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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Machine Learning meets Algebraic Combinatorics: A Suite of Benchmark Datasets to Accelerate AI for Mathematics Research

The use of benchmark datasets has become an important engine of progress in machine learning (ML) over the past 15 years. Recently there has been growing interest in utilizing machine learning to drive advances in research-level mathematics. However, off-the-shelf solutions often fail to deliver the types of insights required by mathematicians. This suggests the need for new ML methods specifically designed with mathematics in mind. The question then is: what benchmarks should the community use to evaluate these? On the one hand, toy problems such as learning the multiplicative structure of small finite groups have become popular in the mechanistic interpretability community whose perspective on explainability aligns well with the needs of mathematicians. While toy datasets are a useful benchmark for initial work, they lack the scale, complexity, and sophistication of many of the principal objects of study in modern mathematics. To address this, we introduce a new collection of benchmark datasets, Algebraic Combinatorics Benchmarks (ACBench), representing either classic or open problems in algebraic combinatorics, a subfield of mathematics that studies discrete structures arising from abstract algebra. After describing the datasets, we discuss the challenges involved in constructing “good” mathematics benchmarks, describe baseline model performance, and discuss some of the insights these datasets can provide that may be of interest even to those who are not interested in mathematics research itself.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Interpretation of autoencoder-learned collective variables using Morse–Smale complex and sublevelset persistent homology: An application on molecular trajectories

Dimensionality reduction often serves as the first step toward a minimalist understanding of physical systems as well as the accelerated simulations of them. In particular, neural network-based nonlinear dimensionality reduction methods, such as autoencoders, have shown promising outcomes in uncovering collective variables (CVs). However, the physical meaning of these CVs remains largely elusive. In this work, we constructed a framework that (1) determines the optimal number of CVs needed to capture the essential molecular motions using an ensemble of hierarchical autoencoders and (2) provides topology-based interpretations to the autoencoder-learned CVs with Morse–Smale complex and sublevelset persistent homology. Furthermore, this approach was exemplified using a series of n-alkanes and can be regarded as a general, explainable nonlinear dimensionality reduction method.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Fault Detection on Seismic Structural Images Using a Nested Residual U-Net

Automatic identification of faults on seismic structural images is a challenging yet crucial task in quantitative seismic interpretation. Human picking or attribute-based fault detection methods may misidentify faults on noisy, complex seismic images. In this work, we develop a new automatic fault detection method using a nested residual U-shaped convolutional neural network. Each of the encoders and decoders in this neural network is a residual U-Net, leading to a nested architecture. The final fault map results from the fusion of three fault maps with low, medium, and high fault resolutions. We demonstrate the excellent fault-detection capability of our nested neural network using a series of synthetic and field seismic images. We find that our approach produces clearer and more interpretable fault maps than the current state-of-the-art U-Net fault detection method, particularly on noisy seismic images. Our new automatic fault detection method can facilitate reliable quantitative seismic interpretation on field seismic images.

58 GEOSCIENCES↗
DOE OSTI2022

Data-Centric Approach to Capture Non-Polynomial Nonlinear Dynamics

We propose an analytical construction of observable functions in the extended dynamic mode decomposition (EDMD) algorithm. EDMD is a numerical method for approximating the spectral properties of the Koopman operator. The choice of observable functions is fundamental for applying EDMD to nonlinear problems arising in systems and control. Existing methods either start from a set of dictionary functions and look for the subset that best fits the underlying nonlinear dynamics or rely on machine learning algorithms to “learn” observable functions. Conversely, in this paper, we start from the dynamical system model and lift it through the Lie derivatives, rendering it into a polynomial form. This proposed transformation into a polynomial form is exact and provides an adequate set of observable functions. The strength of the proposed approach is its applicability to a broader class of nonlinear dynamical systems, particularly those with nonpolynomial functions and compositions thereof. Moreover, it retains the physical interpretability of the underlying dynamical system and can be readily integrated into existing numerical libraries. We demonstrate the proposed approach with an application to electric power systems. The modeled system consists of a single generator connected to an infinite bus, where nonlinear terms include sine and cosine functions. The results demonstrate the effectiveness of the proposed procedure in off-attractor nonlinear dynamics for estimation and prediction; the observable functions obtained from the proposed construction outperform methods that use dictionary functions comprising monomials or radial basis functions.

extended dynamic mode decomposition↗
DOE OSTI2026

Generative models on phase space

Deep generative models such as diffusion and flow matching are powerful machine learning tools capable of learning and sampling from high-dimensional distributions. They are particularly useful when the training data appears to be concentrated on a submanifold of the data embedding space. For high-energy physics data, consisting of collections of relativistic energy-momentum 4-vectors, this submanifold can enforce extremely strong physically-motivated priors, such as energy and momentum conservation. If these constraints are learned only approximately, rather than exactly, this can inhibit the interpretability and reliability of such generative models. To remedy this deficiency, we introduce generative models which are, by construction, confined at every step of their sampling trajectory to the manifold of massless N-particle Lorentz-invariant phase space in the center-of-momentum frame. In the case of diffusion models, the "pure noise" forward process endpoint corresponds to the uniform distribution on phase space, which provides a clear starting point from which to identify how correlations among the particles emerge during the reverse (de-noising) process. We demonstrate that our models are able to learn both few-particle and many-particle distributions with various singularity structures, paving the way for future interpretability studies using generative models trained on simulated jet data.

Bogorad, Zachary [Fermilab]↗
DOE OSTI2026

A machine learning pipeline for identifying infiltration managed aquifer recharge locations from satellite imagery in the San Joaquin Valley, California

This study focuses on an agricultural region in California’s Central Valley, USA, where Managed Aquifer Recharge (MAR) is widely implemented to mitigate groundwater depletion under increasing water demand and climate variability. A deep learning and machine learning framework was developed to identify infiltration-MAR locations using satellite imagery and environmental data. The framework integrates surface water detection from Sentinel-2 imagery, geospatial delineation of water bodies, spatiotemporal tracking of water body dynamics, and supervised classification using meteorological, environmental, and topographic variables. The framework was applied to a 2379 km² study area southwest of Fresno, where 765 water bodies were detected, including 139 identified MAR sites based on publicly available datasets and expert knowledge. The classification model achieved an accuracy of 0.94 and an F1 score of 0.85. Feature importance analysis indicates that cropland, normalized difference vegetation index (NDVI), and evaporation are among the most influential predictors for infiltration-MAR. Notably, the framework suggests that engineered water management in infiltration-MAR systems can disrupt or even reverse the expected positive correlation between surface water extent and precipitation. These findings provide physically interpretable insights into the characteristics of existing infiltration-MAR facilities and demonstrate the potential of the proposed framework as a reproducible, interpretable, and potentially transferable tool for data-driven infiltration-MAR identification and inventory development under growing climatic and hydrological uncertainty.

Classification↗
DOE OSTI2026

Model-Agnostic Signal Discovery with Machine Learning: Bridging the Gap Between Theory and Practice

Searches for new phenomena in complex scientific data are predominantly model-dependent, optimized for specific hypotheses, and therefore limited in their coverage of the space of possible signals. Recently, new AI-based model-agnostic search strategies, many of which have been pioneered in high-energy physics, have been proposed which provide a complementary paradigm, prioritizing broad exploration over tailored analyses. These techniques offer an opportunity to enhance the overall discovery potential of modern experiments, especially in regimes where theoretical guidance is scarce. In this document, we review the conceptual framework behind the main classes of AI-based model-agnostic strategies. We discuss the potential pitfalls of these methods, and strategies for their validation and interpretation. We aim for this document to serve as a useful reference both for practitioners and for researchers interested in learning more about these model-agnostic search strategies.

Amram, Oz [Fermilab] (ORCID:0000000237653123)↗
DOE OSTI2024

Automated Gold Nanorod Spectral Morphology Analysis Pipeline

The development of a colloidal synthesis procedure to produce nanomaterials with high shape and size purity is often a time-consuming, iterative process. This is often due to quantitative uncertainties in the required reaction conditions and the time, resources, and expertise intensive characterization methods required for quantitative determination of nanomaterial size and shape. Absorption spectroscopy is often the easiest method for colloidal nanomaterial characterization. However, due to the lack of a reliable method to extract nanoparticle shapes from absorption spectroscopy, it is generally treated as a more qualitative measure for metal nanoparticles. This work demonstrates a gold nanorod (AuNR) spectral morphology analysis tool, called AuNR-SMA, which is a fast and accurate method to extract quantitative structural information from colloidal AuNR absorption spectra. To demonstrate the practical utility of this model, we apply it to three distinct applications. First, we demonstrate this model's utility as an automated analysis tool in a high-throughput AuNR synthesis procedure by generating quantitative size information from optical spectra. Second, we use the predictions generated by this model to train a machine learning model to predict the resulting AuNR size distributions under specified reaction conditions. Third, we apply this model to spectra extracted from the literature where no size distributions are reported and impute unreported quantitative information on AuNR synthesis. This approach can potentially be extended to any other nanocrystal system where absorption spectra are size dependent, and accurate numerical simulation of absorption spectra is possible. In addition, this pipeline could be integrated into automated synthesis apparatuses to provide interpretable data from simple measurements, help explore the synthesis science of nanoparticles in a rational manner, or facilitate closed-loop workflows.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Search for brown dwarfs in IC 1396 with Subaru HSC: interpreting the impact of environmental factors on substellar population

ABSTRACT Young stellar clusters are predominantly the hub of star formation and hence, ideal to perform comprehensive studies over the least explored substellar regime. Various unanswered questions like the mass distribution in brown dwarf regime and the effect of diverse cluster environment on brown dwarf formation efficiency still plague the scientific community. The nearby young cluster, IC 1396 with its feedback-driven environment, is ideal to conduct such study. In this paper, we adopt a multiwavelength approach, using deep Subaru HSC along with other data sets and machine learning techniques to identify the cluster members complete down to ∼ 0.03 M⊙ in the central 22 arcmin area of IC 1396. We identify 458 cluster members including 62 brown dwarfs which are used to determine mass distribution in the region. We obtain a star-to-brown dwarf ratio of ∼ 6 for a stellar mass range 0.03–1 M⊙ in the studied cluster. The brown dwarf fraction is observed to increase across the cluster as radial distance from the central OB-stars increases. This study also compiles 15 young stellar clusters to check the variation of star-to-brown dwarf ratio relative to stellar density and ultraviolet (UV) flux ranging within 4–2500 stars pc−2 and 0.7–7.3 G0, respectively. The brown dwarf fraction is observed to increase with stellar density but the results about the influence of incident UV flux are inconclusive within this range. This is the deepest study of IC 1396 as of yet and it will pave the way to understand various aspects of brown dwarfs using spectroscopic observations in future.

Gupta, Saumya (ORCID:0000000161843958)↗
DOE OSTI2024

Mechanism of Antiferroelectricity in Polycrystalline ZrO 2

The size and electric field dependent induction of polarization in antiferroelectric ZrO 2 is the key to several technological applications that are unimaginable a decade ago. However, the lack of a deeper understanding of the mechanism hinders progress. Molecular dynamics simulations of polycrystalline ZrO 2 , based on machine-learned interatomic forces with near ab initio quality, shed light on the fundamental mechanism of the size effect on the transition fields. Stress in the oxygen sublattice is the most important factor. The so constructed interatomic forces allow the calculation of the transition fields as a function of the ZrO 2 film thickness and predict the ferroelectricity at large thickness. The simulation results are validated with electrical and piezo response force microscopy measurements. The results allow a clear interpretation of the properties of the double-hysteresis loops as well as the construction of the free energy landscape of ZrO 2 grains.

36 MATERIALS SCIENCE↗
DOE OSTI2022

New tool for kinematic regime estimation in semi-inclusive deep-inelastic scattering

We introduce a new phenomenological tool based on momentum region indicators to guide the analysis and interpretation of semi-inclusive deep-inelastic scattering measurements. The new tool, referred to as “affinity”, is devised to help visualize and quantify the proximity of any experimental kinematic bin to a particular hadron production region, such as that associated with transverse momentum dependent factorization. We apply the affinity estimator to existing HERMES and COMPASS data and expected data from Jefferson Lab and the future Electron-Ion Collider. We also provide an interactive notebook based on Machine Learning for fast evaluation of affinity.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Bayesian differential programming for robust systems identification under uncertainty

This paper presents a machine learning framework for Bayesian systems identification from noisy, sparse and irregular observations of nonlinear dynamical systems. The proposed method takes advantage of recent developments in differentiable programming to propagate gradient information through ordinary differential equation solvers and perform Bayesian inference with respect to unknown model parameters using Hamiltonian Monte Carlo sampling. This allows an efficient inference of the posterior distributions over plausible models with quantified uncertainty, while the use of sparsity-promoting priors enables the discovery of interpretable and parsimonious representations for the underlying latent dynamics. A series of numerical studies is presented to demonstrate the effectiveness of the proposed methods, including nonlinear oscillators, predator–prey systems and examples from systems biology. Taken together, our findings put forth a flexible and robust workflow for data-driven model discovery under uncertainty. All codes and data accompanying this article are available at https://bit.ly/34FOJMj .

Science & Technology - Other Topics↗
DOE OSTI2023

An exploration of machine learning models for the determination of reaction coordinates associated with conformational transitions

Determining collective variables (CVs) for conformational transitions is crucial to understanding their dynamics and targeting them in enhanced sampling simulations. Often, CVs are proposed based on intuition or prior knowledge of a system. However, the problem of systematically determining a proper reaction coordinate (RC) for a specific process in terms of a set of putative CVs can be achieved using committor analysis (CA). Identifying essential degrees of freedom that govern such transitions using CA remains elusive because of the high dimensionality of the conformational space. Various schemes exist to leverage the power of machine learning (ML) to extract an RC from CA. Here, we extend these studies and compare the ability of 17 different ML schemes to identify accurate RCs associated with conformational transitions. We tested these methods on an alanine dipeptide in vacuum and on a sarcosine dipeptoid in an implicit solvent. Our comparison revealed that the light gradient boosting machine method outperforms other methods. In order to extract key features from the models, we employed Shapley Additive exPlanations analysis and compared its interpretation with the “feature importance” approach. For the alanine dipeptide, our methodology identifies ϕ and θ dihedrals as essential degrees of freedom in the C7ax to C7eq transition. For the sarcosine dipeptoid system, the dihedrals ψ and ω are the most important for the cisαD to transαD transition. We further argue that analysis of the full dynamical pathway, and not just endpoint states, is essential for identifying key degrees of freedom governing transitions.

Chemistry↗
DOE OSTI2021

Constrained non-negative matrix factorization enabling real-time insights of in situ and high-throughput experiments

Non-negative matrix factorization (NMF) is an appealing class of methods for performing unsupervised learning on streaming spectral data, particularly in time-sensitive applications such as in situ characterization of materials. These methods seek to decompose a dataset into a small number of components and weights that can compactly represent the underlying signal while effectively reconstructing the observations with minimal error. However, canonical NMF methods have no underlying requirement that the reconstruction uses components or weights that are representative of the true physical processes. In this work, we demonstrate how constraining a subset of the NMF weights or components as rigid priors, provided as known or assumed values, can provide significant improvement in revealing true underlying phenomena. We present a PyTorch-based method for efficiently applying constrained NMF and demonstrate its application to several synthetic examples. Our implementation allows an expert researcher-in-the-loop to provide and dynamically adjust the constraints during a live experiment involving streaming spectral data. Such interactive priors allow researchers to specify known or identified independent components, as well as functional expectations about the mixing or transitions between the components. We further demonstrate the application of this method to measured synchrotron x-ray total scattering data from in situ beamline experiments. In such a context, constrained NMF can result in a more interpretive and scientifically relevant decomposition than canonical NMF or other decomposition techniques. As a result, the details of the method are provided, along with general guidance for employing constrained NMF in the extraction of critical information and insights during time-sensitive experimental applications.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Search for new particles in events with energetic jets and large missing transverse momentum in proton-proton collisions at $ \sqrt{s} $ = 13 TeV

A search is presented for new particles produced at the LHC in proton-proton collisions at s√ = 13 TeV, using events with energetic jets and large missing transverse momentum. The analysis is based on a data sample corresponding to an integrated luminosity of 101 fb -1 , collected in 2017–2018 with the CMS detector. Machine learning techniques are used to define separate categories for events with narrow jets from initial-state radiation and events with large-radius jets consistent with a hadronic decay of a W or Z boson. A statistical combination is made with an earlier search based on a data sample of 36 fb -1 , collected in 2016. No significant excess of events is observed with respect to the standard model background expectation determined from control samples in data. The results are interpreted in terms of limits on the branching fraction of an invisible decay of the Higgs boson, as well as constraints on simplified models of dark matter, on first-generation scalar leptoquarks decaying to quarks and neutrinos, and on models with large extra dimensions. Several of the new limits, specifically for spin-1 dark matter mediators, pseudoscalar mediators, colored mediators, and leptoquarks, are the most restrictive to date.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

ChemEcho v1.0

ChemEcho is a tool that converts tandem mass spectra into embeddings used to build machine learning (ML) models with fully explainable predictions. It provides an API for transforming raw tandem mass spectral data into embeddings, along with functions for training and validating ML models. Additionally, it includes utilities for retrieving and cleaning training data. ChemEcho is broadly applicable in ML pipelines that use tandem mass spectra for a variety of tasks, such as chemical classification or bioactivity mining. While there are existing methods to generate embeddings from fragmentation data, ChemEcho's approach ensures that predictions remain interpretable, enabling experts to evaluate results and generate hypotheses about the underlying data.

Harwood, Thomas [Lawrence Berkeley National Labora↗
DOE OSTI2022

Classification of Nuclear Reactor Operations Using Spatial Importance and Multisensor Networks

Distributed multisensor networks record multiple data streams that can be used as inputs to machine learning models designed to classify operations relevant to proliferation at nuclear reactors. The goal of this work is to demonstrate methods to assess the importance of each node (a single multisensor) and region (a group of proximate multisensors) to machine learning model performance in a reactor monitoring scenario. This, in turn, provides insight into model behavior, a critical requirement of data-driven applications in nuclear security. Using data collected at the High Flux Isotope Reactor at Oak Ridge National Laboratory via a network of Merlyn multisensors, two different models were trained to classify the reactor’s operational state: a hidden Markov model (HMM), which is simpler and more transparent, and a feed-forward neural network, which is less inherently interpretable. Traditional wrapper methods for feature importance were extended to identify nodes and regions in the multisensor network with strong positive and negative impacts on the classification problem. These spatial-importance algorithms were evaluated on the two different classifiers. The classification accuracy was then improved relative to baseline models via feature selection from 0.583 to 0.839 and from 0.811 ± 0.005 to 0.884 ± 0.004 for the HMM and feed-forward neural network, respectively. While some differences in node and region importance were observed when using different classifiers and wrapper methods, the nodes near the facility’s cooling tower were consistently identified as important—a conclusion further supported by studies on feature importance in decision trees. Node and region importance methods are model-agnostic, inform feature selection for improved model performance, and can provide insight into opaque classification models in the nuclear security domain.

Tibbetts, Jake↗
DOE OSTI2022

Fiber Bundle Morphisms as a Framework for Modeling Many-to-Many Maps

While it is not generally reflected in the `nice' datasets used for benchmarking machine learning algorithms, the real-world is full of processes that would be best described as many-to-many. That is, a single input can potentially yield many different outputs (whether due to noise, imperfect measurement, or intrinsic stochasticity in the process) and many different inputs can yield the same output (that is, the map is not injective). For example, imagine a sentiment analysis task where, due to linguistic ambiguity, a single statement can have a range of different sentiment interpretations while at the same time many distinct statements can represent the same sentiment. When modeling such a multivalued function $f: X \rightarrow Y$, it is frequently useful to be able to model the distribution on $f(x)$ for specific input $x$ as well as the distribution on fiber $f^{-1}(y)$ for specific output $y$. Such an analysis helps the user (i) better understand the variance intrinsic to the process they are studying and (ii) understand the range of specific input $x$ that can be used to achieve output $y$. Following existing work which used a fiber bundle framework to better model many-to-one processes we describe how morphisms of fiber bundles provide a template for building models which naturally capture the structure of many-to-many processes.

Coda, Elizabeth D.↗