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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Hypothesis-learning-driven automated scanning probe microscopy allows physical discovery during experiments, where the hypothesis learning algorithm implemented on an operating microscope identifies the physical mechanism behind the material’s response
Aqueous organic redox flow batteries (AORFBs) have gained popularity in renewable energy storage due to their low cost, environmental friendliness and scalability. The rapid discovery of aqueous soluble organic (ASO) redox-active materials necessitates efficient machine learning surrogates for predicting battery performance. The physics-guided continual learning (PGCL) method proposed in this study can incrementally learn data from new ASO electrolytes while addressing catastrophic forgetting issues in conventional machine learning. Using a AORFB database with a thousand potential materials generated by a 780 $\text{cm}^2$ interdigitated cell model, PGCL incorporates AORFB physics to optimize the continual learning task formation and training strategies to retain previously learned battery material knowledge. Finally, the trained PGCL demonstrates its capability in assessing emerging ASO materials within the established parameter space when evaluated with the dihydroxyphenazine isomers.
This tutorial paper focuses on safe physics-informed machine learning in the context of dynamics and control, providing a comprehensive overview of how to integrate physical models and safety guarantees. As machine learning techniques enhance the modeling and control of complex dynamical systems, ensuring safety and stability remains a critical challenge, especially in safety-critical applications like autonomous vehicles, robotics, medical decision-making, and energy systems. We explore various approaches for embedding and ensuring safety constraints, including structural priors, Lyapunov and Control Barrier Functions, predictive control, projections, and robust optimization techniques. Additionally, we delve into methods for uncertainty quantification and safety verification, including reachability analysis and neural network verification tools, which help validate that control policies remain within safe operating bounds even in uncertain environments. The paper includes illustrative examples demonstrating the implementation aspects of safe learning frameworks that combine the strengths of data-driven approaches with the rigor of physical principles, offering a path toward the safe control of complex dynamical systems.
In the past decade, dramatic progress has been made in the field of machine learning. This paper explores the possibility of applying deep learning in power system state estimation. Traditionally, physics-based models are used including weighted least square (WLS) or weighted least absolute value (WLAV). These models typically consider a single snapshot of the system without capturing temporal correlations of system states. In this paper, a physics-guided deep learning (PGDL) method is proposed. Specifically, inspired by autoencoders, deep neural networks (DNNs) are used to learn the temporal correlations. The estimated system states from DNNs are then checked against physics laws by running through a set of power flow equations. Hence, the proposed PGDL is both data-driven and physics-guided. The accuracy and robustness of the proposed PGDL method are compared with traditional methods in standard IEEE cases. Simulations show promising results and the applicability is further discussed.
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.
This Git repository contains codes for the 'Graph Learning in Physical-informed Mesh-reduced Space for Real-world Dynamic Systems' paper that will be published in 2023 SIGKDD. This work uses physical-informed prior (PiP) information to learn and predict fluid dynamics in a reduced mesh space. We propose a two-stage graph-based model for fluid velocity field reconstruction and prediction. In the first stage, we learn a subgraph autoencoder to summarize the information in a mesh-reduced space using physical-informed priors. In the second stage, we learn a dynamics predictor to predict subgraph evolution. We demonstrate the effectiveness of our model on two fluid flow datasets: lid-driven cavity flow data and cylinder flow data. This code is also applicable for any other dynamic systems with corresponding data.
Learning the unknown interactions that govern a quantum system is crucial for quantum information processing, device benchmarking, and quantum sensing. The problem, known as Hamiltonian learning, is well understood under the assumption that interactions are local, but this assumption may not hold for arbitrary Hamiltonians. Previous methods all require high-order inverse polynomial dependency with precision, unable to surpass the standard quantum limit and reach the gold-standard Heisenberg-limited scaling. Whether Heisenberg-limited Hamiltonian learning is possible without prior assumptions about the interaction structures, a challenge we term ansatz-free Hamiltonian learning , remains an open question. In this work, we present a quantum algorithm to learn arbitrary sparse Hamiltonians without any structure constraints using only black-box queries of the system’s real-time evolution and minimal digital controls to attain Heisenberg-limited scaling in estimation error. Our method is also resilient to state-preparation-and-measurement errors, enhancing its practical feasibility. We numerically demonstrate our ansatz-free protocol for learning physical Hamiltonians and validating analog quantum simulations, benchmarking our performance against the state-of-the-art Heisenberg-limited learning approach. Moreover, we establish a fundamental trade-off between total evolution time and quantum control on learning arbitrary interactions, revealing the intrinsic interplay between controllability and total evolution-time complexity for any learning algorithm. These results pave the way for further exploration into Heisenberg-limited Hamiltonian learning in complex quantum systems under minimal assumptions, potentially enabling new benchmarking and verification protocols.
Recent applications of machine learning, in particular deep learning, motivate the need to address the generalizability of the statistical inference approaches in physical sciences. In this Letter, we introduce a modular physics guided machine learning framework to improve the accuracy of such data-driven predictive engines. The chief idea in our approach is to augment the knowledge of the simplified theories with the underlying learning process. To emphasize their physical importance, our architecture consists of adding certain features at intermediate layers rather than in the input layer. To demonstrate our approach, we select a canonical airfoil aerodynamic problem with the enhancement of the potential flow theory. We include the features obtained by a panel method that can be computed efficiently for an unseen configuration in our training procedure. By addressing the generalizability concerns, our results suggest that the proposed feature enhancement approach can be effectively used in many scientific machine learning applications, especially for the systems where we can use a theoretical, empirical, or simplified model to guide the learning module.
We would like to disclose a code based on Python/Pytorch, in which we implement the data-driven physics-informed machine learning of Lagrangian large eddy simulation that is described in the manuscript "Lagrangian Large Eddy Simulations via Physics-Informed Machine Learning ". High-Reynolds number Homogeneous Isotropic Turbulence is fully described within the Navier-Stokes (NS) equations, which are notoriously difficult to solve numerically. Engineers, interested primarily in describing turbulence at a reduced range of resolved scales, have designed heuristics, known as Large Eddy Simulation (LES). LES is described in terms of the temporally evolving Eulerian velocity field defined over a spatial grid with the mean-spacing correspondent to the resolved scale. This classic Eulerian LES depends on assumptions about the effects of sub-grid scales on the resolved scales. Here, we take an alternative approach and design novel LES heuristics stated in terms of Lagrangian particles moving with the flow. Our \emph{Lagrangian LES}, thus L-LES, is described by equations generalizing the weakly compressible Smoothed Particle Hydrodynamics formulation with extended parametric and functional freedom, which is then resolved via Machine Learning training on Lagrangian data from Direct Numerical Simulations of the NS equations. The L-LES model includes physics-informed parameterization and functional form, by combining physics-based parameters and physics-inspired Neural Networks to describe the evolution of turbulence within the resolved range of scales. The sub-grid scale contributions are modeled separately with physical constraints to account for the effects from un-resolved scales. We build the resulting model under the Differentiable Programming framework to facilitate efficient training. We experiment with loss functions of different types, including physics-informed ones accounting for statistics of Lagrangian particles. We show that our Lagrangian LES model is capable of reproducing Eulerian and unique Lagrangian turbulence structures and statistics over a range of turbulent Mach numbers.
Transfer learning refers to the use of knowledge gained while solving a machine learning task and applying it to the solution of a closely related problem. Such an approach has enabled scientific breakthroughs in computer vision and natural language processing where the weights learned in state-of-the-art models can be used to initialize models for other tasks which dramatically improve their performance and save computational time. Here we demonstrate an unsupervised learning approach augmented with basic physical principles that achieves fully transferrable learning for problems in statistical physics across different physical regimes. By coupling a sequence model based on a recurrent neural network to an extensive deep neural network, we are able to learn the equilibrium probability distributions and inter-particle interaction models of classical statistical mechanical systems. Our approach, distribution-consistent learning, DCL, is a general strategy that works for a variety of canonical statistical mechanical models (Ising and Potts) as well as disordered interaction potentials. Using data collected from a single set of observation conditions, DCL successfully extrapolates across all temperatures, thermodynamic phases, and can be applied to different length-scales. This constitutes a fully transferrable physics-based learning in a generalizable approach.
The Advanced Test Reactor (ATR) at INL measures reactor power through various methods, two of them being thermal and Nitrogen-16 (N-16) activity. Water power calculator (WPC) is a thermal power system that measures flow and temperature to determine thermal quadrant powers. The N-16 system utilizes a beta detector that outputs Nitrogen activation levels to calculate lobe power through an algorithm called Lobe Power Calculation and Indication system (LPCIS). The LPCIS utilizes the N-16 system and the WPC system to determine reactor core power levels. The WPC provides accurate calculations of quadrant and total reactor thermal power. With the use of WPC measurements, thermal-to-N-16 (T2N) power ratios are produced to determine if the two indication systems agree on core power. Relative magnitude equations are used to utilize N-16 coefficients and multipliers to improve the indications of the LPCIS. These correct indications are crucial for maintaining safety limits because operators rely on this information for decision making. Currently, the LPCIS system uses linear equations and matrices to calculate lobe power through multipliers and coefficients. Advancements in technology and system upgrades have increased the accuracy of power readings by making the system more dynamic. The new proposed coefficient and multiplier method implements a cycle specific and physics-based model intended for changing coefficients during operation. This calibration experiment focused on power splitting, outer shim and neck shim, as well as fuel burning into the reactor digital acquisition system (RDAS) weighting factors. Results demonstrated that the physics learning method yields a smaller error margin inside of the desired power range for the data set 166-A. Continuing to improve the physics-based model will help improve the power accuracy of the LPCIS system.
Abstract We develop a physics‐informed machine learning approach for large‐scale data assimilation and parameter estimation and apply it for estimating transmissivity and hydraulic head in the two‐dimensional steady‐state subsurface flow model of the Hanford Site given synthetic measurements of said variables. In our approach, we extend the physics‐informed conditional Karhunen‐Loéve expansion (PICKLE) method to modeling subsurface flow with unknown flux (Neumann) and varying head (time‐dependent Dirichlet) boundary conditions. We demonstrate that the PICKLE method is comparable in accuracy with the standard maximum a posteriori (MAP) method, but is significantly faster than MAP for large‐scale problems. Both methods use a mesh to discretize the computational domain. In MAP, the parameters and states are discretized on the mesh; therefore, the size of the MAP parameter estimation problem directly depends on the mesh size. In PICKLE, the mesh is used to evaluate the residuals of the governing equation, while the parameters and states are approximated by the truncated conditional Karhunen‐Loéve expansions with the number of parameters controlled by the smoothness of the parameter and state fields, and not by the mesh size. For a considered example, we demonstrate that the computational cost of PICKLE increases near linearly (as N 1.15 ) with the number of grid nodes N , while that of MAP increases much faster (as N 3.28 ). We also show that once trained for one set of Dirichlet boundary conditions (i.e., one river stage), the PICKLE method provides accurate estimates of the hydraulic head for any value of the Dirichlet boundary conditions (i.e., for any river stage).
A combined machine learning–physics–based approach is explored for molecular and materials engineering. Specifically, collective variables, akin to those used in enhanced sampled simulations, are constructed using a machine learning model trained on data gathered from a single system. Through the constructed collective variables, it becomes possible to identify critical molecular interactions in the considered system, the modulation of which enables a systematic tailoring of the system’s free energy landscape. To explore the efficacy of the proposed approach, we use it to engineer allosteric regulation and uniaxial strain fluctuations in a complex disordered elastic network. Its successful application in these two cases provides insights regarding how functionality is governed in systems characterized by extensive connectivity and points to its potential for design of complex molecular systems.
This implementation of a Physics Guided Neural Network (PHYGNN) augments a traditional neural network loss function with a generic term that can be used to guide the neural network to learn physical or theoretical constraints.
Reaction rates at spatially heterogeneous, unstable interfaces are notoriously difficult to quantify, yet are essential in engineering many chemical systems, such as batteries and electrocatalysts. Experimental characterizations of such materials by operando microscopy produce rich image datasets, but data-driven methods to learn physics from these images are still lacking because of the complex coupling of reaction kinetics, surface chemistry and phase separation. Here we show that heterogeneous reaction kinetics can be learned from in situ scanning transmission X-ray microscopy (STXM) images of carbon-coated lithium iron phosphate (LFP) nanoparticles. Combining a large dataset of STXM images with a thermodynamically consistent electrochemical phase-field model, partial differential equation (PDE)-constrained optimization and uncertainty quantification, we extract the free-energy landscape and reaction kinetics and verify their consistency with theoretical models. We also simultaneously learn the spatial heterogeneity of the reaction rate, which closely matches the carbon-coating thickness profiles obtained through Auger electron microscopy (AEM). Across 180,000 image pixels, the mean discrepancy with the learned model is remarkably small (<7%) and comparable with experimental noise. Our results open the possibility of learning nonequilibrium material properties beyond the reach of traditional experimental methods and offer a new non-destructive technique for characterizing and optimizing heterogeneous reactive surfaces.
Reaction rates at spatially heterogeneous, unstable interfaces are notoriously difficult to quantify, yet are essential in engineering many chemical systems, such as batteries 1 and electrocatalysts 2. Experimental characterizations of such materials by operando microscopy produce rich image datasets 3–6, but data-driven methods to learn physics from these images are still lacking because of the complex coupling of reaction kinetics, surface chemistry and phase separation 7. Here we show that heterogeneous reaction kinetics can be learned from in situ scanning transmission X-ray microscopy (STXM) images of carbon-coated lithium iron phosphate (LFP) nanoparticles. Combining a large dataset of STXM images with a thermodynamically consistent electrochemical phase-field model, partial differential equation (PDE)-constrained optimization and uncertainty quantification, we extract the free-energy landscape and reaction kinetics and verify their consistency with theoretical models. We also simultaneously learn the spatial heterogeneity of the reaction rate, which closely matches the carbon-coating thickness profiles obtained through Auger electron microscopy (AEM). Across 180,000 image pixels, the mean discrepancy with the learned model is remarkably small (<7%) and comparable with experimental noise. Our results open the possibility of learning nonequilibrium material properties beyond the reach of traditional experimental methods and offer a new non-destructive technique for characterizing and optimizing heterogeneous reactive surfaces.
In this work, we evaluate the feasibility of using physics-informed machine learning (PIML) for underground energy-related pressure management. To this end, we develop a PIML framework to manage underground reservoir pressures by training neural networks to determine fluid extraction rates for dedicated extraction wells during fluid injection operations given a range of reservoir conditions (e.g., transmissivity and storativity). We implement an automatically-differentiable analytical physics model of fluid flow in porous media within the PIML framework as a proxy for more complicated models. This allows us to execute a sufficient number of training scenarios to fully evaluate the feasibility of using PIML to support pressure management activities. We quantify the number of physics-model parameters required for automatic differentiation to become more efficient than finite-difference gradient calculations. We use a simple scenario with a single injector, extractor, and critical location for our feasibility analysis. We evaluate the effect of the size of the training dataset (i.e., the number of reservoir condition samples) on the accuracy and efficiency of the PIML framework. For an equivalent number of model evaluations, the larger training dataset took less time to train and produced a neural network that was able to more accurately manage reservoir pressures. We also evaluate the effect of the training dataset batch size (i.e., number of reservoir condition samples used to update the neural network coefficients during training; i.e., how the training dataset is partitioned). While training ran faster with larger batch sizes, they produced neural networks that managed pressures less accurately. We demonstrate the approach on a more complex scenario involving 10 injectors, 10 extractors, and 4 critical locations (a relatively high well density of 20 wells/km2). We provide the number of forward and adjoint model evaluations required in each case as an indication of the feasibility of using PIML for pressure management when more complicated physics models with longer execution times are used.
The Advanced Test Reactor (ATR) at INL measures reactor power through two methods, thermal and Nitrogen-16 (N-16) activity. Water power calculator (WPC) is a thermal power system that measures flow and temperature to determine the thermal quadrant powers. The N-16 system utilizes a beta chamber detector that outputs reactivity levels to calculate lobe power through an algorithm called lobe power calculation and indication system (LPCIS). The LPCIS utilizes the N-16 system and the WPC system to determine reactor core power levels. The WPC provides accurate calculations of quadrant and total reactor thermal power. With the use of WPC measurements, thermal-to-N-16 (T2N) power ratios are produced to determine if the two indication systems agree on core power. Relative magnitude equations are used to utilize N-16 coefficients and multipliers to improve the indications of the LPCIS. This is crucial for maintaining safety limits. Currently, the LPCIS system uses linear equations and matrices to calculate lobe power through multipliers and coefficients. Advancements in technology and system upgrades have assisted system engineers at INL with the objective to reach a more dynamic system. In return the system demonstrates an increase in the accuracy of power reading while maintaining safety margins. The new proposed coefficient and multiple method implements a cycle specific, and a physics-based model intended for changing coefficients during operation. This calibration experiment focuses on power splitting, outer shim and neck shim, as well as fuel burning into the RDAS weighting factors. Results show that the Physics learning method yields a smaller error margin inside of the desired power range for the data set 166-A. This proved true for both constrained and unconstrained testing. This is most likely due to the physics data fitting approach that resulted in favorable coefficients and multipliers for 166-A. Continuing to improve the physics-based model will help improve the power accuracy of the LPCIS system.