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DOE OSTI2025

Learning and discovering multiple solutions using physics-informed neural networks with random initialization and deep ensemble

In this work we explore the capability of physics-informed neural networks (PINNs) to discover multiple solutions. Many real-world phenomena governed by nonlinear differential equations (DEs), such as fluid flow, exhibit multiple solutions under the same conditions, yet capturing this solution multiplicity remains a significant challenge. A key difficulty lies in providing appropriate initial conditions or guesses, as widely used time-marching schemes and Newton’s method are highly sensitive to these choices when solving complex computational problems. While machine learning models, particularly PINNs, have shown promise in solving DEs, their ability to capture multiple solutions remains underexplored. In this work, we propose a simple and practical approach using PINNs to learn and discover multiple solutions. We first demonstrate that PINNs, when combined with random initialization and deep ensemble method—originally developed for uncertainty quantification—can effectively uncover multiple solutions to nonlinear ordinary and partial DEs. Although training large ensembles of PINNs may appear computationally demanding, this can be done efficiently using vectorization techniques supported by modern deep learning frameworks, allowing many networks to be trained simultaneously. Our approach highlights the critical role of initialization in shaping solution diversity, addressing an often-overlooked aspect of machine learning for scientific computing. Furthermore, we propose utilizing PINN-generated solutions as initial conditions or initial guesses for conventional numerical solvers to enhance accuracy and efficiency in capturing multiple solutions. Extensive numerical experiments, including the Allen–Cahn equation and cavity flow, where our approach successfully identifies both stable and unstable solutions, validate the effectiveness of our method. These findings establish a general and efficient framework for addressing solution multiplicity in nonlinear DEs.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

End-to-End Optimization for Battery Materials and Molecules by Combining Graph Neural Networks and Reinforcement Learning

The National Renewable Energy Laboratory (NREL), together with the Colorado School of Mines (CSM) and Colorado State University (CSU), has developed a machine learning-enhanced approach to the design of new battery materials. Currently, such materials are designed in part via numerous expensive high-fidelity computational simulations that predict the performance of a given composition. Even with computational screening tools, the vast landscape of possible molecular or crystal structures exceeds current and future computational capacity. Improving the efficiency by which new materials can be optimized will therefore disrupt the cost, risk, and time required to bring new energy solutions to the marketplace. Predicting the properties of an organic molecule or periodic crystalline material given its structure has grown increasingly common. These approaches leverage large-scale computational and experimental databases and ML approaches such as graph neural networks. The inverse design problem of finding a material that possesses desired properties is substantially more challenging, since enumerating all valid material structures is not feasible. In this project, we leveraged recent success in reinforcement learning to efficiently navigate this high-dimensional search space. Just as algorithms can find the optimal chess moves from nearly limitless options, we train an approach to evolve a simple starting structure into a complex structure that possess the desired properties. Our solution has been demonstrated by applying it to two related design application tasks for short- and long-term energy storage, respectively: (1) the design of solid-state ion conductors and (2) the design of organic redox-active materials. The project has resulted an open-source software library for material design, documented examples of applying the library to both organic and inorganic material optimization, and peer-reviewed publications detailing the data, computational models, and resulting candidate materials.

25 ENERGY STORAGE↗

DOE OSTI2020

State-of-the-art on research and applications of machine learning in the building life cycle

Fueled by big data, powerful and affordable computing resources, and advanced algorithms, machine learning has been explored and applied to buildings research for the past decades and has demonstrated its potential to enhance building performance. This study systematically surveyed how machine learning has been applied at different stages of building life cycle. By conducting a literature search on the Web of Knowledge platform, we found 9579 papers in this field and selected 153 papers for an in-depth review. The number of published papers is increasing year by year, with a focus on building design, operation, and control. However, no study was found using machine learning in building commissioning. There are successful pilot studies on fault detection and diagnosis of HVAC equipment and systems, load prediction, energy baseline estimate, load shape clustering, occupancy prediction, and learning occupant behaviors and energy use patterns. None of the existing studies were adopted broadly by the building industry, due to common challenges including (1) lack of large scale labeled data to train and validate the model, (2) lack of model transferability, which limits a model trained with one data-rich building to be used in another building with limited data, (3) lack of strong justification of costs and benefits of deploying machine learning, and (4) the performance might not be reliable and robust for the stated goals, as the method might work for some buildings but could not be generalized to others. Finally, findings from the study can inform future machine learning research to improve occupant comfort, energy efficiency, demand flexibility, and resilience of buildings, as well as to inspire young researchers in the field to explore multidisciplinary approaches that integrate building science, computing science, data science, and social science.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2024

Acceleration of Graph Neural Network-Based Prediction Models in Chemistry via Co-Design Optimization on Intelligence Processing Units

Atomic structure prediction and associated property calculations are the bedrock of chemical physics. Since high-fidelity ab initio modeling techniques for computing the structure and properties can be prohibitively expensive, this motivates the development of machine-learning (ML) models that make these predictions more efficiently. Training graph neural networks over large atomistic databases introduces unique computational challenges such as the need to process millions of small graphs with variable size and support communication patterns that are distinct from learning over large graphs such as social networks. We demonstrate a novel hardware-software co-design approach to scale up the training of atomistic graph neural networks (GNN) for structure and property prediction. First, to eliminate redundant computation and memory associated with alternative padding techniques and to improve throughput via minimizing communication, we formulate the effective coalescing of the batches of variable-size atomistic graphs as the bin packing problem and introduce a hardware-agnostic algorithm to pack these batches. In addition, we propose hardware-specific optimizations including a planner and vectorization for the gather-scatter operations targeted for Graphcore’s Intelligence Processing Unit (IPU), as well as model-specific optimizations such as merged communication collectives and optimized softplus. Putting these all together, we demonstrate the effectiveness of the proposed co-design approach by providing an implementation of a well-established atomistic GNN on the Graphcore IPUs. We evaluate the training performance on multiple atomistic graph databases with varying degrees of graph counts, sizes and sparsity. Here, we demonstrate that such a co-design approach can reduce the training time of atomistic GNNs and can improve the performance by up to 1.5× compared to the baseline implementation of the model on the IPUs. Additionally, we compare our IPU implementation with a Nvidia GPU-based implementation and show that our atomistic GNN implementation on the IPUs can run 1.8× faster on average compared to the execution time on the GPUs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Assessing the Application of a Genomic Network Analysis in Population Ecology: Inferring Patterns of Dispersal and Geographic Structure in the Emerging Pathogen, Coccidioides

A challenge in population ecology studies is identifying how to best group individuals into populations, especially when individual origin is unknown. Machine learning has improved upon traditional methods of identifying population structure and is more efficient at handling large, complex datasets. We demonstrate the applicability of a machine learning method to identify hierarchical population structure in an emerging pathogen, Coccidioides spp., the causative agent of Valley fever. We compared the network clusters to structure identified by traditional tools as a validation of the network performance. We used publicly available whole-genome data for 48 C. immitis and 102 C. posadasii, resulting in 168,211 genome-wide SNPs among the two species. The network analysis grouped samples into populations comparable to the literature for these species but also identified fine-scale geographic structure and travel-associated cases not reported thus far. Exploring different resolutions in the network made it easy to identify unique genotypes specific to California and possibly Nevada, as well as Phoenix- and Tucson-acquired infections in non-endemic areas, regardless of reported travel history. The present study provides a promising example of how a ML-based network analysis can improve our ability to understand pathogen ecology, group cases into populations and infer travel-associated infections.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2024

Peridynamic neural operators: A data-driven nonlocal constitutive model for complex material responses

Neural operators, which can act as implicit solution operators of hidden governing equations, have recently become popular tools for learning the responses of complex real-world physical systems. Nevertheless, most neural operator applications have thus far been data-driven and neglect the intrinsic preservation of fundamental physical laws in data. Here, in this work, we introduce a novel integral neural operator architecture called the Peridynamic Neural Operator (PNO) that learns a nonlocal constitutive law from data. This neural operator provides a forward model in the form of state-based peridynamics, with objectivity and momentum balance laws automatically guaranteed. As applications, we demonstrate the expressivity and efficacy of our model in learning complex material behaviors from both synthetic and experimental data sets. We also compare the performances with baseline models that use predefined constitutive laws. We show that, owing to its ability to capture complex responses, our learned neural operator achieves improved accuracy and efficiency. Moreover, by preserving the essential physical laws within the neural network architecture, the PNO is robust in treating noisy data. The method shows generalizability to different domain configurations, external loadings, and discretizations.

42 ENGINEERING↗

DOE OSTI2022

Composition design of high-entropy alloys with deep sets learning

High entropy alloys (HEAs) are an important material class in the development of next-generation structural materials, but the astronomically large composition space cannot be efficiently explored by experiments or first-principles calculations. Machine learning (ML) methods might address this challenge, but ML of HEAs has been hindered by the scarcity of HEA property data. In this work, the EMTO-CPA method was used to generate a large HEA dataset (spanning a composition space of 14 elements) containing 7086 cubic HEA structures with structural properties, 1911 of which have the complete elastic tensor calculated. The elastic property dataset was used to train a ML model with the Deep Sets architecture. The Deep Sets model has better predictive performance and generalizability compared to other ML models. Association rule mining was applied to the model predictions to describe the compositional dependence of HEA elastic properties and to demonstrate the potential for data-driven alloy design.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Closure Learning for Nonlinear Model Reduction Using Deep Residual Neural Network

Developing accurate, efficient, and robust closure models is essential in the construction of reduced order models (ROMs) for realistic nonlinear systems, which generally require drastic ROM mode truncations. We propose a deep residual neural network (ResNet) closure learning framework for ROMs of nonlinear systems. The novel ResNet-ROM framework consists of two steps: (i) In the first step, we use ROM projection to filter the given nonlinear system and construct a spatially filtered ROM. This filtered ROM is low-dimensional, but is not closed. (ii) In the second step, we use ResNet to close the filtered ROM, i.e., to model the interaction between the resolved and unresolved ROM modes. We emphasize that in the new ResNet-ROM framework, data is used only to complement classical physical modeling (i.e., only in the closure modeling component), not to completely replace it. We also note that the new ResNet-ROM is built on general ideas of spatial filtering and deep learning and is independent of (restrictive) phenomenological arguments, e.g., of eddy viscosity type. The numerical experiments for the 1D Burgers equation show that the ResNet-ROM is significantly more accurate than the standard projection ROM. The new ResNet-ROM is also more accurate and significantly more efficient than other modern ROM closure models.

Xie, Xuping↗

DOE OSTI2021

Deep learning classification of lipid droplets in quantitative phase images

We report the application of supervised machine learning to the automated classification of lipid droplets in label-free, quantitative-phase images. By comparing various machine learning methods commonly used in biomedical imaging and remote sensing, we found convolutional neural networks to outperform others, both quantitatively and qualitatively. We describe our imaging approach, all implemented machine learning methods, and their performance with respect to computational efficiency, required training resources, and relative method performance measured across multiple metrics. Overall, our results indicate that quantitative-phase imaging coupled to machine learning enables accurate lipid droplet classification in single living cells. As such, the present paradigm presents an excellent alternative of the more common fluorescent and Raman imaging modalities by enabling label-free, ultra-low phototoxicity, and deeper insight into the thermodynamics of metabolism of single cells.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2026

Technical Report for Bayesian Optimization and Reinforcement Learning for Beam Polarization Increase in the BNL Hadron Injectors

This project developed and evaluated physics-informed Bayesian learning and machine learning (ML)-based optimization methods for improving beam polarization preservation in the BNL hadron injector chain. The work focused on uncertainty-aware digital twin modeling, Bayesian calibration of accelerator simulations using beam measurements, and data-efficient optimization strategies including Bayesian optimization and reinforcement learning. These methods were applied to injector tuning and RF control problems in realistic accelerator settings to support improved operational robustness and readiness for RHIC operations and future Electron–Ion Collider facilities. No subject inventions were disclosed under this award.

43 PARTICLE ACCELERATORS↗

DOE OSTI2022

Li-ion Battery Material phase prediction through Hierarchical Curriculum Learning

Li-ion Batteries (LIB), one of the most efficient energy storage devices, are widely adopted in many industrial applications. Imaging data of these battery electrodes obtained from X-ray tomography can explain the distribution of material constituents and allow reconstructions to study electron transport pathways. Therefore, it can eventually help quantify various associated properties of electrodes (e.g., volume-specific surface area, porosity) which determine the performance of batteries. However, these images often suffer from low image contrast between multiple material constituents , making it difficult for humans to distinguish and characterize these constituents through visualization. A minor error in detecting distributions among the material constituents can lead to a high error in the calculated parameters of material properties.We present a novel hierarchical curriculum learning framework to address the complex task of estimating material constituent distribution in battery electrodes. To provide spatially smooth prediction, our framework comprises three modules: (i) an uncertainty-aware model trained to yield inferences conditioned upon global knowledge of material distribution, (ii) a technique to capture relatively more fine-grained (local) distributional signals, (iii) an aggregator to appropriately fuse the local and global effects towards obtaining the final distribution.

Tabassum, Anika↗

DOE OSTI2021

IoT Intrusion Detection Taxonomy, Reference Architecture, and Analyses

This paper surveys the deep learning (DL) approaches for intrusion-detection systems (IDSs) in Internet of Things (IoT) and the associated datasets toward identifying gaps, weaknesses, and a neutral reference architecture. A comparative study of IDSs is provided, with a review of anomaly-based IDSs on DL approaches, which include supervised, unsupervised, and hybrid methods. All techniques in these three categories have essentially been used in IoT environments. To date, only a few have been used in the anomaly-based IDS for IoT. For each of these anomaly-based IDSs, the implementation of the four categories of feature(s) extraction, classification, prediction, and regression were evaluated. We studied important performance metrics and benchmark detection rates, including the requisite efficiency of the various methods. Four machine learning algorithms were evaluated for classification purposes: Logistic Regression (LR), Support Vector Machine (SVM), Decision Tree (DT), and an Artificial Neural Network (ANN). Therefore, we compared each via the Receiver Operating Characteristic (ROC) curve. The study model exhibits promising outcomes for all classes of attacks. The scope of our analysis examines attacks targeting the IoT ecosystem using empirically based, simulation-generated datasets (namely the Bot-IoT and the IoTID20 datasets).

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Mapping out the thermodynamic stability of a QCD equation of state with a critical point using active learning

The Beam Energy Scan Theory (BEST) collaboration's equation of state (EoS) incorporates a three-dimensional Ising model critical point into the quantum chromodynamics (QCD) equation of state from lattice simulations. Furthermore, it contains four free parameters related to the size and location of the critical region in the QCD phase diagram. Certain combinations of the free parameters lead to acausal or unstable realizations of the EoS that should not be considered. In this work, we use an active learning framework to rule out pathological EoS efficiently. We find that checking stability and causality for a small portion of the parameters' range is sufficient to construct algorithms that perform with > 96 % accuracy across the entire parameter space. Though in this work we focus on a specific case, our approach can be generalized to any EoS containing a parameter space-class correspondence.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

MatPhase: Material phase prediction for Li-ion Battery Reconstruction using Hierarchical Curriculum Learning

Li-ion Batteries (LIB), one of the most efficient energy storage devices, are used extensively in many industrial applications. These batteries consist of electrodes that are put together with heterogeneous material compositions. Imaging data of these battery electrodes obtained from X-ray tomography can explain the distribution of material constituents and allow reconstructions to study electron transport pathways. Such reconstructions of material constituents help quantify various associated properties of electrodes (e.g., volume-specific surface area, porosity) which determine the performance of batteries. These images often suffer from low image contrast between multiple material constituents, hence making it difficult for humans to distinguish and characterize these constituents through visual inspection. A minor error in detecting distributions of the material constituents can lead to magnified errors in the calculated parameters of material properties (e.g., porosity). We present MatPhase, a novel hierarchical curriculum learning technique to address the complex task of estimating material constituent distribution in battery electrodes. MatPhase comprises three modules: (i) an uncertainty-aware global model trained to yield inferences conditioned upon global knowledge of material distribution, (ii) a local model to capture relatively more fine-grained (local) distributional signals, (iii) an aggregator model to appropriately fuse the local and global effects towards obtaining the final distribution. On average, MatPhase improves prediction up to 8.5% relative to other sophisticated modeling pipelines and state-of-the-arts (SOTA) object detection models employed in the performance comparison.

Tabassum, Anika↗

DOE OSTI2024

Differentiable modeling and optimization of non-aqueous Li-based battery electrolyte solutions using geometric deep learning

Electrolytes play a critical role in designing next-generation battery systems, by allowing efficient ion transfer, preventing charge transfer, and stabilizing electrode-electrolyte interfaces. In this work, we develop a differentiable geometric deep learning (GDL) model for chemical mixtures, DiffMix, which is applied in guiding robotic experimentation and optimization towards fast charging battery electrolytes. In particular, we extend mixture thermodynamic and transport laws by creating GDL-learnable physical coefficients. We evaluate our model with mixture thermodynamics and ion transport properties, where we show improved prediction accuracy and model robustness of Diff-Mix than its purely data-driven variants. Furthermore, with a robotic experimentation setup, Clio, we improve ionic conductivity of electrolytes by over 18.8% within 10 experimental steps, via differentiable optimization built on DiffMix gradients. By combining GDL, mixture physics laws, and robotic experimentation, DiffMix expands the predictive modeling methods for chemical mixtures and enables efficient optimization in large chemical spaces.

25 - ENERGY STORAGE↗

DOE OSTI2023

Quantum mixed state compiling

The task of learning a quantum circuit to prepare a given mixed state is a fundamental quantum subroutine. We present a variational quantum algorithm (VQA) to learn mixed states which is suitable for near-term hardware. Our algorithm represents a generalization of previous VQAs that aimed at learning preparation circuits for pure states. We consider two different ansätze for compiling the target state; the first is based on learning a purification of the state and the second on representing it as a convex combination of pure states. In both cases, the resources required to store and manipulate the compiled state grow with the rank of the approximation. Thus, by learning a lower rank approximation of the target state, our algorithm provides a means of compressing a state for more efficient processing. As a byproduct of our algorithm, one effectively learns the principal components of the target state, and hence our algorithm further provides a new method for principal component analysis. We investigate the efficacy of our algorithm through extensive numerical implementations, showing that typical random states and thermal states of many body systems may be learnt this way. Additionally, we demonstrate on quantum hardware how our algorithm can be used to study hardware noise-induced states.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

A machine-learning approach to measure 3D sample properties from 2D Transmission Electron Microscopy images

Transmission Electron Microscopy (TEM) is a powerful tool for the characterization of materials at the nanoscale; however, its inherent two-dimensional (2D) nature poses significant challenges to accurately measure three-dimensional (3D) properties. We introduce a supervised machine-learning model that predicts 3D structural information, such as sample thickness and curvature, from a series of conventional 2D TEM images. The model, a U-Net convolutional neural network, is trained on a large synthetic dataset generated from dynamical diffraction simulations that model TEM’s complex, nonlinear image formation, accounting for sample thickness and curvature. This physically realistic framework enables exploration of a broad parameter space impractical to sample experimentally. We demonstrate that the trained model has accurate predictions for experimental single-crystal silicon samples, achieving performance comparable to established measurement techniques. This work highlights the critical role of robust, simulation-based training in overcoming the limitations of real-world imaging artifacts and inconsistent sample geometries. By integrating machine learning with numerical simulations, we offer an efficient and scalable framework for quantitative TEM analysis, paving the way for more sophisticated 3D characterization of complex materials.

Dynamical diffraction↗

DOE OSTI2025

Surrogate modeling of Cellular-Potts agent-based models as a segmentation task using the U-Net neural network architecture

The Cellular-Potts model is a powerful and ubiquitous framework for developing computational models for simulating complex multicellular biological systems. Cellular-Potts models (CPMs) are often computationally expensive due to the explicit modeling of interactions among large numbers of individual model agents and diffusive fields described by partial differential equations (PDEs). In this work, we develop a convolutional neural network (CNN) surrogate model using a U-Net architecture that accounts for periodic boundary conditions. We use this model to accelerate the evaluation of a mechanistic CPM previously used to investigate in vitro vasculogenesis. The surrogate model was trained to predict 100 computational steps ahead (Monte-Carlo steps, MCS), accelerating simulation evaluations by a factor of 562 times compared to single-core CPM code execution on CPU. Over short timescales of up to 3 recursive evaluations, or 300 MCS, our model captures the emergent behaviors demonstrated by the original Cellular-Potts model such as vessel sprouting, extension and anastomosis, and contraction of vascular lacunae. This approach demonstrates the potential for deep learning to serve as a step toward efficient surrogate models for CPM simulations, enabling faster evaluation of computationally expensive CPM simulations of biological processes.

97 MATHEMATICS AND COMPUTING↗