to a new 1,354-bus system, standard fine-tuning causes severe forgetting with error increases exceeding 1000% on base systems, while our experience replay and elastic weight consolidation strategy keeps error increases below 2% and in some cases improves base-system performance. Interpretability analysis shows that learned attention weights correlate with physical branch parameters (susceptance: r=0.38 ; thermal limits: r=0.22 ), and feature importance analysis supports that the model captures established power flow relationships.
Differentiable multiphase flow model for physics-informed machine learning in reservoir pressure management
Accurate subsurface reservoir pressure control is extremely challenging due to geological heterogeneity and multiphase fluid-flow dynamics. Predicting behavior in this setting relies on high-fidelity physics-based simulations that are computationally expensive. Yet, the uncertain, heterogeneous properties that control these flows make it necessary to perform many of these expensive simulations, which is often prohibitive. To address these challenges, we introduce a physics-informed machine learning workflow that couples a fully differentiable multiphase flow simulator, which is implemented in the DPFEHM framework with a convolutional neural network (CNN). The CNN learns to predict fluid extraction rates from heterogeneous permeability fields to enforce pressure limits at critical reservoir locations. By incorporating transient multiphase flow physics into the training process, our method enables more practical and accurate predictions for realistic injection-extraction scenarios compared to previous works. To speed up training, we pretrain the model on single-phase, steady-state simulations and then finetune it on full multiphase scenarios, which dramatically reduces the computational cost. We demonstrate that high-accuracy training can be achieved with fewer than three thousand full-physics multiphase flow simulations – compared to previous estimates requiring up to ten million. This drastic reduction in the number of simulations is achieved by leveraging transfer learning from much less expensive single phase simulations.
NuGraph2 with context-aware inputs: physics-inspired improvements in semantic segmentation
Graph neural networks have recently shown strong promise for event reconstruction tasks in Liquid Argon Time Projection Chambers, yet their performance remains limited for underrepresented classes of particles, such as Michel electrons. In this work, we investigate physics-informed strategies to improve semantic segmentation within the NuGraph2 architecture. We explore three complementary approaches: (i) enriching the input representation with context-aware features derived from detector geometry and track continuity, (ii) introducing auxiliary decoders to capture class-level correlations, and (iii) incorporating energy-based regularization terms motivated by Michel electron energy distributions. Experiments on MicroBooNE public datasets show that physics-inspired feature augmentation yields the largest gains, particularly boosting Michel electron precision and recall by disentangling overlapping latent space regions. In contrast, auxiliary decoders and energy-regularization terms provided limited improvements, partly due to the hit-level nature of NuGraph2, which lacks explicit particle- or event-level representations. Our findings highlight that embedding physics context directly into node-level inputs is more effective than imposing task-specific auxiliary losses, and suggest that future hierarchical architectures such as NuGraph3, with explicit particle- and event-level reasoning, will provide a more natural setting for advanced decoders and physics-based regularization. The code for this work is publicly available on Github at https://github.com/vitorgrizzi/nugraph_phys/tree/main_phys.
Machine learning-enabled multiscale modeling of mechanical deformation of aluminum and Al-SiC nanocomposites
A machine learning-enabled multiscale framework is developed for modeling the mechanical response of both pure metal and nanoparticle-reinforced metal matrix nanocomposites (MMNCs). Using aluminum–silicon carbide (Al-SiC) as an example MMNC, atomistic simulations reveal three distinct deformation mechanisms (i.e., defect-free, dislocation-based, and interface separation) governed by the interfaces between the Al matrix and SiC nanoparticles. As compared with single crystal Al, the lattice undergoes a more abrupt failure once the dislocation network becomes extensive and void nucleation initiates, whereas in Al-SiC, nanoparticle interfaces enable a more gradual progression of damage. These mechanisms are captured through a combined classification-regression neural network surrogate model that bridges atomic-scale insights with continuum-scale finite element analysis. Machine learning-enabled multiscale modeling of pure Al accurately predicted strain localization and confirmed by in-situ scanning electron microscopic tensile testing on perforated Al specimens. This study underscores the promise of integrating physics-informed machine learning with hierarchical modeling to capture the interface dominated phenomena and guide the design of advanced MMNCs.
Development and Evaluation of a General Drag Model for Gas-Solid Flows via Deep Learning
This project presents the development and evaluation of a general drag model for gas–solid multiphase flows using deep learning techniques. A comprehensive database of more than 4,000 experimental and numerical data points for spherical and non spherical particles was compiled, incorporating geometric features such as sphericity, aspect ratio, and orientation. Several predictive approaches—including traditional em pirical correlations, machine learning, and deep neural networks—were benchmarked, with the proposed Drag Coefficient Correlation-aided Deep Neural Network (DCC DNN) demonstrating superior accuracy. To account for particle–particle interactions, additional drag data were generated using CFD-based simulations of packed and flu idized beds, leading to the development of a retrained model capable of incorporat ing volume fraction effects. Integration of the trained model with the MFiX CFD solver was achieved using FTorch, enabling drag predictions during discrete element method (DEM) simulations. Validation against experimental data for single particles and fluidized beds confirmed the model’s improved predictive ability, particularly for non-spherical geometries. While the model performed strongly under fluidized con ditions, limitations remained in unfluidized regimes, suggesting a need for expanded datasets. Overall, this study demonstrates the feasibility of combining deep learning with physics-informed CFD to improve drag modeling for gas–solid flows, with promis ing implications for scaling multiphase simulations in industrial applications.
Moltensaltpropnet
MoltenSaltPropnet is a physics-informed machine learning framework that aims to predict the thermophysical properties of molten fluoride and chloride salt mixtures, which are crucial for the design and safety of Generation IV molten salt reactors. The code processes data from the Molten-Salt Thermal Properties Database (MSTDB-TP) and the Janz compendium, converting critically evaluated correlations into fast, differentiable surrogate models for density, viscosity, thermal conductivity, and heat capacity across 448 distinct salt systems. The implementation consists of several key components: 1. Data Curation: The code parses and cleans the raw data, normalizing elemental mole fractions and extracting relevant regression coefficients for various thermophysical properties. 2. Feature Engineering: It generates fixed-length numerical descriptors that encapsulate the composition and temperature, incorporating polynomial interaction terms and dimensionality-reduction techniques to optimize model performance. 3. Coefficient Learning: Four different machine learning architectures are employed: a deep residual network (ResNet), a Kolmogorov–Arnold network (KAN), a sparsity-inducing neural network (SNN), and classical regression models. Each model learns to predict coefficients that define the temperature-dependent correlations for the thermophysical properties. 4. Property Reconstruction: The predicted coefficients are used to compute temperature-dependent property values, ensuring positivity and monotonic trends through a composite loss function that enforces physical constraints. 5. User Interface: An open-source web application enables users to filter the database, train task-specific models, and visualize the results, allowing for rapid exploration of candidate salt mixtures. MoltenSaltPropnet bridges the gap between limited experimental data and high-fidelity reactor simulations, providing a powerful tool for researchers in the field of molten salt reactors and advanced nuclear energy systems.
Ferroelectric Fractals: Switching Mechanism of Wurtzite AlN
The advent of wurtzite ferroelectrics is enabling new ferroelectric devices for computer memory that have the potential to bypass the von Neumann bottleneck due to their robust polarization and silicon compatibility. However, the atomistic switching mechanism of wurtzites is still undetermined due to the limitations of density functional theory simulation size and experimental temporal and spatial resolution. Thus, physics-informed materials engineering to reduce coercive field and breakdown in these devices has been limited. In this work, the atomistic mechanism of domain wall migration and domain growth in aluminum nitride-based wurtzites is uncovered using molecular dynamics and Monte Carlo simulations. We reveal the anomalous switching mechanism of fast 1D single columns of atoms propagating from a slow-moving 2D fractallike domain wall. We find that the critical nucleus is a single aluminum ion that breaks its bond with one nitrogen and bonds to another nitrogen; this creates a cascade that flips atoms directly only in the same column, due to the extreme locality (sharpness) of the domain walls in wurtzites. We further show how the fractallike shape of the domain wall in the 2D plane breaks assumptions in the Kolmogorov, Avrami, and Ishibashi (KAI) model and leads to the anomalously fast switching in wurtzite structured ferroelectrics.
Physics vs structure: A systematic benchmark of learning strategies for multi-zone building thermal dynamics
Recent advances in physics-informed and data-driven machine learning promise improved thermal models for advanced building control, yet there is limited quantitative evidence on when added physics structure and architectural complexity are beneficial. Here, this work presents a systematic benchmark of five representative system identification methods for modeling multi-zone building thermal dynamics: linear state-space models, multi-layer perceptrons, neural state-space models, neural ordinary differential equations, and physically-consistent neural networks. The methods are evaluated across multiple data regimes and zone coupling strategies. Using a high-fidelity multi-zone commercial building emulator, we examine short-term and long-term prediction accuracy, computational efficiency, and ease of development. Our results reveal critical trade-offs between prediction performance, model complexity, and physical consistency. We demonstrate that decoupled, nonlinear black-box models consistently outperform coupled physics-constrained architectures in both predictive accuracy and out-of-distribution robustness in majority of the test cases for the building type considered in the study. Our findings quantify the cost of complexity in building thermal modeling and provide concrete, actionable, scenario-based guidelines for selecting model classes for control-oriented applications.
Gearbox bearing crack growth prognostics and uncertainty quantification with physics-informed machine learning
This paper introduces the extreme theory of functional connections (X-TFC), a physics-informed machine learning algorithm, and tailors it to estimate the remaining useful life (RUL) of wind turbine gearbox bearings experiencing fatigue crack growth. Unlike purely data-driven methods, X-TFC embeds a physics model, based on Head's theory in this work, into its training objective. The core of X-TFC is a random-projection single-layer neural network trained via an extreme learning machine, which requires only limited damage progression data and solves for output weights with a least-squares optimization algorithm. A composite loss function balances the network's fit to observed degradation data against the residuals of the governing crack growth differential equation, ensuring the learned damage trajectory remains physically plausible. When applied to a vibration-based health-index (HI) dataset measured during the growth of a crack on the inner ring of a high-speed bearing in a wind turbine gearbox (Bechhoefer and Dubé, 2020), X-TFC achieves near-zero prediction bias. Even when trained on only the first 10 %–20 % of the damage progression data, with sufficient physics weighting its predictions remain monotonic and smooth, delivering high prognosability and trendability. To quantify the epistemic uncertainty, we employ a Monte Carlo ensemble of independently initialized X-TFC models trained on noise-perturbed data, which yields confidence intervals around each RUL estimate and captures both model-parameter and epistemic uncertainty. In addition to a vibration-based HI, we demonstrate that the proposed framework can be directly applied to a supervisory control and data acquisition (SCADA) data-based HI (Eftekhari Milani et al., 2026) measured during similar wind turbine gearbox bearing crack faults, preserving its accuracy and interpretability. This extension shows the versatility of our approach, which is applicable to bearings of multiple gearbox manufacturers, models, and ratings using only SCADA data. By integrating domain knowledge with machine learning, X-TFC offers a rapid, reliable tool for crack prognostics. Its adaptability to other bearing failure modes, such as pitch bearing ring cracks, positions X-TFC as a powerful enabler of data-driven, physics-informed asset management in the wind energy sector and beyond.
ECLEIRS: Exact conservation law embedded identification of reduced states for parameterized nonlinear conservation laws from sparse and noisy data
Multi-query applications such as parameter estimation, uncertainty quantification and design optimization for parameterized partial differential equation (PDE) systems are expensive. While reduced/latent state dynamics approaches for parameterized PDEs offer a viable alternative, these approaches rely on high-quality data and struggle with highly sparse spatiotemporal noisy measurements typically obtained from experiments. Furthermore, there is no guarantee that these models satisfy governing physical conservation laws. In this article, we propose a reduced state dynamics approach, referred to as ECLEIRS, that embeds exact conservation in the solution and flux representation by utilizing a space-time divergence-free neural network formulation. We compare ECLEIRS with other reduced state dynamics approaches, those that do not enforce any physical constraints and those with physics-informed loss functions, for three shock-propagation problems: 1-D advection, 1-D Burgers and 2-D Euler equations. In conclusion, the numerical experiments conducted in this study demonstrate that ECLEIRS provides the most accurate prediction of dynamics for unseen parameters even in the presence of highly sparse and noisy data.
An interactive machine learning platform for analyzing multi-particle coincidence data from cold target recoil ion momentum spectroscopy
We present SCULPT (Supervised Clustering and Uncovering Latent Patterns with Training), a comprehensive software platform for analyzing tabulated high-dimensional multi-particle coincidence data from Cold Target Recoil Ion Momentum Spectroscopy (COLTRIMS) experiments. The software addresses critical challenges in modern momentum spectroscopy by integrating advanced machine learning techniques with physics-informed analysis in an interactive web-based environment. SCULPT implements uniform manifold approximation and projection for non-linear dimensionality reduction to reveal correlations in high-dimensional data. We also discuss potential extensions to deep autoencoders for feature learning and genetic programming for automated discovery of physically meaningful observables. A novel adaptive confidence scoring system provides quantitative reliability assessments by evaluating user-selected clustering quality metrics with predefined weights that reflect each metric’s robustness. The platform features configurable molecular profiles for different experimental systems, interactive visualization with selection tools, and comprehensive data filtering capabilities. Utilizing a subset of SCULPT’s capabilities, we analyze photo-double-ionization data measured using the COLTRIMS method for three-body dissociation of the D 2 O molecule, revealing distinct fragmentation channels and their correlations with physics parameters. The software’s modular architecture and web-based implementation make it accessible to the broader atomic and molecular physics community, significantly reducing the time required for complex multi-dimensional analyses. This opens the door to finding and isolating rare events exhibiting non-linear correlations on the fly during experimental measurements, which can help steer exploration and improve the efficiency of experiments.