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Machine learning approaches for structural and thermodynamic properties of a Lennard-Jones fluid
Predicting the functional properties of many molecular systems relies on understanding how atomistic interactions give rise to macroscale observables. However, current attempts to develop predictive models for the structural and thermodynamic properties of condensed-phase systems often rely on extensive parameter fitting to empirically selected functional forms whose effectiveness is limited to a narrow range of physical conditions. Here, we illustrate how these traditional fitting paradigms can be superseded using machine learning. Specifically, we use the results of molecular dynamics simulations to train machine learning protocols that are able to produce the radial distribution function, pressure, and internal energy of a Lennard-Jones fluid with increased accuracy in comparison to previous theoretical methods. The radial distribution function is determined using a variant of the segmented linear regression with the multivariate function decomposition approach developed by Craven et al. [J. Phys. Chem. Lett. 11, 4372 (2020)]. The pressure and internal energy are determined using expressions containing the learned radial distribution function and also a kernel ridge regression process that is trained directly on thermodynamic properties measured in simulation. The presented results suggest that the structural and thermodynamic properties of fluids may be determined more accurately through machine learning than through human-guided functional forms.
Explaining machine-learning models for gamma-ray detection and identification
As more complex predictive models are used for gamma-ray spectral analysis, methods are needed to probe and understand their predictions and behavior. Recent work has begun to bring the latest techniques from the field of Explainable Artificial Intelligence (XAI) into the applications of gamma-ray spectroscopy, including the introduction of gradient-based methods like saliency mapping and Gradient-weighted Class Activation Mapping (Grad-CAM), and black box methods like Local Interpretable Model-agnostic Explanations (LIME) and SHapley Additive exPlanations (SHAP). In addition, new sources of synthetic radiological data are becoming available, and these new data sets present opportunities to train models using more data than ever before. In this work, we use a neural network model trained on synthetic NaI(Tl) urban search data to compare some of these explanation methods and identify modifications that need to be applied to adapt the methods to gamma-ray spectral data. We find that the black box methods LIME and SHAP are especially accurate in their results, and recommend SHAP since it requires little hyperparameter tuning. We also propose and demonstrate a technique for generating counterfactual explanations using orthogonal projections of LIME and SHAP explanations.
State Predictor of Classification Cognitive Engine Applied to Channel Fading
This study presents the application of machine learning (ML) to a space-to-ground communication link, showing how ML can be used to detect the presence of detrimental channel fading. Using this channel state information, the communication link can be used more efficiently by reducing the amount of lost data during fading. The motivation for this work is based on channel fading observed during on-orbit operations with NASA's Space Communication and Navigation (SCaN) testbed on the International Space Station (ISS). This paper presents the process to extract a target concept (fading and not-fading) from the raw data. The pre-processing and data exploration effort is explained in detail, with a list of assumptions made for parsing and labelling the dataset. The model selection process is explained, specifically emphasizing the benefits of using an ensemble of algorithms with majority voting for binary classification of the channel state. Experimental results are shown, highlighting how an end-to-end communication system can utilize knowledge of the channel fading status to identity fading and take appropriate action. With a laboratory testbed to emulate channel fading, the overall performance is compared to standard adaptive methods without fading knowledge, such as adaptive coding and modulation.
Mathematical nuances of Gaussian process-driven autonomous experimentation
Abstract The fields of machine learning (ML) and artificial intelligence (AI) have transformed almost every aspect of science and engineering. The excitement for AI/ML methods is in large part due to their perceived novelty, as compared to traditional methods of statistics, computation, and applied mathematics. But clearly, all methods in ML have their foundations in mathematical theories, such as function approximation, uncertainty quantification, and function optimization. Autonomous experimentation is no exception; it is often formulated as a chain of off-the-shelf tools, organized in a closed loop, without emphasis on the intricacies of each algorithm involved. The uncomfortable truth is that the success of any ML endeavor, and this includes autonomous experimentation, strongly depends on the sophistication of the underlying mathematical methods and software that have to allow for enough flexibility to consider functions that are in agreement with particular physical theories. We have observed that standard off-the-shelf tools, used by many in the applied ML community, often hide the underlying complexities and therefore perform poorly. In this paper, we want to give a perspective on the intricate connections between mathematics and ML, with a focus on Gaussian process-driven autonomous experimentation. Although the Gaussian process is a powerful mathematical concept, it has to be implemented and customized correctly for optimal performance. We present several simple toy problems to explore these nuances and highlight the importance of mathematical and statistical rigor in autonomous experimentation and ML. One key takeaway is that ML is not, as many had hoped, a set of agnostic plug-and-play solvers for everyday scientific problems, but instead needs expertise and mastery to be applied successfully. Graphical abstract
Multitask methods for predicting molecular properties from heterogeneous data
Data generation remains a bottleneck in training surrogate models to predict molecular properties. We demonstrate that multitask Gaussian process regression overcomes this limitation by leveraging both expensive and cheap data sources. In particular, we consider training sets constructed from coupled-cluster (CC) and density functional theory (DFT) data. We report that multitask surrogates can predict at CC-level accuracy with a reduction in data generation cost by over an order of magnitude. Of note, our approach allows the training set to include DFT data generated by a heterogeneous mix of exchange–correlation functionals without imposing any artificial hierarchy on functional accuracy. More generally, the multitask framework can accommodate a wider range of training set structures—including the full disparity between the different levels of fidelity—than existing kernel approaches based on Δ-learning although we show that the accuracy of the two approaches can be similar. Consequently, multitask regression can be a tool for reducing data generation costs even further by opportunistically exploiting existing data sources.
Graph Metric Learning Quantifies Morphological Differences between Two Genotypes of Shoot Apical Meristem Cells in Arabidopsis
We present a method for learning “spectrally descriptive” edge weights for graphs. We generalize a previously known distance measure on graphs (Graph Diffusion Distance), thereby allowing it to be tuned to minimize an arbitrary loss function. Because all steps involved in calculating this modified GDD are differentiable, we demonstrate that it is possible for a small neural network model to learn edge weights which minimize loss. We apply this method to discriminate between graphs constructed from shoot apical meristem images of two genotypes of Arabidopsis thaliana specimens: wild-type and trm678 triple mutants with cell division phenotype. Training edge weights and kernel parameters with contrastive loss produces a learned distance metric with large margins between these graph categories. We demonstrate this by showing improved performance of a simple k-nearest-neighbors classifier on the learned distance matrix. We also demonstrate a further application of this method to biological image analysis. Once trained, we use our model to compute the distance between the biological graphs and a set of graphs output by a cell division simulator. Comparing simulated cell division graphs to biological ones allows us to identify simulation parameter regimes which characterize mutant vs. wild-type Arabidopsis cells. We find that trm678 mutant cells are characterized by increased randomness of division planes and decreased ability to avoid previous vertices between cell walls.
Gaussian Kernel Methods for Seismic Fragility and Risk Assessment of Mid-Rise Buildings
Seismic fragility functions can be evaluated using the cloud analysis method with linear regression which makes three fundamental assumptions about the relation between structural response and seismic intensity: log-linear median relationship, constant standard deviation, and Gaussian distributed errors. While cloud analysis with linear regression is a popular method, the degree to which these individual and compounded assumptions affect the fragility and the risk of mid-rise buildings needs to be systematically studied. This paper conducts such a study considering three building archetypes that make up a bulk of the building stock: RC moment frame, steel moment frame, and wood shear wall. Gaussian kernel methods are employed to capture the data-driven variations in the median structural response and standard deviation and the distributions of residuals with the intensity level. With reference to the Gaussian kernels approach, it is found that while the linear regression assumptions may not affect the fragility functions of lower damage states, this conclusion does not hold for the higher damage states (such as the Complete state). In addition, the effects of linear regression assumptions on the seismic risk are evaluated. For predicting the demand hazard, it is found that the linear regression assumptions can impact the computed risk for larger structural response values. However, for predicting the loss hazard with downtime as the decision variable, linear regression can be considered adequate for all practical purposes.
Non-uniform active learning for Gaussian process models with applications to trajectory informed aerodynamic databases
The ability to non-uniformly weight the input space is desirable for many applications, and has been explored for space-filling approaches. Increased interests in linking models, such as in a digital twinning framework, increases the need for sampling emulators where they are most likely to be evaluated. In particular, here we apply non-uniform sampling methods for the construction of aerodynamic databases. This paper combines non-uniform weighting with active learning for Gaussian Processes (GPs) to develop a closed-form solution to a non-uniform active learning criterion. We accomplish this by utilizing a kernel density estimator as the weight function. We demonstrate the need and efficacy of this approach with an atmospheric entry example that accounts for both model uncertainty as well as the practical state space of the vehicle, as determined by forward modeling within the active learning loop.
Predicting impurity spectral functions using machine learning
The Anderson Impurity Model (AIM) is a canonical model of quantum many-body physics. Here we investigate whether machine learning models, both neural networks (NN) and kernel ridge regression (KRR), can accurately predict the AIM spectral function in all of its regimes, from empty orbital, to mixed valence, to Kondo. To tackle this question, we construct two large spectral databases containing approximately 410 000 and 600 000 spectral functions of the single-channel impurity problem. We show that the NN models can accurately predict the AIM spectral function in all of its regimes, with pointwise mean absolute errors down to 0.003 in normalized units. We find that the trained NN models outperform models based on KRR and enjoy a speedup on the order of 10 5 over traditional AIM solvers. Finally, the required size of the training set of our model can be significantly reduced using farthest point sampling in the AIM parameter space, which is important for generalizing our method to more complicated multichannel impurity problems of relevance to predicting the properties of real materials.
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.
Emulation With Uncertainty Quantification of Regional Sea‐Level Change Caused by the Antarctic Ice Sheet
Abstract Projecting regional sea‐level change under various climate‐change scenarios typically involves running forward simulations of the Earth's gravitational, rotational and deformational (GRD) response to ice‐mass change, which requires substantial computational cost if applied to probabilistic frameworks requiring thousands to millions of samples. Here we build emulators of regional sea‐level change at 27 coastal locations, due to the GRD effects associated with future Antarctic Ice Sheet mass change over the 21st century. The emulators are evaluated against a numerical sea‐level model applied to an ensemble of ice‐sheet model simulations of the Antarctic Ice Sheet through 2100. We build a physics‐based emulator using a recent sensitivity kernel approach and compare it to machine learning based emulators (neural network and conditional variational autoencoder methods). In order to quantify uncertainty, we derive well‐calibrated prediction intervals for regional sea‐level change via split‐conformal inference and linear regression, and show that Monte Carlo dropout does not yield well‐calibrated uncertainties in this instance. We also demonstrate substantial gains in computational efficiency using both the physics‐based emulator and neural networks in comparison to the numerical model for the complete regional sea‐level solution. Overall, we find the physics‐based emulator modestly outperforms the machine learning emulators for this problem.
Sparse Cholesky factorization for solving nonlinear PDEs via Gaussian processes
In recent years, there has been widespread adoption of machine learning-based approaches to automate the solving of partial differential equations (PDEs). Among these approaches, Gaussian processes (GPs) and kernel methods have garnered considerable interest due to their flexibility, robust theoretical guarantees, and close ties to traditional methods. They can transform the solving of general nonlinear PDEs into solving quadratic optimization problems with nonlinear, PDE-induced constraints. However, the complexity bottleneck lies in computing with dense kernel matrices obtained from pointwise evaluations of the covariance kernel, and its partial derivatives, a result of the PDE constraint and for which fast algorithms are scarce. The primary goal of this paper is to provide a near-linear complexity algorithm for working with such kernel matrices. We present a sparse Cholesky factorization algorithm for these matrices based on the near-sparsity of the Cholesky factor under a novel ordering of pointwise and derivative measurements. The near-sparsity is rigorously justified by directly connecting the factor to GP regression and exponential decay of basis functions in numerical homogenization. We then employ the Vecchia approximation of GPs, which is optimal in the Kullback-Leibler divergence, to compute the approximate factor. This enables us to compute ϵ-approximate inverse Cholesky factors of the kernel matrices with complexity O(N log d (N/ϵ)) in space and O(N log 2d (N/ϵ)) in time. We integrate sparse Cholesky factorizations into optimization algorithms to obtain fast solvers of the nonlinear PDE. We numerically illustrate our algorithm’s near-linear space/time complexity for a broad class of nonlinear PDEs such as the nonlinear elliptic, Burgers, and Monge-Ampère equations. In summary, we provide a fast, scalable, and accurate method for solving general PDEs with GPs and kernel methods.
Using Machine-Learning Methods and Expert Prediction Probabilities to Forecast Solar Flares
It has long been known that studying connection between solar flares and properties of magnetic field in active regions is very important for understanding the flare physics and developing space weather forecasts. The Helioseismic and Magnetic Imager onboard the Solar Dynamics Observatory (SDO/HMI) obtains tremendous amounts of magnetic field data products. However the operational NOAA Space Weather Prediction Center (SWPC) forecasts of solar flares still represent prediction probabilities issued by the experts. In this research we investigate the possibilities to enhance the daily operational flare forecasts performed at the SWPC by developing a synergy of the expert predictions and physics-based criteria, and by employing machine-learning methods. Among the physics-based criteria we consider the descriptors of the Polarity Inversion Line (PIL) and Space weather HMI Active Region Patches (SHARP), and derive from them daily characteristics of the entire Sun. We also consider the daily descriptors of the GOES Soft X-Ray (SXR) 1-8 Angstroms flux such as the flare history of the previous days and averaged X-Ray flux. We estimate the effectiveness in separation of flaring and non-flaring cases for each characteristic, as well as for the expert prediction probabilities, and find that some PIL, SHARP and SXR descriptors are as effective as the expert prediction probabilities and should be considered to issue the flare forecast. Finally, we train and test several Machine-Learning classification algorithms (Support Vector Classifiers with various kernel functions, k-Nearest Neighbor Classifier, Random Forest Classifier, and Neural Networks) using the most effective descriptors and expert prediction probabilities, and compare the obtained predictions with the current SWPC forecasts.
Tensorized Feature Spaces for Feature Explosion
In this paper 1 1 This manuscript has been authored by UT-Battelle, LLC under Contract No. DE-AC05-000R22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan) This research used resources of the Oak Ridge Leadership Computing Facility, which is a DOE Office of Science User Facility supported under Contract DE-AC05-000R22725., we present a novel framework that uses tensor factorization to generate richer feature spaces for pixel classification in hyperspectral images. In particular, we assess the performance of different tensor rank decomposition methods as compared to the traditional kernel-based approaches for the hyperspectral image classification problem. We propose Orion, which takes as input a hyperspectral image tensor and a rank and outputs an enhanced feature space from the factor matrices of the decomposed tensor. Our method is a feature explosion technique that inherently maps low dimensional input space in $\mathbb{R}^{K}$ to high dimensional space in $\mathbb{R}^{R}$ , where $R\gg K$ , say in the order of 1000x, like a kernel. We show how the proposed method exploits the multi-linear structure of hyperspectral three dimensional tensor. We demonstrate the effectiveness of our method with experiments on three publicly available hyperspectral datasets with labeled pixels and compare their classification performance against traditional linear and non-linear supervised learning methods such as SVM with Linear, Polynomial, RBF kernels, and the Multi-Layer Perceptron model. Finally, we explore the relationship between the rank of the tensor decomposition and the classification accuracy using several hyperspectral datasets with ground truth.
Kohn–Sham accuracy from orbital-free density functional theory via Δ-machine learning
Here, we present a Δ-machine learning model for obtaining Kohn–Sham accuracy from orbital-free density functional theory (DFT) calculations. In particular, we employ a machine-learned force field (MLFF) scheme based on the kernel method to capture the difference between Kohn–Sham and orbital-free DFT energies/forces. We implement this model in the context of on-the-fly molecular dynamics simulations and study its accuracy, performance, and sensitivity to parameters for representative systems. We find that the formalism not only improves the accuracy of Thomas–Fermi–von Weizsäcker orbital-free energies and forces by more than two orders of magnitude but is also more accurate than MLFFs based solely on Kohn–Sham DFT while being more efficient and less sensitive to model parameters. We apply the framework to study the structure of molten Al 0.88 Si 0.12 , the results suggesting no aggregation of Si atoms, in agreement with a previous Kohn–Sham study performed at an order of magnitude smaller length and time scales.
QASMBench: A Low-Level Quantum Benchmark Suite for NISQ Evaluation and Simulation
The rapid development of quantum computing (QC) in the NISQ era urgently demands a low-level benchmark suite and insightful evaluation metrics for characterizing the properties of prototype NISQ devices, the efficiency of QC programming compilers, schedulers and assemblers, and the capability of quantum system simulators in a classical computer. In this work, we fill this gap by proposing a low-level, easy-to-use benchmark suite called QASMBench based on the OpenQASM assembly representation. It consolidates commonly used quantum routines and kernels from a variety of domains including chemistry, simulation, linear algebra, searching, optimization, arithmetic, machine learning, fault tolerance, cryptography, and so on, trading-off between generality and usability. To analyze these kernels in terms of NISQ device execution, in addition to circuit width and depth, we propose four circuit metrics including gate density, retention lifespan, measurement density, and entanglement variance, to extract more insights about the execution efficiency, the susceptibility to NISQ error, and the potential gain from machine-specific optimizations. Applications in QASMBench can be launched and verified on several NISQ platforms, including IBM-Q, Rigetti, IonQ and Quantinuum. For evaluation, we measure the execution fidelity of a subset of QASMBench applications on 12 IBM-Q machines through density matrix state tomography, comprising 25K circuit evaluations. In addition we also compare the fidelity of executions among the IBM-Q machines, the IonQ QPU and the Rigetti Aspen M-1 system.
Navigating Transition-Metal Chemical Space: Artificial Intelligence for First-Principles Design
Conspectus The variability of chemical bonding in open-shell transition-metal complexes not only motivates their study as functional materials and catalysts but also challenges conventional computational modeling tools. Here, tailoring ligand chemistry can alter preferred spin or oxidation states as well as electronic structure properties and reactivity, creating vast regions of chemical space to explore when designing new materials atom by atom. Although first-principles density functional theory (DFT) remains the workhorse of computational chemistry in mechanism deduction and property prediction, it is of limited use here. DFT is both far too computationally costly for widespread exploration of transition-metal chemical space and also prone to inaccuracies that limit its predictive performance for localized d electrons in transition-metal complexes. These challenges starkly contrast with the well-trodden regions of small-organic-molecule chemical space, where the analytical forms of molecular mechanics force fields and semiempirical theories have for decades accelerated the discovery of new molecules, accurate DFT functional performance has been demonstrated, and gold-standard methods from correlated wavefunction theory can predict experimental results to chemical accuracy. The combined promise of transition-metal chemical space exploration and lack of established tools has mandated a distinct approach. In this Account, we outline the path we charted in exploration of transition-metal chemical space starting from the first machine learning (ML) models (i.e., artificial neural network and kernel ridge regression) and representations for the prediction of open-shell transition-metal complex properties. The distinct importance of the immediate coordination environment of the metal center as well as the lack of low-level methods to accurately predict structural properties in this coordination environment first motivated and then benefited from these ML models and representations. Once developed, the recipe for prediction of geometric, spin state, and redox potential properties was straightforwardly extended to a diverse range of other properties, including in catalysis, computational “feasibility”, and the gas separation properties of periodic metal–organic frameworks. Interpretation of selected features most important for model prediction revealed new ways to encapsulate design rules and confirmed that models were robustly mapping essential structure–property relationships. Encountering the special challenge of ensuring that good model performance could generalize to new discovery targets motivated investigation of how to best carry out model uncertainty quantification. Distance-based approaches, whether in model latent space or in carefully engineered feature space, provided intuitive measures of the domain of applicability. With all of these pieces together, ML can be harnessed as an engine to tackle the large-scale exploration of transition-metal chemical space needed to satisfy multiple objectives using efficient global optimization methods. In practical terms, bringing these artificial intelligence tools to bear on the problems of transition-metal chemical space exploration has resulted in ML-model assessments of large, multimillion compound spaces in minutes and validated new design leads in weeks instead of decades.