Learning of Discrete Graphical Models with Neural Networks
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This PowerPoint presentation was presented virtually at the American Geophysical Union (AGU) Fall Meeting 2020.
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Nonlinear power flow constraints render a variety of power system optimization problems computationally intractable. Emerging research shows, however, that the nonlinear AC power flow equations can be successfully modeled using neural networks. These neural networks can be exactly transformed into mixed integer linear programs and embedded inside challenging optimization problems, thus replacing nonlinearities that are intractable for many applications with tractable piecewise linear approximations. Such approaches, though, suffer from an explosion of the number of binary variables needed to represent the neural network. Accordingly, this paper develops a technique for training an "optimally compact'' neural network, i.e., one that can represent the power flow equations with a sufficiently high degree of accuracy while still maintaining a tractable number of binary variables. We demonstrate the use of this neural network as an approximator of the nonlinear power flow equations by embedding it in the AC unit commitment problem, transforming the problem from a mixed integer nonlinear program into a more manageable mixed integer linear program. We use the 14-, 57-, and 89-bus networks as test cases and compare the AC-feasibility of commitment decisions resulting from the neural network, DC, and linearized power flow approximations. Our results show that the neural network model outperforms both the DC and linearized power flow approximations when embedded in the unit commitment problem. The neural network formulation most often selects a feasible unit commitment schedule, and furthermore, it only s
High-density synchrophasors provide valuable information for power grid situational awareness, operation and control. Unfortunately, due to factors including communication instability and hardware failure, their data quality can be greatly deteriorated by anomalies. Since the anomalies can impact the performance of the synchrophasor applications, it is of paramount significance to propose a model to detect anomalies in synchrophasor. In this study, a convolutional neural network model is established to detect and classify the anomalies in the synchrophasor measurements. Additionally, four types of anomalies observed in actual synchrophasors including erroneous patterns, random spikes, missing points and high-frequency interferences are considered in this study. The proposed model is extensively evaluated via field-collected measurements from the synchrophasor network in Jiangsu grid, China. The superior performance of the proposed model indicates the great potential of using deep learning for the detection of abnormal synchrophasor measurements.
Multiverse is a code repository for a set of tools for Bayesian model selection for neural networks. The goal of the tools is to provide capabilities for selecting among prior and model specifications for Bayesian neural networks. Multiverse will include tools for creating Bayesian neural networks, evaluating the Bayesian model evidence, and performing inference in Bayesian neural networks. These components are written in Python, a high-level programming language that takes advantage of the Python ecosystem of high-quality open-source packages for machine learning and signal processing.
The recent success of deep neural network models with physical constraints (so-called, Physics-Informed Neural Networks, PINNs) has led to renewed interest in the incorporation of mechanistic information in predictive models. Statisticians and others have long been interested in this problem, which has led to several practical and innovative solutions dating back decades. In this overview, we focus on the problem of data-driven prediction and inference of dynamic spatio-temporal processes that include mechanistic information, such as would be available from partial differential equations, with a strong focus on the quantification of uncertainty associated with data, process, and parameters. Here, we give a brief review of several paradigms and focus our attention on Bayesian implementations given they naturally accommodate uncertainty quantification. We then show that it is straight-forward to include the Bayesian PINN (B-PINN) within the Bayesian hierarchical model (BHM) framework that has long been considered for modeling dynamic spatio-temporal processes. Such a BHM-PINN is illustrated via a simulation study in which a latent nonlinear Burgers’ equation PDE governs the dynamics of Poisson distributed spatio-temporal data. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.
To expedite new molecular compound development, a long-sought goal within the chemistry community has been to predict molecules’ bulk properties of interest a priori to synthesis from a chemical structure alone. In this work, we demonstrate that machine learning methods can indeed be used to directly learn the relationship between chemical structures and bulk crystalline properties of molecules, even in the absence of any crystal structure information or quantum mechanical calculations. We focus specifically on a class of organic compounds categorized as energetic materials called high explosives (HE) and predicting their crystalline density. An ongoing challenge within the chemistry machine learning community is deciding how best to featurize molecules as inputs into machine learning models—whether expert handcrafted features or learned molecular representations via graph-based neural network models—yield better results and why. We evaluate both types of representations in combination with a number of machine learning models to predict the crystalline densities of HE-like molecules curated from the Cambridge Structural Database, and we report the performance and pros and cons of our methods. Our message passing neural network (MPNN) based models with learned molecular representations generally perform best, outperforming current state-of-the-art methods at predicting crystalline density and performing well even when testing on a data set not representative of the training data. However, these models are traditionally considered black boxes and less easily interpretable. Here, to address this common challenge, we also provide a comparison analysis between our MPNN-based model and models with fixed feature representations that provides insights as to what features are learned by the MPNN to accurately predict density.
This paper presents an uncertainty quantification (UQ) framework for the physics-based model prediction of material response with a large number of parameters. The application problem presented in this work is that of predicting creep in Grade 91 steel at 600°C. The material response is defined with a physically based microstructural model with constitutive equations emulating several observed phenomena in Grade 91 and embodied into an explicit geometry mesoscale finite element model for prior austenite grains and grain boundaries. Creep within the grains and in grain boundaries are represented by crystal plasticity for dislocation motion and a physics-based model for cavity growth and nucleation, respectively. The creep behavior of this material is influenced by several parameters, some of which have a wide range of variation based on experimental data. UQ combined with microstructural modeling can discover the core microstructural causes of experimental variability, leading to improved materials with lower variability in critical long-term material properties. In this study, we investigate the model's uncertainty to identify material properties that may be modified during production to increase creep life and analyze different components of the crystal plasticity model for improvements. For this purpose, a quantity of interest is defined as time to minimum creep rate, which correlates well to the creep failure of the material. A deep neural network model was trained and validated to be used as a surrogate for the finite element model. Then, a variance-based sensitivity analysis is performed on the surrogate model to find the Sobol indices of the input parameters in respect to the output quantity of interest. The Sobol indices are used to reduce the dimensionality of the model. Generalized polynomial chaos expansion is used on the reduced basis models to propagate the uncertainty from the input parameters to the quantity of interest using the deep neural network surrogate model. These results are benchmarked against uncertainty propagation using Monte Carlo simulations. In conclusion, the UQ performed through the reduced basis model captures almost all the uncertainty in the model with significantly fewer simulations, making it possible to perform the UQ directly via simulations with the finite element model rather than surrogate machine-learned models.
Accurately predicting small molecule partitioning and hydrophobicity is critical in the drug discovery process. There are many heterogeneous chemical environments within a cell and entire human body. For example, drugs must be able to cross the hydrophobic cellular membrane to reach their intracellular targets, and hydrophobicity is an important driving force for drug–protein binding. Atomistic molecular dynamics (MD) simulations are routinely used to calculate free energies of small molecules binding to proteins, crossing lipid membranes, and solvation but are computationally expensive. Machine learning (ML) and empirical methods are also used throughout drug discovery but rely on experimental data, limiting the domain of applicability. We present atomistic MD simulations calculating 15,000 small molecule free energies of transfer from water to cyclohexane. This large data set is used to train ML models that predict the free energies of transfer. We show that a spatial graph neural network model achieves the highest accuracy, followed closely by a 3D-convolutional neural network, and shallow learning based on the chemical fingerprint is significantly less accurate. A mean absolute error of ~4 kJ/mol compared to the MD calculations was achieved for our best ML model. We also show that including data from the MD simulation improves the predictions, tests the transferability of each model to a diverse set of molecules, and show multitask learning improves the predictions. This work provides insight into the hydrophobicity of small molecules and ML cheminformatics modeling, and our data set will be useful for designing and testing future ML cheminformatics methods.
Power system frequency disturbances are caused by various generation and transmission events including generator trips, load disconnections, line trips, etc. Accurate detections of the events are crucial to bulk power system situation awareness and event investigation. This paper utilizes the recent advances of deep learning to build a convolutional neural network model to detect events in an accurate yet straightforward manner. Herein, the rate of change of frequency and the relative angle shift are converted to images as the inputs of the proposed model. Finally, this paper uses two convolutional neural networks and classifier fusion to achieve the detection result. Compared with the conventional event detection algorithm and the frequency only deep learning model, the proposed model improves the detection accuracy by over 48%. As a promising tool for bulk power system situation awareness, the proposed model requires a short decision time, which is suitable for practical scenarios.
4 page paper submitted to ANS Student conference. Summary of paper similar to the following abstract: The ability to predict how a reactor will operate, understand when anomalous conditions arise, and ensure a reactor is being operated as expected is crucial for deploying new nuclear facilities. Digital twins serve as a unique solution to recognizing reactor behavior; however, they require data to be useful. For next-generation reactors, this data may not currently be available. To explore how synthetic physics-informed reactor data can be used to predict reactor operations, a recurrent neural network was implemented for the Idaho State University AGN-201 digital twin. The goal of this work is to determine how synthetic data can be used to train a recurrent neural network model for predicting the reactor power of the AGN-201. The recurrent neural network was validated using both synthetic and real operational data. We envision this approach will help bridge the gap between the virtual and physical sides of a digital twin, where reactor physics models based on as-built data can be corrected for actual operating parameters to ensure the virtual model mirrors reality.
Sparse deep neural networks have gained increasing attention recently in achieving speedups on inference with reduced memory footprints. However, the real-world applications are little shown with specialized optimizations, yet a wide variety of DNN tasks remain dense without exploiting the advantages of sparsity in networks. Recent work presented by MIT/IEEE/Amazon GraphChallenge has demonstrated significant speedups and various techniques. Still, we find that there is limited investigation of the impact of various Python and C\slash C++ based programming models to explore new opportunities in general cases. In this work, we provide performance evaluation through different programming models using CuPy, cuSPARSE, and OpenMP to discuss the advantages and disadvantages of our sparse implementations on single-GPU and multiple GPUs of NVIDIA DGX-A100 40GB/80GB platforms.
We investigate the use of approximate Bayesian neural networks (BNNs) in modeling hundreds of time delay gravitational lenses for Hubble constant (H 0 ) determination. Here, our BNN was trained on synthetic Hubble Space Telescope quality images of strongly lensed active galactic nuclei with lens galaxy light included. The BNN can accurately characterize the posterior probability density functions (PDFs) of model parameters governing the elliptical power-law mass profile in an external shear field. We then propagate the BNN-inferred posterior PDFs into an ensemble H 0 inference, using simulated time delay measurements from a plausible dedicated monitoring campaign. Assuming well-measured time delays and a reasonable set of priors on the environment of the lens, we achieve a median precision of 9.3% per lens in the inferred H 0 . A simple combination of a set of 200 test lenses results in a precision of 0.5 km s –1 Mpc –1 (0.7%), with no detectable bias in this H 0 recovery test. The computation time for the entire pipeline—including the generation of the training set, BNN training and H0 inference—translates to 9 minutes per lens on average for 200 lenses and converges to 6 minutes per lens as the sample size is increased. Being fully automated and efficient, our pipeline is a promising tool for exploring ensemble-level systematics in lens modeling for H 0 inference.
Abstract Particle accelerators are complex and comprise thousands of components, with many pieces of equipment running at their peak power. Consequently, they can fault and abort operations for numerous reasons, lowering efficiency and science output. To avoid these faults, we apply anomaly detection techniques to predict unusual behavior and perform preemptive actions to improve the total availability. Supervised machine learning (ML) techniques such as siamese neural network models can outperform the often-used unsupervised or semi-supervised approaches for anomaly detection by leveraging the label information. One of the challenges specific to anomaly detection for particle accelerators is the data’s variability due to accelerator configuration changes within a production run of several months. ML models fail at providing accurate predictions when data changes due to changes in the configuration. To address this challenge, we include the configuration settings into our models and training to improve the results. Beam configurations are used as a conditional input for the model to learn any cross-correlation between the data from different conditions and retain its performance. We employ conditional siamese neural network (CSNN) models and conditional variational auto encoder (CVAE) models to predict errant beam pulses at the spallation neutron source under different system configurations and compare their performance. We demonstrate that CSNNs outperform CVAEs in our application.
With a goal of exploiting additive manufacturing to improve the manufacturing of existing reactor materials, we developed a chemical composition-based machine learning model to predict the printability of any given alloy in laser powder bed fusion (L-PBF) using experimental data from peer-reviewed literature. We defined printability as the ability to avoid defects like cracking, balling, porosity, and lack of fusion, that are caused by thermal stresses (during solidification or liquation), molten pool disintegration into disconnected small beads or lack of heat input respectively. Our models predict the tendency of balling defect formation and porosity percentage for a given composition, under a given set of processing conditions. To predict the likelihood of balling defect, three models: a random forest classifier, a gradient boost regressor and a neural network were trained on a dataset containing both traditional alloys and high entropy alloys. The neural network model showed the highest accuracy of 92.3 % in predicting the balling defect formation. A random forest regressor, gradient boost regressor and neural network were trained and tested on a dataset of various alloys to predict porosity. The random forest regressor showed the best predictions with an R 2 score of 0.97. The models also revealed the relative importance of the input descriptors on defect-formation tendency. Of particular significance was the identification of carbon as an important element in determining the occurrence of balling and percent porosity in alloys like steel, as well as being moderately important to the percentage porosity in other alloys as well as steel. Manganese was also identified as a key descriptor for the percentage of porosity in steel and other alloys. Manganese’s low thermal conductivity and consistent presence in the dataset is the likely cause for its contribution. Carbon’s role is attributable to its relatively high specific heat and high melting temperature. In conclusion, our model serves as a swift, chemistry-based tool to design experiments and find modified compositions better suited for additive manufacturing.
Electrochemical reduction of CO 2 gas is a novel CO 2 utilization technique that has the potential to mitigate the global climate crisis caused by anthropogenic CO 2 emissions, and enable the large-scale storage of energy generated from renewable sources in the form of carbon-based chemicals and fuels. However, due to the complexity of the electrochemical reactions, the explicit first-principles models for CO2 reduction are not available yet, and there has been a limited effort to develop process modeling, optimization and control of CO 2 electrochemical reactors. To this end, a rotating cylinder electrode (RCE) reactor has been constructed at UCLA to understand the mass transfer and reaction kinetics effects separately on the productivity. In the RCE reactor, the applied potential strongly influences the reaction energetics and the electrode rotation speed affects the hydrodynamic boundary layer and modifies the film mass transfer coefficient, which involves convective and diffusive transport. Further, the present work aims to develop a multi-input multi-output (MIMO) control scheme for the RCE reactor that integrates techniques from artificial and recurrent neural network modeling, nonlinear optimization, and process controller design. Specifically, production rates of two products from the experimental reactor, ethylene and carbon monoxide, are controlled by manipulating two inputs, applied potential and catalyst rotation speed. Process dynamics and controllability are analyzed, a feedback control strategy is designed and the controllers are tuned accordingly. The experimental electrochemical cell is employed to gather data for process modeling and implement the multivariable control system. Finally, the experimental results are presented which demonstrate excellent closed-loop performance by the control system and regulation of the outputs at three different set-points including an economically-optimal set-point.