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29 records · Page 2

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

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 (

Exploring the energy landscape of RBMs: reciprocal space insights into bosons, hierarchical learning and symmetry breaking

Deep generative models have become ubiquitous due to their ability to learn and sample from complex distributions. Despite the proliferation of various frameworks, the relationships among these models remain largely unexplored, a gap that hinders the development of a unified theory of AI learning. In this work, we address two central challenges: clarifying the connections between different deep generative models and deepening our understanding of their learning mechanisms. We focus on Restricted Boltzmann Machines (RBMs), a class of generative models known for their universal approximation capabilities for discrete distributions. By introducing a reciprocal space formulation for RBMs, we reveal a connection between these models, diffusion processes, and systems of coupled bosons. Our analysis shows that at initialization, the RBM operates at a saddle point, where the local curvature is determined by the singular values of the weight matrix, whose distribution follows the Marc̆enko-Pastur law and exhibits rotational symmetry. During training, this rotational symmetry is broken due to hierarchical learning, where different degrees of freedom progressively capture features at multiple levels of abstraction. This leads to a symmetry breaking in the energy landscape, reminiscent of Landau’s theory. This symmetry breaking in the energy landscape is characterized by the singular values and the weight matrix eigenvector matrix. We derive the corresponding free energy in a mean-field approximation. We show that in the limit of infinite size RBM, the reciprocal variables are Gaussian distributed. Our findings indicate that in this regime, there will be some modes for which the diffusion process will not converge to the Boltzmann distribution. To illustrate our results, we trained replicas of RBMs with different hidden layer sizes using the MNIST dataset. Our findings not only bridge the gap between disparate generative frameworks but also shed light on the fundamental processes underpinning learning in deep generative models.

97 MATHEMATICS AND COMPUTING

Machine learning for seismic low-frequency extrapolation

The cycle-skipping problem that plagues full waveform inversion (FWI) can be at least partially mitigated if low frequencies (which encode the kinematics of wave propagation in seismic data) are recorded. However, seismic sources and receivers are band-limited, so seismic data does not generally include signals down to 0 Hz. To improve our ability to solve the seismic inverse problem, one can synthesize this missing low-frequency (LF) content from the recorded high-frequency (HF) data using machine learning (ML) models. Deep learning models such as convolutional neural networks (CNNs) demonstrate impressive ability to perform low frequency extrapolation. However, such models require powerful hardware (GPU machines) and careful training. We assess the extrapolation capabilities of three different ML models that do not require GPU machines, namely, random forest, Gaussian process regression and gradient boosting, on both synthetic and real data. Experimental results on two synthetic data sets (generated from a low velocity lens embedded in a homogeneous medium, and the Marmousi model) demonstrate that FWI applied to the extrapolated data consistently improves inversion accuracy relative to FWI applied to the original data sets that do not contain low frequencies. Application of low-frequency extrapolation to real data from the Northwest Shelf of Australia demonstrates that tree-based ML models such as gradient boosting can outperform CNNs in terms of both accuracy and computational cost on non-GPU architectures.

58 GEOSCIENCES

MOOSE ProbML: Parallelized probabilistic machine learning and uncertainty quantification for computational energy applications

Here, this paper presents the development and demonstration of massively parallel probabilistic machine learning (ML) and uncertainty quantification (UQ) capabilities within the Multiphysics Object-Oriented Simulation Environment (MOOSE), an open-source computational platform for parallel finite element and finite volume analyses. In addressing the computational expense and uncertainties inherent in complex multiphysics simulations, this paper integrates Gaussian process (GP) variants, active learning, Bayesian inverse UQ, adaptive forward UQ, Bayesian optimization, evolutionary optimization, and Markov chain Monte Carlo (MCMC) within MOOSE. It also elaborates on the interaction among key MOOSE systems — Sampler, MultiApp, Reporter, and Surrogate — in enabling these capabilities. The modularity offered by these systems enables development of a multitude of probabilistic ML and UQ algorithms in MOOSE. Example code demonstrations include parallel active learning and parallel Bayesian inference via active learning. The impact of these developments is illustrated through five applications relevant to computational energy applications: UQ of nuclear fuel fission product release, using parallel active learning Bayesian inference; very rare events analysis in nuclear microreactors using active learning; advanced manufacturing process modeling using multi-output GPs (MOGPs) and dimensionality reduction; fluid flow using deep GPs (DGPs); and tritium transport model parameter optimization for fusion energy, using batch Bayesian optimization. These capabilities are part of the MOOSE framework.

97 - MATHEMATICS AND COMPUTING

Combining High-Throughput Experiments and Active Learning to Characterize Deep Eutectic Solvents

The high tunability of deep eutectic solvents (DESs) stems from the ease of changing their precursors and relative compositions. However, measuring the physicochemical properties across large composition and temperature ranges, necessary to properly design target-specific DESs, is tedious and error-prone and represents a bottleneck in the advancement and scalability of DES-based applications. As such, active learning (AL) methodologies based on Gaussian processes (GPs) were developed in this work to minimize the experimental effort necessary to characterize DESs. Owing to its importance for large-scale applications, the reduction of DES viscosity through the addition of a low-molecular-weight solvent was explored as a case study. A high-throughput experimental screening was initially performed on nine different ternary DESs. Then, GPs were successfully trained to predict DES viscosity from its composition and temperature, showcasing the ability of these stochastic, nonparametric models to accurately describe the physicochemical properties of complex mixtures. Finally, the ability of GPs to provide estimates of their own uncertainty was leveraged through an AL framework to minimize the number of data points necessary to obtain accurate viscosity modes. This led to a significant reduction in data requirements, with many systems requiring only five independent viscosity data points to be properly described.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Automated Bayesian high-throughput estimation of plasma temperature and density from emission spectroscopy

Here, this paper introduces a novel approach for automated high-throughput estimation of plasma temperature and density using atomic emission spectroscopy, integrating Bayesian inference with sophisticated physical models. We provide an in-depth examination of Bayesian methods applied to the complexities of plasma diagnostics, supported by a robust framework of physical and measurement models. Our methodology is demonstrated using experimental observations in the field of magneto-inertial fusion, focusing on individual and sequential shot analyses of the Plasma Liner Experiment at LANL. The results demonstrate the effectiveness of our approach in enhancing the accuracy and reliability of plasma parameter estimation and in using the analysis to reveal the deep hidden structure in the data. This study not only offers a new perspective of plasma analysis but also paves the way for further research and applications in nuclear instrumentation and related domains.

Bayesian inference

Quantum Simulation of Molecular Dynamics Processes─A Benchmark Study Using a Classical Simulator and Present-Day Quantum Hardware

Here, we explore how the fundamental problems in quantum molecular dynamics can be modeled using classical simulators (emulators) of quantum computers and the actual quantum hardware available to us today. The list of problems we tackle includes propagation of a free wave packet, vibration of a harmonic oscillator, and tunneling through a barrier. Each of these problems starts with the initial wave packet setup. Although Qiskit provides a general method for initializing wave functions, in most cases it generates deep quantum circuits. While these circuits perform well on noiseless simulators, they suffer from excessive noise on quantum hardware. To overcome this issue, we designed a shallower quantum circuit for preparing a Gaussian-like initial wave packet, which improves the performance of real hardware. Next, quantum circuits are implemented to apply the kinetic and potential energy operators for the evolution of a wave function over time. The results of our modeling on classical emulators of quantum hardware agree perfectly with the results obtained using the traditional (classical) methods. This serves as a benchmark and demonstrates that the quantum algorithms and Qiskit codes we developed are accurate. However, the results obtained on the actual quantum hardware available today, such as IBM’s superconducting qubits and IonQ’s trapped ions, indicate large discrepancies due to hardware limitations. This work highlights both the potential and challenges of using quantum computers to solve fundamental quantum molecular dynamics problems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Active deep kernel learning of molecular properties from structural embeddings

As vast databases of chemical identities become increasingly available, the challenge shifts to how we effectively explore and leverage these resources to study molecular properties. This paper presents an active learning approach for molecular discovery using deep kernel learning (DKL), demonstrated on the QM9 dataset. DKL links structural embeddings directly to properties, creating organized latent spaces that prioritize relevant property information. By iteratively recalculating embedding vectors in alignment with target properties, DKL uncovers concentrated maxima representing key molecular properties and reveals unexplored regions with potential for innovation. This approach underscores DKL’s potential in advancing molecular research and discovery.

Artificial neural networks

Yet Another Discriminant Analysis (YADA): A Probabilistic Model for Machine Learning Applications

This paper presents a probabilistic model for various machine learning (ML) applications. While deep learning (DL) has produced state-of-the-art results in many domains, DL models are complex and over-parameterized, which leads to high uncertainty about what the model has learned, as well as its decision process. Further, DL models are not probabilistic, making reasoning about their output challenging. In contrast, the proposed model, referred to as Yet Another Discriminate Analysis(YADA), is less complex than other methods, is based on a mathematically rigorous foundation, and can be utilized for a wide variety of ML tasks including classification, explainability, and uncertainty quantification. YADA is thus competitive in most cases with many state-of-the-art DL models. Ideally, a probabilistic model would represent the full joint probability distribution of its features, but doing so is often computationally expensive and intractable. Hence, many probabilistic models assume that the features are either normally distributed, mutually independent, or both, which can severely limit their performance. YADA is an intermediate model that (1) captures the marginal distributions of each variable and the pairwise correlations between variables and (2) explicitly maps features to the space of multivariate Gaussian variables. Numerous mathematical properties of the YADA model can be derived, thereby improving the theoretic underpinnings of ML. Validation of the model can be statistically verified on new or held-out data using native properties of YADA. However, there are some engineering and practical challenges that we enumerate to make YADA more useful.

97 MATHEMATICS AND COMPUTING

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