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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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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Joint Modeling of Quasar Variability and Accretion Disk Reprocessing Using Latent Stochastic Differential Equations

Quasars are bright active galactic nuclei powered by the accretion of matter around supermassive black holes at the center of galaxies. Their stochastic brightness variability depends on the physical properties of the accretion disk and black hole. The upcoming Rubin Observatory Legacy Survey of Space and Time (LSST) is expected to observe tens of millions of quasars, so there is a need for efficient techniques like machine learning that can handle the large volume of data. Quasar variability is believed to be driven by an X-ray corona, which is reprocessed by the accretion disk and emitted as UV/optical variability. We are the first to introduce an auto-differentiable simulation of the accretion disk and reprocessing. We use the simulation as a direct component of our neural network to jointly model the driving variability and reprocessing, trained with supervised learning on simulated LSST-like 10 yr quasar light curves. We encode the light curves using a transformer encoder, and the driving variability is reconstructed using latent stochastic differential equations, a physically motivated generative deep learning method that can model continuous-time stochastic dynamics. By embedding the physical processes of the driving signal and reprocessing into our network, we achieve a model that is more robust and interpretable. We demonstrate that our model outperforms a Gaussian process regression baseline and can infer accretion disk parameters and time delays between wave bands, even for out-of-distribution driving signals. Our approach provides a powerful framework that can be adapted to solve other inverse problems in multivariate time series.

Fagin, Joshua [City Univ. of New York (CUNY), NY (↗
DOE OSTI2023

Recipes for when physics fails: recovering robust learning of physics informed neural networks

Abstract Physics-informed neural networks (PINNs) have been shown to be effective in solving partial differential equations by capturing the physics induced constraints as a part of the training loss function. This paper shows that a PINN can be sensitive to errors in training data and overfit itself in dynamically propagating these errors over the domain of the solution of the PDE. It also shows how physical regularizations based on continuity criteria and conservation laws fail to address this issue and rather introduce problems of their own causing the deep network to converge to a physics-obeying local minimum instead of the global minimum. We introduce Gaussian process (GP) based smoothing that recovers the performance of a PINN and promises a robust architecture against noise/errors in measurements. Additionally, we illustrate an inexpensive method of quantifying the evolution of uncertainty based on the variance estimation of GPs on boundary data. Robust PINN performance is also shown to be achievable by choice of sparse sets of inducing points based on sparsely induced GPs. We demonstrate the performance of our proposed methods and compare the results from existing benchmark models in literature for time-dependent Schrödinger and Burgers’ equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Photometric redshifts for the S-PLUS Survey: Is machine learning up to the task?

The Southern Photometric Local Universe Survey (S-PLUS) is a novel project that aims to map the Southern Hemisphere using a twelve filter system, comprising five broad-band SDSS-like filters and seven narrow-band filters optimized for important stellar features in the local universe. In this paper we use the photometry and morphological information from the first S-PLUS data release (S-PLUS DR1) cross-matched to unWISE data and spectroscopic redshifts from Sloan Digital Sky Survey DR15. We explore three different machine learning methods (Gaussian Processes with GPz and two Deep Learning models made with TensorFlow) and compare them with the currently used template-fitting method in the S-PLUS DR1 to address whether machine learning methods can take advantage of the twelve filter system for photometric redshift prediction. Using tests for accuracy for both single-point estimates such as the calculation of the scatter, bias, and outlier fraction, and probability distribution functions (PDFs) such as the Probability Integral Transform (PIT), the Continuous Ranked Probability Score (CRPS) and the Odds distribution, we conclude that a deep-learning method using a combination of a Bayesian Neural Network and a Mixture Density Network offers the most accurate photometric redshifts for the current test sample. In conclusion, it achieves single-point photometric redshifts with scatter (σ NMAD ) of 0.023, normalized bias of -0.001, and outlier fraction of 0.64% for galaxies with r_auto magnitudes between 16 and 21.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Latent Stochastic Differential Equations for Modeling Quasar Variability and Inferring Black Hole Properties

Quasars are bright and unobscured active galactic nuclei (AGN) thought to be powered by the accretion of matter around supermassive black holes at the centers of galaxies. The temporal variability of a quasar’s brightness contains valuable information about its physical properties. The UV/optical variability is thought to be a stochastic process, often represented as a damped random walk described by a stochastic differential equation (SDE). Upcoming wide-field telescopes such as the Rubin Observatory Legacy Survey of Space and Time (LSST) are expected to observe tens of millions of AGN in multiple filters over a ten year period, so there is a need for efficient and automated modeling techniques that can handle the large volume of data. Latent SDEs are machine learning models well suited for modeling quasar variability, as they can explicitly capture the underlying stochastic dynamics. In this work, we adapt latent SDEs to jointly reconstruct multivariate quasar light curves and infer their physical properties such as the black hole mass, inclination angle, and temperature slope. Our model is trained on realistic simulations of LSST ten year quasar light curves, and we demonstrate its ability to reconstruct quasar light curves even in the presence of long seasonal gaps and irregular sampling across different bands, outperforming a multioutput Gaussian process regression baseline. Our method has the potential to provide a deeper understanding of the physical properties of quasars and is applicable to a wide range of other multivariate time series with missing data and irregular sampling.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Improving Dark Energy Constraints Using Low-Redshift Large-Scale Structures

The primary goal of this project was to improve constraints on dark energy measurements by improving our ability to extract cosmological information from low redshift large-scale structures. PI Clowe's project's primary aim was to reduce the bias in measurements of the masses of clusters of galaxies to a level where the evolution of the cluster mass function can be used in the Vera Rubin Observatory's Legacy Survey of Space and Time Dark Energy Science Collaboration survey to improve the accuracy of the measurement of dark energy and other cosmological parameters. Co-PI Seo's project studied observational systematics affecting large-scale clustering of galaxies, which will be used to improve dark energy constraints from the Dark Energy Spectroscopic Instrument (DESI). The cluster lensing project employed a series of simulations and observations of clusters of galaxies to test numerous potential systematic errors in cluster mass measurements using weak gravitational lensing as the accuracy of current weak lensing measurements are more than order of magnitude worse than what is required to use clusters of galaxies for accurate determination of dark energy parameters. PI Clowe and group developed and analyzed simulations to test for, and correct biases introduced in, the weak lensing measurement process. Finally, PI Clowe and group developed a method of detecting clusters using galaxy overdensities and applied the method to the BLISS and DES surveys. The success of spectroscopic dark energy mission such as the extended Baryon Oscillation Spectroscopic Survey (eBOSS) and the Dark Energy Spectroscopic Instrument (DESI) will depend on a thorough understanding of various observational systematics in the target density fluctuations that would give rise to spurious, non-cosmological signals. PI Seo and group developed a deep learning, artificial neural network (ANN) technique that modeled and mitigated such effects, aimed at deriving more robust galaxy clustering signals not only for the baryon acoustic oscillation feature and redshift-space distortions but also for primordial non-Gaussianity constraint.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Electron energy loss spectroscopy database synthesis and automation of core-loss edge recognition by deep-learning neural networks

Abstract The ionization edges encoded in the electron energy loss spectroscopy (EELS) spectra enable advanced material analysis including composition analyses and elemental quantifications. The development of the parallel EELS instrument and fast, sensitive detectors have greatly improved the acquisition speed of EELS spectra. However, the traditional way of core-loss edge recognition is experience based and human labor dependent, which limits the processing speed. So far, the low signal–noise ratio and the low jump ratio of the core-loss edges on the raw EELS spectra have been challenging for the automation of edge recognition. In this work, a convolutional-bidirectional long short-term memory neural network (CNN-BiLSTM) is proposed to automate the detection and elemental identification of core-loss edges from raw spectra. An EELS spectral database is synthesized by using our forward model to assist in the training and validation of the neural network. To make the synthesized spectra resemble the real spectra, we collected a large library of experimentally acquired EELS core edges. In synthesize the training library, the edges are modeled by fitting the multi-Gaussian model to the real edges from experiments, and the noise and instrumental imperfectness are simulated and added. The well-trained CNN-BiLSTM network is tested against both the simulated spectra and real spectra collected from experiments. The high accuracy of the network, 94.9%, proves that, without complicated preprocessing of the raw spectra, the proposed CNN-BiLSTM network achieves the automation of core-loss edge recognition for EELS spectra with high accuracy.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Peri-Net-Pro: the neural processes with quantified uncertainty for crack patterns

Abstract This paper develops a deep learning tool based on neural processes (NPs) called the Peri-Net-Pro, to predict the crack patterns in a moving disk and classifies them according to the classification modes with quantified uncertainties. In particular, image classification and regression studies are conducted by means of convolutional neural networks (CNNs) and NPs. First, the amount and quality of the data are enhanced by using peridynamics to theoretically compensate for the problems of the finite element method (FEM) in generating crack pattern images. Second, case studies are conducted with the prototype microelastic brittle (PMB), linear peridynamic solid (LPS), and viscoelastic solid (VES) models obtained by using the peridynamic theory. The case studies are performed to classify the images by using CNNs and determine the suitability of the PMB, LBS, and VES models. Finally, a regression analysis is performed on the crack pattern images with NPs to predict the crack patterns. The regression analysis results confirm that the variance decreases when the number of epochs increases by using the NPs. The training results gradually improve, and the variance ranges decrease to less than 0.035. The main finding of this study is that the NPs enable accurate predictions, even with missing or insufficient training data. The results demonstrate that if the context points are set to the 10th, 100th, 300th, and 784th, the training information is deliberately omitted for the context points of the 10th, 100th, and 300th, and the predictions are different when the context points are significantly lower. However, the comparison of the results of the 100th and 784th context points shows that the predicted results are similar because of the Gaussian processes in the NPs. Therefore, if the NPs are employed for training, the missing information of the training data can be supplemented to predict the results.

Mathematics↗
DOE OSTI2022

Accelerating Hydraulic Fracture Imaging by Deep Transfer Learning

Deep transfer learning has a great success story in computer vision (CV), natural language processing, and many other fields. In this communication, we are going to push forward the deep transfer learning to the hydraulic fracture imaging problem by proposing a two-step approach: 1) train a convolutional neural network (CNN) to reconstruct target geometries by a relatively large amount of approximated field patterns generated from a simplified model and 2) fine-tune the top layers of transferred CNN by a small amount of true field patterns generated through a full model. The advantages include the rapid generation of large amount of data through the simplified model and the high reconstruction accuracy through a careful design of the deep transfer learning. Here, the CNN trained through the deep transfer learning can accurately reconstruct the lateral extent and direction of fractures with unseen conductivity and white Gaussian noise, showing a notable acceleration/accuracy enhancement over the previous CNN trained by mixing a small number of true data into the approximated data as data augmentation.

02 PETROLEUM↗
DOE OSTI2022

Discriminative Dimensionality Reduction using Deep Neural Networks for Clustering of LIGO Data

In this paper, leveraging the capabilities of neural networks for modeling the non-linearities that exist in the data, we propose several models that can project data into a low dimensional, discriminative, and smooth manifold. The proposed models can transfer knowledge from the domain of known classes to a new domain where the classes are unknown. A clustering algorithm is further applied in the new domain to find potentially new classes from the pool of unlabeled data. The research problem and data for this paper originated from the Gravity Spy project which is a side project of Advanced Laser Interferometer Gravitational-wave Observatory (LIGO). The LIGO project aims at detecting cosmic gravitational waves using huge detectors. However non-cosmic, non-Gaussian disturbances known as "glitches", show up in gravitational-wave data of LIGO. This is undesirable as it creates problems for the gravitational wave detection process. Gravity Spy aids in glitch identification with the purpose of understanding their origin. Since new types of glitches appear over time, one of the objective of Gravity Spy is to create new glitch classes. Towards this task, we offer a methodology in this paper to accomplish this.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2026

Describing Point Defect Topology in 2D Energy Materials Through Computer Vision

Point defects such as vacancies and impurity atoms strongly impact the performance of 2D materials. Traditional efforts often rely on manual detection, a process that is time-intensive, prone to human error, and challenging to scale. Here we leverage machine learning (ML) methods to identify and quantify vacancies within 2D transition metal carbides (Ti3C2, MXenes), aiming to expedite detection while improving accuracy. MXenes exhibit valuable defect-defined electrochemical properties, but we currently lack statistical understanding of defect topology needed to fully harness these materials. Here we employ a convolutional neural network for semantic segmentation of experimental MXene images, opening an opportunity to conduct a rigorous statistical study on defect hierarchy while investigating local relaxation in the lattice. We show how the integration of ML can yield fundamental insight into point defects, providing a powerful tool that will play an increasingly crucial role in the future of materials science. ML is often not just a matter of straightforward application, and pretrained models proved ineffective in this case. Instead, we trained our own neural network (NN) and applied data augmentation techniques and fine-tuning to the training dataset. Since labeled microscopy data is often scarce, we developed training data from a previously published wide-frame MXene image, using customized Gaussian fitting to locate atomic positions. Our trained model was then applied to a large dataset of experimental images, enabling a statistical study of defect configurations across three samples prepared with different HF etchant concentrations (5%, 9.1%, and 12.5%), as shown in Fig. 1. This also allowed us to investigate local strain around vacancies, though we find that we are limited by the precision of measurements using high-angle annular dark field (HAADF) images, as shown in Fig. 2. This study demonstrates how ML enables large-scale, quantitative analysis of atomic defects - an otherwise infeasible task with traditional methods. While our NN was specialized for Ti3C2 MXenes, the pipeline we developed provides a foundation for future ML models tailored to other materials. Ultimately, we envision embedding the NN onto the microscope to give real-time feedback to the user. To make this a reality, continued work is necessary to fully understand the NN's capabilities and limitations. This study gets one step closer to our goals of automated experimentation moving away from traditional methods of manual labeling. As ML capabilities advance, we hope to continue adapting and applying these techniques in microscopy.

2D materials↗
DOE OSTI2022

A survey of unsupervised learning methods for high-dimensional uncertainty quantification in black-box-type problems

Constructing surrogate models for uncertainty quantification (UQ) on complex partial differential equations (PDEs) having inherently high-dimensional O(10 n ), n ≥ 2, stochastic inputs (e.g., forcing terms, boundary conditions, initial conditions) poses tremendous challenges. The “curse of dimensionality” can be addressed with suitable unsupervised learning techniques used as a pre-processing tool to encode inputs onto lower-dimensional subspaces while retaining its structural information and meaningful properties. In this work, we review and investigate thirteen dimension reduction methods including linear and nonlinear, spectral, blind source separation, convex and non-convex methods and utilize the resulting embeddings to construct a mapping to quantities of interest via polynomial chaos expansions (PCE). Here, we refer to the general proposed approach as manifold PCE (m-PCE), where manifold corresponds to the latent space resulting from any of the studied dimension reduction methods. To investigate the capabilities and limitations of these methods we conduct numerical tests for three physics-based systems (treated as black-boxes) having high-dimensional stochastic inputs of varying complexity modeled as both Gaussian and non-Gaussian random fields to investigate the effect of the intrinsic dimensionality of input data. We demonstrate both the advantages and limitations of the unsupervised learning methods and we conclude that a suitable m-PCE model provides a cost-effective approach compared to alternative algorithms proposed in the literature, including recently proposed expensive deep neural network-based surrogates and can be readily applied for high-dimensional UQ in stochastic PDEs.

42 ENGINEERING↗
DOE OSTI2022

Deep Learning of Dark Energy Spectroscopic Instrument Mock Spectra to Find Damped Lyα Systems

We have updated and applied a convolutional neural network (CNN) machine-learning model to discover and characterize damped Ly α systems (DLAs) based on Dark Energy Spectroscopic Instrument (DESI) mock spectra. We have optimized the training process and constructed a CNN model that yields a DLA classification accuracy above 99% for spectra that have signal-to-noise ratios (S/N) above 5 per pixel. The classification accuracy is the rate of correct classifications. This accuracy remains above 97% for lower S/N ≈1 spectra. This CNN model provides estimations for redshift and H i column density with standard deviations of 0.002 and 0.17 dex for spectra with S/N above 3 pixel -1 . Also, this DLA finder is able to identify overlapping DLAs and sub-DLAs. Further, the impact of different DLA catalogs on the measurement of baryon acoustic oscillations (BAO) is investigated. The cosmological fitting parameter result for BAO has less than 0.61% difference compared to analysis of the mock results with perfect knowledge of DLAs. This difference is lower than the statistical error for the first year estimated from the mock spectra: above 1.7%. We also compared the performances of the CNN and Gaussian Process (GP) models. Our improved CNN model has moderately 14% higher purity and 7% higher completeness than an older version of the GP code, for S/N > 3. Both codes provide good DLA redshift estimates, but the GP produces a better column density estimate by 24% less standard deviation. A credible DLA catalog for the DESI main survey can be provided by combining these two algorithms.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

A novel conditional generative model for efficient ensemble forecasts of state variables in large-scale geological carbon storage

Integrating monitoring data to efficiently update reservoir pressure and CO 2 plume distribution forecasts presents a significant challenge in geological carbon storage (GCS) applications. Inverse modeling techniques are commonly used to fuse observational data and refine reservoir model parameters, thereby improving state variable forecasts. However, these techniques often rely on linear or Gaussian assumptions, which can limit their effectiveness in accurately predicting state variables. Moreover, simulating large-scale three-dimensional (3D) GCS problems is computationally expensive, making iterative runs in inverse problems prohibitive. To address these challenges, we propose a conditional generative model utilizing the score-based diffusion method for real-time 3D pressure and saturation field distribution predictions. Our approach involves solving the score function with a mini-batch-based Monte Carlo estimator to generate labeled data. This data is subsequently employed to train a fully connected neural network, enabling it to learn the conditional sample generator within a supervised learning framework. This method enables the rapid generation of a large ensemble of predictions, facilitating comprehensive uncertainty quantification of state variables. Here we applied our method to forecast the dynamic 3D distributions of pressure and saturation fields over a 30-year injection period. The statistical assessment with low root mean square error (RMSE) values demonstrates that our method can accurately predict the spatiotemporal distributions of both pressure and saturation fields. Moreover, the developed conditional generative model shows high computational efficiency by generating 100 ensemble forecasts of 3D state variables in less than 10 min. The consistency between ensemble averages and ground truth values further illustrates the model’s capability to capture state variable dynamics during the CO 2 plume injection process. Notably, the ground truth values fall within the ensemble forecasts, indicating that our uncertainty quantification effectively captures variability and potential noise in the observations. Thus, the developed conditional generative model proves to be a more efficient, accurate, and practical tool for GCS applications, facilitating timely risk analysis and informed decision-making.

58 GEOSCIENCES↗
DOE OSTI2024

Forward variable selection enables fast and accurate dynamic system identification with Karhunen-Loève decomposed Gaussian processes

A promising approach for scalable Gaussian processes (GPs) is the Karhunen-Loève (KL) decomposition, in which the GP kernel is represented by a set of basis functions which are the eigenfunctions of the kernel operator. Such decomposed kernels have the potential to be very fast, and do not depend on the selection of a reduced set of inducing points. However KL decompositions lead to high dimensionality, and variable selection thus becomes paramount. This paper reports a new method of forward variable selection, enabled by the ordered nature of the basis functions in the KL expansion of the Bayesian Smoothing Spline ANOVA kernel (BSS-ANOVA), coupled with fast Gibbs sampling in a fully Bayesian approach. It quickly and effectively limits the number of terms, yielding a method with competitive accuracies, training and inference times for tabular datasets of low feature set dimensionality. Theoretical computational complexities are O ( N P 2 ) in training and O ( P ) per point in inference, where N is the number of instances and P the number of expansion terms. The inference speed and accuracy makes the method especially useful for dynamic systems identification, by modeling the dynamics in the tangent space as a static problem, then integrating the learned dynamics using a high-order scheme. The methods are demonstrated on two dynamic datasets: a ‘Susceptible, Infected, Recovered’ (SIR) toy problem, along with the experimental ‘Cascaded Tanks’ benchmark dataset. Comparisons on the static prediction of time derivatives are made with a random forest (RF), a residual neural network (ResNet), and the Orthogonal Additive Kernel (OAK) inducing points scalable GP, while for the timeseries prediction comparisons are made with LSTM and GRU recurrent neural networks (RNNs) along with the SINDy package.

Hayes, Kyle↗
DOE OSTI2020

Probabilistic Prediction of Geomagnetic Storms and the K p index

Geomagnetic activity is often described using summary indices to summarize the likelihood of space weather impacts, as well as when parameterizing space weather models. The geomagnetic index K p in particular, is widely used for these purposes. Current state-of-the-art forecast models provide deterministic K p predictions using a variety of methods – including empirically-derived functions, physics-based models, and neural networks – but do not provide uncertainty estimates associated with the forecast. This paper provides a sample methodology to generate a 3-hour-ahead K p prediction with uncertainty bounds and from this provide a probabilistic geomagnetic storm forecast. Specifically, we have used a two-layered architecture to separately predict storm (K p ≥ 5 – ) and non-storm cases. As solar wind-driven models are limited in their ability to predict the onset of transient-driven activity we also introduce a model variant using solar X-ray flux to assess whether simple models including proxies for solar activity can improve the predictions of geomagnetic storm activity with lead times longer than the L1-to-Earth propagation time. By comparing the performance of these models we show that including operationally-available information about solar irradiance enhances the ability of predictive models to capture the onset of geomagnetic storms and that this can be achieved while also enabling probabilistic forecasts.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Deep learning categorization of infrasound array data

Here we develop a deep learning-based infrasonic detection and categorization methodology that uses convolutional neural networks with self-attention layers to identify stationary and non-stationary signals in infrasound array processing results. Using features extracted from the coherence and direction-of-arrival information from beamforming at different infrasound arrays, our model more reliably detects signals compared with raw waveform data. Using three infrasound stations maintained as part of the International Monitoring System, we construct an analyst-reviewed data set for model training and evaluation. We construct models using a 4-category framework, a generalized noise vs non-noise detection scheme, and a signal-of-interest (SOI) categorization framework that merges short duration stationary and non-stationary categories into a single SOI category. We evaluate these models using a combination of k-fold cross-validation, comparison with an existing “state-of-the-art” detector, and a transportability analysis. Although results are mixed in distinguishing stationary and non-stationary short duration signals, f-scores for the noise vs non-noise and SOI analyses are consistently above 0.96, implying that deep learning-based infrasonic categorization is a highly accurate means of identifying signals-of-interest in infrasonic data records.

47 OTHER INSTRUMENTATION↗
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 OSTI2025

Divide and conquer: separating the two probabilities in seismic phase picking

There are two fundamental probabilities in the seismic phase picking process—the probability of the existence of a seismic phase (detection probability) and the probability associated with the phase arrival time estimation (timing probability). The nearly ubiquitous approach in developing deep learning phase picking models is to use a kernel, such as a truncated Gaussian, to mask the labelled phase arrival time and train a segmentation model. Once a model is trained, the times of the peaks in the output are taken as phase arrival times (picks), and the height of the peaks are taken as ‘probability’ of the picks. Here, we show that this ‘probability’ represents neither the detection nor the timing probability because this approach forces the output to follow the shape of the kernel. We introduce an approach using two models to estimate these two distinct probabilities. We use a binary classifier with a calibrated confidence to address the detection probability and a multiclass classifier to obtain a probability mass function to address the timing probability. This new approach can make the deep learning-based phase picking process more interpretable and provide options to logically control seismic monitoring workflows.

58 GEOSCIENCES↗