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At least 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Quantum-Inspired Bayesian Sampling for Uncertainty Quantification and Machine Learning (Final Technical Report)

With increasing simulation and measurement data, machine learning and artificial intelligence have been widely used in computational decision-making of complex engineering systems. The resulting tools, such as uncertainty quantification solvers, reinforcement learning, and physics-informed machine learning, have achieved great success in critical DOE tasks such as material discovery and design, energy system modeling and control, and numerical weather and climate prediction. A core topic in scientific machine learning and artificial intelligence is Bayesian inference: given an observed data set, people want to estimate the posterior distribution of a (possibly large) number of hidden parameters. Due to the flexibility and weak assumptions, Bayesian sampling has been the mainstream Bayesian inference solvers despite the rapid progress of approximate Bayesian inference. Classical Bayesian sampling methods such as Markov-chain Monte Carlo suffer from a low-acceptance rate due to the random walk nature, therefore state-of-the-art techniques use Hamiltonian Monte Carlo and its variants to efficiently draw posterior samples in a high dimension. The key idea of Hamiltonian Monte Carlo and its variants is to simulate the Hamiltonian dynamics of a classical particle with a fixed mass, and their performance significantly degrades when the posterior distribution is highly spiky or has multiple modes. Leveraging the idea of quantum physics, this project has investigated new theory, algorithms and applications of Bayesian inference (especially Bayesian sampling). The main results include: (1) novel quantum-inspired Bayesian sampling methods that can lead to better accuracy for challenging multi-modal or spiky distributions, (2) more scalable machine learning framework leveraging tensor-compressed Bayesian inference, and (3) Bayesian and sampling approaches for verifying the robustness of continuous and binary neural networks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

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.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Comparison of source-location algorithms for atmospheric samplers

Numerous algorithms have been developed to determine the source characteristics for an atmospheric release, e.g., (Bieringer et al., 2017). This study compares three models that have been applied to the data collected by the International Monitoring System operated by the Comprehensive Nuclear-Test-Ban Treaty Preparatory Commission to estimate source event parameters. Each model uses a different approach to estimate the parameters. A deterministic model uses a possible source region (PSR) approach (Ringbom et al., 2014) that is based on the correlation between predicted and measured sample values. An unnamed model developed at Pacific Northwest National Laboratory (herein called BAYEST) uses a Bayesian formulation (Eslinger et al., 2019; Eslinger et al., 2020; Eslinger and Schrom, 2016). The FREAR model uses a different Bayesian formulation (De Meutter and Hoffman, 2020; De Meutter et al., 2021; Pieter De Meutter, 2021). The performance of the three source-location models is evaluated with 100 synthetic release cases for the single xenon isotope, 133 Xe. The release cases resulted in detections in a fictitious network with 120 noble gas samplers. All three source-location models use the same sampling data. The two Bayesian models yield more accurate location estimates than the deterministic PSR model, with FREAR having slightly better location performance than BAYEST. Samplers with collection periods of 3, 6, 8, 12, and 24-h were used. Results from BAYEST show that location accuracy improves with each reduction in sample collection length. The BAYEST model is slightly better for estimating the start time of the release. The PSR model has about the same spread in start times as the FREAR model, but the PSR results have a better average start time. The Bayesian source-location algorithms give more accurate results than the PSR approach, and provide release magnitude estimates, while the base PSR model does not estimate the release magnitude. This investigation demonstrates that a reasonably dense sampling grid will sometimes yield poor location and time estimates regardless of the model. The poor estimates generally coincide with cases where there is a much larger distance between the release point and the first detecting sampler than the average sampler spacing.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
DOE OSTI2024

Rapid Inverse Parameter Inference Using Physics-Informed Neural Network

As Li-ion batteries become more essential in today's economy, tools need to be developed to accurately and rapidly diagnose a battery's internal state-of-health. Using a Li-ion battery's (high-rate) voltage response, it is proposed to determine a battery's internal state through Bayesian calibration. However, Bayesian calibration is notoriously slow and requires thousands of model runs. To accelerate parameter inference using Bayesian calibration, a surrogate model is developed to replace the underlying physics-based Li-ion model. Developing a surrogate model for rapid Bayesian calibration analysis is discussed for both the single particle model (SPM) and the pseudo two-dimensional (P2D) model. Surrogate models are constructed using physics-informed neural networks (PINNs) that encode the influence of internal properties on observed voltage responses. In practice, a neural network can be trained by: 1) using simulation results of the physics-based model (i.e., a data-loss approach); 2) using the residuals of the governing equations themselves (i.e., a physics-loss approach); or 3) using a combination of simulation results and governing equation residuals. In the present work, PINNs are developed using a variety of training losses and neural network architectures. In this analysis, it is shown that a PINN surrogate model can be reliably trained with only physics-informed loss. However, using a coupled data-informed and physics-loss approach produced the most accurate PINNs.

Bayesian calibration↗
DOE OSTI2025

Multi-head physics-informed neural networks for learning functional priors and uncertainty quantification

In numerous applications, the integration of prior knowledge and historical information is essential, particularly for tasks requiring the solution of ordinary or partial differential equations (ODEs/PDEs) in data-sparse or noisy environments. For instance, achieving accurate solutions to time-dependent PDEs with limited initial condition measurements necessitates an effective strategy for embedding prior knowledge. Hard-parameter sharing architectures in neural networks (NNs) have demonstrated success in both traditional and scientific machine learning domains, facilitating the learning of informative representations. Here, in this study, we introduce a novel, yet efficient, method to enhance physics-informed neural networks (PINNs) by incorporating a multi-head structure that enables the learning of functional priors from both empirical data and governing physical laws. This prior information can then be used to address data sparsity and high-level noise in solving ODE/PDE problems with uncertainty quantification (UQ). The approach, termed Multi-Head PINN (MH-PINN), consists of a shared body NN and multiple head NNs, each corresponding to an individual PINN instance. Our framework for functional prior learning is carried out in two stages: (1) training the MH-PINNs to develop a shared body NN alongside multiple head NNs, and (2) employing these trained head NNs to estimate a prior distribution through a normalizing flow-based density estimator. The learned functional prior can then be applied as a regularization mechanism in deterministic contexts or as an informative prior within a Bayesian inference framework, aiding in the resolution of subsequent ODE/PDE tasks. We evaluate the efficacy of MH-PINNs across five benchmark problems, including a high-dimensional parametric PDE, all characterized by data sparsity or substantial noise levels. Our findings reveal that MH-PINNs deliver accurate solutions and robust UQ, demonstrating adaptability across a range of complex and challenging scenarios.

Bayesian inference↗
DOE OSTI2023

Bayesian averaging for ground state masses of atomic nuclei in a Machine Learning approach

We present global predictions of the ground state mass of atomic nuclei based on a novel Machine Learning algorithm. We combine precision nuclear experimental measurements together with theoretical predictions of unmeasured nuclei. This hybrid data set is used to train a probabilistic neural network. In addition to training on this data, a physics-based loss function is employed to help refine the solutions. The resultant Bayesian averaged predictions have excellent performance compared to the testing set and come with well-quantified uncertainties which are critical for contemporary scientific applications. We assess extrapolations of the model’s predictions and estimate the growth of uncertainties in the region far from measurements.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2026

Neural posterior unfolding

Differential cross section measurements are the currency of scientific exchange in particle and nuclear physics. A key challenge for these analyses is the correction for detector distortions, known as deconvolution or unfolding. Binned unfolding of cross section measurements traditionally rely on the regularized inversion of the response matrix that represents the detector response, mapping pre-detector (`particle level') observables to post-detector (`detector level') observables. In this paper we introduce Neural Posterior Unfolding, a modern, Bayesian approach that leverages normalizing flows for unfolding. By using normalizing flows for neural posterior estimation, NPU offers several key advantages including implicit regularization through the neural network architecture, fast amortized inference that eliminates the need for repeated retraining, and direct access to the full uncertainty in the unfolded result. In addition to introducing NPU, we implement a classical Bayesian unfolding method called Fully Bayesian Unfolding (FBU) in modern Python so it can also be studied. These tools are validated on simple Gaussian examples and then tested on simulated jet substructure examples from the Large Hadron Collider (LHC). We find that the Bayesian methods are effective and worth additional development to be analysis ready for cross section measurements at the LHC and beyond.

Analysis and statistical methods↗
DOE OSTI2023

Coexistent Quantum Channel Characterization Using Spectrally Resolved Bayesian Quantum Process Tomography

The coexistence of quantum and classical signals over the same optical fiber with minimal degradation of the transmitted quantum information is critical for operating large-scale quantum networks over the existing communications infrastructure. In this work, we systematically characterize the quantum channel that results from simultaneously distributing approximate single-photon polarization-encoded qubits and classical light of varying intensities through fiber-optic channels of up to 15 km. Using spectrally resolved quantum process tomography with a Bayesian reconstruction method that we develop, we estimate the full quantum channel from experimental photon counting data, both with and without classical background. Furthermore, although we find the exact channel description to be a weak function of the pump polarization, we nevertheless show that the coexistent fiber-based quantum channel has high process fidelity with an ideal depolarizing channel when the noise is dominated by Raman scattering. These results provide a basis for the future development of quantum repeater designs and quantum error-correcting codes for real-world channels and inform models used in the analysis and simulation of quantum networks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A Bayesian Deep Learning Approach to Near-Term Climate Prediction

Since model bias and associated initialization shock are serious shortcomings that reduce prediction skills in state-of-the-art decadal climate prediction efforts, we pursue a complementary machine-learning-based approach to climate prediction. The example problem setting we consider consists of predicting natural variability of the North Atlantic sea surface temperature on the interannual timescale in the pre-industrial control simulation of the Community Earth System Model. While previous works have considered the use of recurrent networks such as convolutional LSTMs and reservoir computing networks in this and other similar problem settings, we currently focus on the use of feedforward convolutional networks. In particular, we find that a feedforward convolutional network with a Densenet architecture is able to outperform a convolutional LSTM in terms of predictive skill. Next, we go on to consider a probabilistic formulation of the same network based on Stein variational gradient descent and find that in addition to providing useful measures of predictive uncertainty, the probabilistic (Bayesian) version improves on its deterministic counterpart in terms of predictive skill. Finally, we characterize the reliability of the ensemble of machine learning models obtained in the probabilistic setting by using analysis tools developed in the context of ensemble numerical weather prediction.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

nautilus : boosting Bayesian importance nested sampling with deep learning

ABSTRACT We introduce a novel approach to boost the efficiency of the importance nested sampling (INS) technique for Bayesian posterior and evidence estimation using deep learning. Unlike rejection-based sampling methods such as vanilla nested sampling (NS) or Markov chain Monte Carlo (MCMC) algorithms, importance sampling techniques can use all likelihood evaluations for posterior and evidence estimation. However, for efficient importance sampling, one needs proposal distributions that closely mimic the posterior distributions. We show how to combine INS with deep learning via neural network regression to accomplish this task. We also introduce nautilus, a reference open-source python implementation of this technique for Bayesian posterior and evidence estimation. We compare nautilus against popular NS and MCMC packages, including emcee, dynesty, ultranest, and pocomc, on a variety of challenging synthetic problems and real-world applications in exoplanet detection, galaxy SED fitting and cosmology. In all applications, the sampling efficiency of nautilus is substantially higher than that of all other samplers, often by more than an order of magnitude. Simultaneously, nautilus delivers highly accurate results and needs fewer likelihood evaluations than all other samplers tested. We also show that nautilus has good scaling with the dimensionality of the likelihood and is easily parallelizable to many CPUs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Quantified limits of the nuclear landscape

The chart of the nuclides is limited by particle drip lines beyond which nuclear stability to proton or neutron emission is lost. Predicting the range of particle-bound isotopes poses an appreciable challenge for nuclear theory as it involves extreme extrapolations of nuclear masses well beyond the regions where experimental information is available. Still, quantified extrapolations are crucial for a wide variety of applications, including the modeling of stellar nucleosynthesis. We use microscopic nuclear global mass models, current mass data, and Bayesian methodology to provide quantified predictions of proton and neutron separation energies as well as Bayesian probabilities of existence throughout the nuclear landscape all the way to the particle drip lines. Here, we apply nuclear density functional theory with several energy density functionals. We also consider two global mass models often used in astrophysical nucleosynthesis simulations. To account for uncertainties, Bayesian Gaussian processes are trained on the separation-energy residuals for each individual model, and the resulting predictions are combined via Bayesian model averaging. This framework allows to account for systematic and statistical uncertainties and propagate them to extrapolative predictions. We establish and characterize the drip-line regions where the probability that the nucleus is particle- bound decreases from 1 to 0. In these regions, we provide quantified predictions for one- and two-nucleon separation energies. According to our Bayesian model averaging analysis, 7759 nuclei with Z ≤ 119 have a probability of existence ≥ 0.5. The extrapolation results obtained in this study will be put through stringent tests when new experimental information on existence and masses of exotic nuclei becomes available. In this respect, the quantified landscape of nuclear existence obtained in this study should be viewed as a dynamical prediction that will be fine-tuned when new experimental information and improved global mass models become available.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Automated Adversary-in-the-Loop Cyber-Physical Defense Planning

Security of cyber-physical systems (CPS) continues to pose new challenges due to the tight integration and operational complexity of the cyber and physical components. To address these challenges, this article presents a domain-aware, optimization-based approach to determine an effective defense strategy for CPS in an automated fashion—by emulating a strategic adversary in the loop that exploits system vulnerabilities, interconnection of the CPS, and the dynamics of the physical components. Our approach builds on an adversarial decision-making model based on a Markov Decision Process (MDP) that determines the optimal cyber (discrete) and physical (continuous) attack actions over a CPS attack graph. The defense planning problem is modeled as a non-zero-sum game between the adversary and defender. We use a model-free reinforcement learning method to solve the adversary’s problem as a function of the defense strategy. We then employ Bayesian optimization (BO) to find an approximate best-response for the defender to harden the network against the resulting adversary policy. This process is iterated multiple times to improve the strategy for both players. We demonstrate the effectiveness of our approach on a ransomware-inspired graph with a smart building system as the physical process. Numerical studies show that our method converges to a Nash equilibrium for various defender-specific costs of network hardening.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Streamflow simulation in data-scarce basins using Bayesian and physics-informed machine learning models

Hydrologic predictions at rural watersheds are important but also challenging due to data shortage. Long short-term memory (LSTM) networks are a promising machine learning approach and have demonstrated good performance in streamflow predictions. However, due to its data-hungry nature, most LSTM applications focus on well-monitored catchments with abundant and high-quality observations. In this work, we investigate predictive capabilities of LSTM in poorly monitored watersheds with short observation records. To address three main challenges of LSTM applications in data-scarce locations, i.e., overfitting, uncertainty quantification (UQ), and out-of-distribution prediction, we evaluate different regularization techniques to prevent overfitting, apply a Bayesian LSTM for UQ, and introduce a physics-informed hybrid LSTM to enhance out-of-distribution prediction. Through case studies in two diverse sets of catchments with and without snow influence, we demonstrate that 1) when hydrologic variability in the prediction period is similar to the calibration period, LSTM models can reasonably predict daily streamflow with Nash–Sutcliffe efficiency above 0.8, even with only 2 years of calibration data; 2) when the hydrologic variability in the prediction and calibration periods is dramatically different, LSTM alone does not predict well, but the hybrid model can improve the out-of-distribution prediction with acceptable generalization accuracy; 3) L2 norm penalty and dropout can mitigate overfitting, and Bayesian and hybrid LSTM have no overfitting; and 4) Bayesian LSTM provides useful uncertainty information to improve prediction understanding and credibility. In conclusion, these insights have vital implications for streamflow simulation in watersheds where data quality and availability are a critical issue.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Empirical radius formulas for canonical neutron stars from bidirectionally selecting features of equations of state in extended Bayesian analyses of observational data

Significant advancement in Bayesian inference of nuclear equation of state (EOS) from gravitational wave and x-ray observations of neutron stars (NSs) has been made by the nuclear astrophysics community especially since GW170817. By extending the traditional Bayesian analysis which normally ends at presenting the marginalized posterior probability distribution functions (PDFs) of individual EOS parameters and their correlations (or sometimes only the Pearson correlation coefficients which are only reliably useful when the variables are linearly correlated while they are actually often not), we search for a data-driven and robust empirical formula for the radius 𝑅 1.4 of canonical NSs in terms of the characteristic EOS parameters (features). We also identify the single most important but currently poorly known EOS parameter for determining the 𝑅 1.4 . Using three regression-model-building methodologies: bidirectional stepwise feature selection, least absolute shrinkage selection operator (LASSO) regression, and neural network regression on a large set of posterior EOSs and the corresponding 𝑅 1.4 values inferred from earlier comprehensive Bayesian analyses of NS observational data, we systematically and rigorously develop the most probable 𝑅 1.4 formulas with varying statistical accuracy and technical complexity. Here, the most important EOS parameters for determining 𝑅 1.4 are found consistently in each of the feature selection processes to be (in order of decreasing importance): curvature 𝐾 sym , slope 𝐿, skewness 𝐽 sym of nuclear symmetry energy, skewness 𝐽 0 , incompressibility 𝐾 0 of symmetric nuclear matter, and the magnitude 𝐸 sym ⁡(𝜌 0 ) of symmetry energy at the saturation density 𝜌 0 of nuclear matter.

Bayesian methods↗
DOE OSTI2024

PINN surrogate of Li-ion battery models for parameter inference, Part II: Regularization and application of the pseudo-2D model

Bayesian parameter inference is useful to improve Li-ion battery diagnostics and can help formulate battery aging models. However, it is computationally intensive and cannot be easily repeated for multiple cycles, multiple operating conditions, or multiple replicate cells. To reduce the computational cost of Bayesian calibration, numerical solvers for physics-based models can be replaced with faster surrogates. A physics-informed neural network (PINN) is developed as a surrogate for the pseudo-2D (P2D) battery model calibration. For the P2D surrogate, additional training regularization was needed as compared to the PINN single-particle model (SPM) developed in Part I. Both the PINN SPM and P2D surrogate models are exercised for parameter inference and compared to data obtained from a direct numerical solution of the governing equations. A parameter inference study highlights the ability to use these PINNs to calibrate scaling parameters for the cathode Li diffusion and the anode exchange current density. By realizing computational speed-ups of ~2250x for the P2D model, as compared to using standard integrating methods, the PINN surrogates enable rapid state-of-health diagnostics. Finally, in the low-data availability scenario, the testing error was estimated to ~2 mV for the SPM surrogate and ~10 mV for the P2D surrogate which could be mitigated with additional data.

25 ENERGY STORAGE↗
DOE OSTI2026

Active operator learning with predictive uncertainty quantification for partial differential equations

With the increased prevalence of neural operators being used to provide rapid solutions to partial differential equations (PDEs), understanding the accuracy of model predictions and the associated error levels is necessary for deploying reliable surrogate models in scientific applications. Existing uncertainty quantification (UQ) frameworks employ ensembles or Bayesian methods, which can incur substantial computational costs during both training and inference. Here, we propose a lightweight predictive UQ method tailored for Deep operator networks (DeepONets) that also generalizes to other operator networks. Numerical experiments on linear and nonlinear PDEs demonstrate that the framework’s uncertainty estimates are unbiased and provide accurate out-of-distribution uncertainty predictions with a sufficiently large training dataset. Our framework provides fast inference and uncertainty estimates that can efficiently drive outer-loop analyses that would be prohibitively expensive with conventional solvers. We demonstrate how predictive uncertainties can be used in the context of Bayesian optimization and active learning problems to yield improvements in accuracy and data-efficiency for outer-loop optimization procedures. In the active learning setup, we extend the framework to Fourier Neural Operators (FNO) and describe a generalized method for other operator networks. To enable real-time deployment, we introduce an inference strategy based on precomputed trunk outputs and a sparse placement matrix, reducing evaluation time by more than a factor of five. Our method provides a practical route to uncertainty-aware operator learning in time-sensitive settings.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Bayesian homodyne and heterodyne tomography

Continuous-variable (CV) photonic states are of increasing interest in quantum information science, bolstered by features such as deterministic resource state generation and error correction via bosonic codes. Data-efficient characterization methods will prove critical in the fine-tuning and maturation of such CV quantum technology. Although Bayesian inference offers appealing properties—including uncertainty quantification and optimality in mean-squared error—Bayesian methods have yet to be demonstrated for the tomography of arbitrary CV states. Here we introduce a complete Bayesian quantum state tomography workflow capable of inferring generic CV states measured by homodyne or heterodyne detection, with no assumption of Gaussianity. As examples, we demonstrate our approach on experimental coherent, thermal, and cat state data, obtaining excellent agreement between our Bayesian estimates and theoretical predictions. Our approach lays the groundwork for Bayesian estimation of highly complex CV quantum states in emerging quantum photonic platforms, such as quantum communications networks and sensors.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Lithium-Ion Battery Diagnostics Using Electrochemical Impedance via Machine-Learning

Diagnosing battery states such as health, state-of-charge, or temperature is crucial for ensuring the safety and reliability of electrochemical energy storage systems. While some states, such as temperature, may be measured using cheap sensors, accurate diagnosis of battery health metrics usually requires time-consuming performance measurements, making them infeasible for use in real-world operation. These health metrics can be measured during lab-testing and then estimated on-line using predictive life models or via state observer algorithms such as Kalman filters, but these predictive methods should be supplemented by actual measurement of battery health whenever possible to ensure reliability. Rapid measurement of battery health may be done by various types of fast diagnostic techniques such as electrochemical impedance spectroscopy (EIS), which can be performed in only a few minutes and require only a fraction of the energy and power needed for a full charge and discharge measurement. But there is a substantial challenge for estimating battery health using EIS data, as EIS is sensitive to cell temperature, state-of-charge, current, and resting time in addition to health. Thus, utilizing EIS data to predict battery capacity requires correcting for all these additional variables, a task that is extremely difficult to handle analytically. This talk utilizes machine-learning methods to estimate the effectiveness of battery capacity prediction from EIS data, leveraging a data set of hundreds of EIS measurements recorded at varying temperature and state-of-charge throughout a 500-day aging study of 32 commercial, large-format NMC-Graphite lithium-ion batteries. Using EIS as input to machine-learning models is complicated by the nonlinear response of impedance to battery health, temperature, and state-of-charge, as well as the collinearity between the impedance response at neighboring frequencies, which can easily lead to overfit models. To train robust models, features from EIS data need to be extracted from the data or some subset of critical frequencies selected. Many approaches for extracting and selecting features from EIS data from electrochemical analysis and machine-learning fields were identified for analysis: using the entire raw spectra; selection of one, two, or many frequencies from the entire spectra; selecting interesting points from the EIS measurement using domain knowledge; fitting EIS with an equivalent-circuit model; calculating statistics on the raw impedance values; and reducing the dimensionality of the data using unsupervised linear (principal component analysis) and non-linear (uniform manifold approximation and projection) methods. These approaches were rigorously compared using a machine-learning pipeline approach, training linear, Gaussian process, and random forest regression models and quantifying performance using cross-validation as well as a held-out test set. An artificial neural network model trained on the raw spectra was also tested. Promising pipelines were fine-tuned via Bayesian hyperparameter optimization using cross-validation loss and training with class-specific weights to counter data set imbalance. The most reliable method for utilizing impedance in this work was the selection of two optimal frequencies through an exhaustive search, resulting in about 2% mean absolute error on test data for both Gaussian process and random forest model architectures. Interrogation of a variety of models reveals critical frequencies of 100 Hz and 103 Hz for this data set, though the optimal set of frequencies is not necessarily intuitive, i.e., the best performing models are not simply those that use impedance at frequencies that have the highest correlation to the relative discharge capacity. The best performing model is an ensemble model, which is able to predict battery capacity with 1.9% mean absolute error for unseen cells using impedance recorded at a variety of temperatures and states-of-charge.

battery↗