PyLEnM: A Machine Learning Framework for Long-Term Groundwater Contamination Monitoring Strategies
Not Available
54 ENVIRONMENTAL SCIENCES↗
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Code for the manuscript titled "Blackout Diffusion: Generative Diffusion Models in Discrete-State Spaces"
We would like to disclose two scripts, written in Jupyter notebook, in which we implement the "Blackout Diffusion Process" described in the manuscript "Blackout Diffusion: Generative Diffusion Models in Discrete-State Spaces" (LA-UR-23-20509), to be submitted to the International Conference of Machine Learning (ICML). The abstract of the manuscript is append below. == Typical generative diffusion models rely on a Gaussian diffusion process for training the backward transformations, which can then be used generate samples from Gaussian noise. However, real world data often takes place in discrete-state spaces, which occur in many scientific applications. Here, we develop a theoretical formulation for arbitrary discrete-state Markov processes in the forward diffusion process. We relate the theory to the existing continuous-state Gaussian diffusion and identify the corresponding reverse-time stochastic process and score function in the continuous-time setting, and the reverse-time mapping in the discrete-time setting. As an example of this framework, we introduce "Blackout Diffusion", which learns to produce samples from an empty image instead of from noise. Numerical experiments on the CIFAR-10 dataset confirm the feasibility of generative diffusion modeling in a discrete space. Generalizing from specific (Gaussian) forward processes to a more general framework also sheds light on how to interpret generative diffusion models and their mathematical structure, which we comment on.
Lin, Yen Ting↗
Latent map Gaussian processes for mixed variable metamodeling
Gaussian processes (GPs) are ubiquitously used in sciences and engineering as metamodels. Standard GPs, however, can only handle numerical or quantitative variables. Here we introduce latent map Gaussian processes (LMGPs) that inherit the attractive properties of GPs and are also applicable to mixed data which have both quantitative and qualitative inputs. The core idea behind LMGPs is to learn a continuous, low-dimensional latent space or manifold which encodes all qualitative inputs. To learn this manifold, we first assign a unique prior vector representation to each combination of qualitative inputs. We then use a low-rank linear map to project these priors on a manifold that characterizes the posterior representations. As the posteriors are quantitative, they can be directly used in any standard correlation function such as the Gaussian or Matern. Hence, the optimal map and the corresponding manifold, along with other hyperparameters of the correlation function, can be systematically learned via maximum likelihood estimation. Through a wide range of analytic and real-world examples, we demonstrate the advantages of LMGPs over state-of-the-art methods in terms of accuracy and versatility. In particular, we show that LMGPs can handle variable-length inputs, have an explainable neural network interpretation, and provide insights into how qualitative inputs affect the response or interact with each other. We also employ LMGPs in Bayesian optimization and illustrate that they can discover optimal compound compositions more efficiently than conventional methods that convert compositions to qualitative variables via manual featurization.
42 ENGINEERING↗
Correspondence between neuroevolution and gradient descent
Abstract We show analytically that training a neural network by conditioned stochastic mutation or neuroevolution of its weights is equivalent, in the limit of small mutations, to gradient descent on the loss function in the presence of Gaussian white noise. Averaged over independent realizations of the learning process, neuroevolution is equivalent to gradient descent on the loss function. We use numerical simulation to show that this correspondence can be observed for finite mutations, for shallow and deep neural networks. Our results provide a connection between two families of neural-network training methods that are usually considered to be fundamentally different.
97 MATHEMATICS AND COMPUTING↗
A Multi-Objective Bayesian Optimization Approach Using the Weighted Tchebycheff Method
Abstract Bayesian optimization (BO) is a low-cost global optimization tool for expensive black-box objective functions, where we learn from prior evaluated designs, update a posterior surrogate Gaussian process model, and select new designs for future evaluation using an acquisition function. This research focuses upon developing a BO model with multiple black-box objective functions. In the standard multi-objective (MO) optimization problem, the weighted Tchebycheff method is efficiently used to find both convex and non-convex Pareto frontiers. This approach requires knowledge of utopia values before we start optimization. However, in the BO framework, since the functions are expensive to evaluate, it is very expensive to obtain the utopia values as a prior knowledge. Therefore, in this paper, we develop a MO-BO framework where we calibrate with multiple linear regression (MLR) models to estimate the utopia value for each objective as a function of design input variables; the models are updated iteratively with sampled training data from the proposed MO-BO. These iteratively estimated mean utopia values are used to formulate the weighted Tchebycheff MO acquisition function. The proposed approach is implemented in two numerical test examples and one engineering design problem of optimizing thin tube geometries under constant loading of temperature and pressure, with minimizing the risk of creep-fatigue failure and design cost, along with risk-based and manufacturing constraints. Finally, the model accuracy with frequentist, Bayesian and without MLR-based calibration are compared to true Pareto solutions.
Engineering↗
Discovery of Probabilistic Dirichlet-to-Neumann Maps on Graphs
Dirichlet-to-Neumann maps enable the coupling of multiphysics simulations across computational subdomains by ensuring continuity of state variables and fluxes at artificial interfaces. We present a novel method for learning Dirichlet-to-Neumann maps on graphs using Gaussian processes, specifically for problems where the data obey a conservation law arising from an underlying partial differential equation. Our approach combines discrete exterior calculus and nonlinear optimal recovery to infer relationships between vertex and edge values. This framework yields data-driven predictions with uncertainty quantification across the entire graph, even when observations are limited to a subset of vertices and edges. By minimizing the reproducing kernel Hilbert space norm while penalizing kernel complexity through maximum likelihood estimation, our method ensures that the resulting surrogate strictly enforces conservation laws without overfitting. We demonstrate our method on two representative applications: subsurface flow in fracture networks and arterial blood flow. Finally, the results demonstrate that the method maintains high accuracy and well-calibrated uncertainty estimates even under severe data scarcity, highlighting its potential for scientific applications where limited data and reliable uncertainty quantification are critical.
Dirichlet-to-Neumann map↗
Optimization of artificial viscosity in production codes based on Gaussian Regression surrogate models
To accurately model flows with shock waves using staggered-grid Lagrangian hydrodynamics, artificial viscosity has to be introduced to convert kinetic energy into internal energy, thereby increasing the entropy across shocks. Determining the appropriate strength of the artificial viscosity is an art and strongly depends on the particular problem and experience of the researcher. The objective of this study is to pose the problem of finding the appropriate strength of artificial viscosity as an optimization problem and solve this problem using machine learning (ML) tools, specifically using surrogate models based on Gaussian Process regression and Bayesian analysis. We describe the optimization method and discuss various practical details of its implementation. The shock-containing problems for which we apply this method all have been implemented in the LANL code FLAG. First, we apply ML to find optimal values to isolated shock problems of different strengths. Second, we apply ML to optimize viscosity for a 1D propagating detonation problem based on Zel’dovich-von Neumann-Doring (ZND) detonation theory using a reactive burn model. We compare results for default (currently used values in FLAG) and optimized values of artificial viscosity for these problems demonstrating the potential for significant improvement in the accuracy of computations.
42 ENGINEERING↗
Explainability and human intervention in autonomous scanning probe microscopy
The broad adoption of machine learning (ML)-based autonomous experiments (AEs) in material characterization and synthesis requires strategies development for understanding and intervention in the experimental workflow. Here, we introduce and realize a post-experimental analysis strategy for deep kernel learning-based autonomous scanning probe microscopy. This approach yields real-time and post-experimental indicators for the progression of an active learning process interacting with an experimental system. We further illustrate how this approach can be applied to human-in-the-loop AEs, where human operators make high-level decisions at high latencies setting the policies for AEs, and the ML algorithm performs low-level, fast decisions. The proposed approach is universal and can be extended to other techniques and applications such as combinatorial library analysis.
47 OTHER INSTRUMENTATION↗
A Comprehensive Review of Latent Space Dynamics Identification Algorithms for Intrusive and Non-Intrusive Reduced-Order-Modeling
Numerical solvers of partial differential equations (PDEs) have been widely employed for simulating physical systems. However, the computational cost remains a major bottleneck in various scientific and engineering applications, which has motivated the development of reduced-order models (ROMs). Recently, machine-learning-based ROMs have gained significant popularity and are promising for addressing some limitations of traditional ROM methods, especially for advection dominated systems. In this chapter, we focus on a particular framework known as Latent Space Dynamics Identification (LaSDI), which transforms the high-fidelity data, governed by a PDE, to simpler and low-dimensional latent-space data, governed by ordinary differential equations (ODEs). These ODEs can be learned and subsequently interpolated to make ROM predictions. Each building block of LaSDI can be easily modulated depending on the application, which makes the LaSDI framework highly flexible. In particular, we present strategies to enforce the laws of thermodynamics into LaSDI models (tLaSDI), enhance robustness in the presence of noise through the weak form (WLaSDI), select high-fidelity training data efficiently through active learning (gLaSDI, GPLaSDI), and quantify the ROM prediction uncertainty through Gaussian processes (GPLaSDI). We demonstrate the performance of different LaSDI approaches on Burgers equation, a non-linear heat conduction problem, and a plasma physics problem, showing that LaSDI algorithms can achieve relative errors of less than a few percent and up to thousands of times speed-ups.
Computational Engineering, Finance, and Science (c↗
Big Data and AI at DoE's Legacy Sites - 20546
More than 30 years have passed since DOE started the decommissioning of nuclear weapon complexes and the clean-up of soil and groundwater. All the sites have been collecting and archiving soil and groundwater monitoring datasets; particularly contaminant concentration time-series. These datasets provide unparalleled opportunities to understand the system behavior (including more fundamental hydrological and geochemical processes, the response to various perturbations, the long-term trend and environmental decay rate towards the regulatory limit). This understanding is critical for providing multiple lines of evidences that can support site closure. In this study, we explore the machine learning (ML) and artificial intelligence (AI) applications to the long-term soil and groundwater management at DoE's legacy sites. ML can improve our understanding of the subsurface systems, which is critical for long-term monitoring and management of the sites, while AI can automate or support some of decision-making processes (e.g., anomaly detection, monitoring well placements). The particular focuses are to develop general algorithms to: (1) to identify distinct spatiotemporal patterns and to identify several groups that have similar temporal behaviors, using unsupervised clustering methods, (2) identify the different temporal scales of hydrological responses to climate perturbations by time-series analysis, and (3) reduce the number of monitoring wells by identifying the minimum sufficient number of wells to capture the heterogeneity of the groundwater contaminant plume and concentration distribution, using the Gaussian Process model. We demonstrate our methodology at the Savannah River Site F-Area. (authors)
12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
MOOSE ProbML: Parallelizable Probabilistic Machine Learning and Uncertainty Quantification Capabilities
The Multiphysics Object Oriented Simulation Environment (MOOSE) is a widely used open- source finite element software for performing multiphysics multiscale simulations in a massively parallel fashion. Recently, the computational team at Idaho National Laboratory (INL) has implemented Probabilistic Machine Learning (ProbML) capabilities in MOOSE—in a parallelized fashion—and enable active learning with large-scale computational models for tasks such as surrogate model development, scale bridging, forward/inverse uncertainty quantification (UQ), Bayesian optimization, etc. This presentation summarizes these developments in MOOSE along with demonstrations on several real applications relevant to nuclear energy. At the fundamental level, samplers like Monte Carlo/Latin Hypercube, variance reduction, parallelized Markov Chain Monte Carlo (MCMC) support uncertainty propagation in both forward and inverse settings. These samplers can be integrated with the Gaussian processes (GP) suite in MOOSE, which offer several variants like scalar GPs, multi-output GPs, and deep GPs, to enable active learning. These GPs can be tuned using gradient-based optimization methods like Adam and its variants or gradient-free methods like the elliptical slice sampler (a variant of MCMC adept under Gaussian settings) for more complex covariance kernels or likelihoods whose gradient computations can be cumbersome. A variety of batch acquisition functions permit parallelized evaluation of the computational model and support different learning objectives with high efficiency like Bayesian inference, global surrogate development, optimization, etc. Furthermore, libtorch integration supports training, evaluation, and re-training of neural networks and other complex machine learning models in active learning settings. The impacts of these developments are shown on several real applications: (1) nuclear fuel inverse UQ and model inadequacy assessment using the Kennedy O’Hagan framework; (2) uncertainty aware surrogate modeling for additive manufacturing to predict field quantities; (3) nuclear reactor rare events analysis; and (4) complex fluid flow prediction using a global surrogate with quantified prediction uncertainty. Finally, the outlook of MOOSE ProbML is discussed for both outer-loop and inner-loop computations in the broad view to accelerate fuels and materials qualification, address gaps in knowledge and data, and assess new reactor/fuel systems.
11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Statistical and machine learning-based durability-testing strategies for energy storage
Not Available
25 ENERGY STORAGE↗
Featureless adaptive optimization accelerates functional electronic materials design
Electronic materials that exhibit phase transitions between metastable states (e.g., metal-insulator transition materials with abrupt electrical resistivity transformations) are challenging to decode. For these materials, conventional machine learning methods display limited predictive capability due to data scarcity and the absence of features that impede model training. In this article, we demonstrate a discovery strategy based on multi-objective Bayesian optimization to directly circumvent these bottlenecks by utilizing latent variable Gaussian processes combined with high-fidelity electronic structure calculations for validation in the chalcogenide lacunar spinel family. We directly and simultaneously learn phase stability and bandgap tunability from chemical composition alone to efficiently discover all superior compositions on the design Pareto front. Previously unidentified electronic transitions also emerge from our featureless adaptive optimization engine. Our methodology readily generalizes to optimization of multiple properties, enabling co-design of complex multifunctional materials, especially where prior data is sparse.
36 MATERIALS SCIENCE↗
A Scalable Gaussian Process Analysis Algorithm for Biomass Monitoring
Biomass monitoring is vital for studying the carbon cycle of earth's ecosystem and has several significant implications, especially in the context of understanding climate change and its impacts. Recently, several change detection methods have been proposed to identify land cover changes in temporal profiles (time series) of vegetation collected using remote sensing instruments, but do not satisfy one or both of the two requirements of the biomass monitoring problem, i.e., {\em operating in online mode} and {\em handling periodic time series}. In this paper, we adapt Gaussian process regression to detect changes in such time series in an online fashion. While Gaussian process (GP) have been widely used as a kernel based learning method for regression and classification, their applicability to massive spatio-temporal data sets, such as remote sensing data, has been limited owing to the high computational costs involved. We focus on addressing the scalability issues associated with the proposed GP based change detection algorithm. This paper makes several significant contributions. First, we propose a GP based online time series change detection algorithm and demonstrate its effectiveness in detecting different types of changes in {\em Normalized Difference Vegetation Index} (NDVI) data obtained from a study area in Iowa, USA. Second, we propose an efficient Toeplitz matrix based solution which significantly improves the computational complexity and memory requirements of the proposed GP based method. Specifically, the proposed solution can analyze a time series of length $t$ in $O(t^2)$ time while maintaining a $O(t)$ memory footprint, compared to the $O(t^3)$ time and $O(t^2)$ memory requirement of standard matrix manipulation based methods. Third, we describe a parallel version of the proposed solution which can be used to simultaneously analyze a large number of time series. We study three different parallel implementations: using threads, MPI, and a hybrid implementation using threads and MPI. Experimental results show that the hybrid implementation scales better than the multi-threaded and MPI based implementations. The application of the proposed scalable algorithm is demonstrated in analyzing massive remote sensing observation data. The hybrid implementation, using 1536 computing cores, can analyze an NDVI data set for the Iowa study area in nearly 5 seconds, while a serial algorithm, using standard Cholesky decomposition based routines, takes several days to process the same data set.
09 BIOMASS FUELS↗
Gaussian Process Classification for Galaxy Blend Identification in LSST
Abstract A significant fraction of observed galaxies in the Rubin Observatory Legacy Survey of Space and Time (LSST) will overlap at least one other galaxy along the same line of sight, in a so-called “blend.” The current standard method of assessing blend likelihood in LSST images relies on counting up the number of intensity peaks in the smoothed image of a blend candidate, but the reliability of this procedure has not yet been comprehensively studied. Here we construct a realistic distribution of blended and unblended galaxies through high-fidelity simulations of LSST-like images, and from this we examine the blend classification accuracy of the standard peak-finding method. Furthermore, we develop a novel Gaussian process blend classifier model, and show that this classifier is competitive with both the peak finding method as well as with a convolutional neural network model. Finally, whereas the peak-finding method does not naturally assign probabilities to its classification estimates, the Gaussian process model does, and we show that the Gaussian process classification probabilities are generally reliable.
79 ASTRONOMY AND ASTROPHYSICS↗
A localized ensemble of approximate Gaussian processes for fast sequential emulation
More attention has been given to the computational cost associated with the fitting of an emulator. Substantially less attention is given to the computational cost of using that emulator for prediction. This is primarily because the cost of fitting an emulator is usually far greater than that of obtaining a single prediction, and predictions can often be obtained in parallel. In many settings, especially those requiring Markov Chain Monte Carlo, predictions may arrive sequentially and parallelization is not possible. In this case, using an emulator procedure which can produce accurate predictions efficiently can lead to substantial time savings in practice. In this paper, we propose a global model approximate Gaussian process framework via extension of a popular local approximate Gaussian process (laGP) framework. Our proposed emulator can be viewed as a treed Gaussian process where the leaf nodes are laGP models, and the tree structure is learned greedily as a function of the prediction stream. The suggested method (called leapGP) has interpretable tuning parameters which control the time‐memory trade‐off. One reasonable choice of settings leads to an emulator with a training cost and makes predictions rapidly with an asymptotic amortized cost of .
97 MATHEMATICS AND COMPUTING↗
Physics-informed Machine Learning Method for Forecasting and Uncertainty Quantification of Partially Observed and Unobserved States in Power Grids
We present a physics-informed Gaussian Process Regression (GPR) model to predict the phase angle, angular speed, and wind mechanical power from a limited number of measurements. In the traditional data-driven GPR method, the form of the Gaussian Process covariance matrix is assumed and its parameters are found from measurements. In the physics-informed GPR, we treat unknown variables (including wind speed and mechanical power) as a random process and compute the covariance matrix from the resulting stochastic power grid equations. We demonstrate that the physics-informed GPR method is significantly more accurate than the standard data-driven one for immediate forecasting of generators' angular velocity and phase angle. We also show that the physics-informed GPR provides accurate predictions of the unobserved wind mechanical power, phase angle, or angular velocity when measurements from only one of these variables are available. The immediate forecast of observed variables and predictions of unobserved variables can be used for effectively managing power grids (electricity market clearing, regulation actions) and early detection of abnormal behavior and faults. The physics-based GPR forecast time horizon depends on the combination of input (wind power, load, etc.) correlation time and characteristic (relaxation) time of the power grid and can be extended to short and medium-range times.
machine learning, power grid, forecasting, Gaussia↗
Tailoring Molecular Space to Navigate Phase Complexity in Cs-Based Quasi-2D Perovskites via Gated-Gaussian-Driven High-Throughput Discovery
Cesium-based quasi-2D halide perovskites (HPs) offer promising functionalities and low-temperature manufacturability, suited to stable tandem photovoltaics. However, the chemical interplays between the molecular spacers and the inorganic building blocks during crystallization cause substantial phase complexities in the resulting matrices. To successfully optimize and implement the quasi-2D HP functionalities, a systematic understanding of spacer chemistry, along with the seamless navigation of the inherently discrete molecular space, is necessary. Herein, by utilizing high-throughput automated experimentation, the phase complexities in the molecular space of quasi-2D HPs are explored, thus identifying the chemical roles of the spacer cations on the synthesis and functionalities of the complex materials. Furthermore, a novel active machine learning algorithm leveraging a two-stage decision-making process, called gated Gaussian process Bayesian optimization is introduced, to navigate the discrete ternary chemical space defined with two distinctive spacer molecules. Through simultaneous optimization of photoluminescence intensity and stability that “tailors” the chemistry in the molecular space, a ternary-compositional quasi-2D HP film realizing excellent optoelectronic functionalities is demonstrated. Finally, this work not only provides a pathway for the rational and bespoke design of complex HP materials but also sets the stage for accelerated materials discovery in other multifunctional systems.
36 MATERIALS SCIENCE↗