Solving inverse problems using conditional invertible neural networks
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Anantha Padmanabha, Govinda↗
SEARCH · Engineering Papers
Results for “conditional invertible neural network”
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Solving high-dimensional inverse problems using amortized likelihood-free inference with noisy and incomplete data
Here, we present a likelihood-free probabilistic inversion method based on normalizing flows for high-dimensional inverse problems. The proposed method is composed of two complementary networks: a summary network for data compression and an inference network for parameter estimation. The summary network encodes raw observations into a fixed-size vector of summary features, while the inference network generates samples of the approximate posterior distribution of the model parameters based on these summary features. The posterior samples are produced in a deep generative fashion by sampling from a latent Gaussian distribution and passing these samples through an invertible transformation. We construct this invertible transformation by sequentially alternating conditional invertible neural network and conditional neural spline flow layers. The summary and inference networks are trained simultaneously. We apply the proposed method to an inversion problem in groundwater hydrology to estimate the posterior distribution of the log-conductivity field conditioned on spatially sparse time-series observations of the system’s hydraulic head responses. The conductivity field is represented with 706 degrees of freedom in the considered problem. Comparison with the likelihood-based iterative ensemble smoother PEST-IES method demonstrates that the proposed method accurately estimates the parameter posterior distribution and the observations’ predictive posterior distribution at a fraction of the inference time of PEST-IES.
conditional invertible neural network↗
Convolutional Neural Network-Based Protection-Zone Classification of Faults in Distribution Feeders with Photovoltaics.
Fault detection and isolation is critical for reliable operation of distribution systems. The ride-through requirements for the distributed energy resources (DER), mandated by the IEEE 1547-2018 standard, makes it challenging to use undervoltage (UV) conditions for fault detection. In addition, with low fault current contribution from these inverter-based DERs, the time-overcurrent relays are also less effective. Thus motivated, this paper presents a learning-based approach for fault detection and localization. A convolutional neural network (CNN)-based model is proposed which uses local voltage and current waveforms from DER locations and feeder substations, for training a zonal classifier. The classifier can be adopted into any relay-like device for discriminating between faults originating from different protection zones. The performance of the proposed approach was tested on publicly available test feeders with distributed photovoltaics (PVs).
Fault localization, convolutional neural networks,↗
Assessing parallel path cooling tower performance via artificial neural networks
Real-time monitoring of a research nuclear reactor, a system in which all generated power is dissipated to the environment, can be performed via analysis of the heat rejection from the cooling system. Given an inlet water temperature and flow rate, the reactor power can be well-approximated from the outlet water temperature; however, the instrumentation to measure outlet conditions may not be robust or accurate. If we know how a cooling tower performs from historical data, but cannot measure the outlet temperature, a mathematical representation of the system can be inverted to obtain the outlet water temperature that describes the cooling capacity. Unfortunately, model inversion processes are computationally expensive. To address this, an artificial neural network (ANN) is implemented to assess the performance of a multi-cell cooling tower for a nuclear reactor. This approach leverages the Merkel model to obtain an extensive data set describing performance of the cooling tower cells throughout a wide array of potential operating conditions. The Merkel model is expressed as a function of four parameters: the inlet and outlet water temperatures, inlet air wet bulb temperature, and ratio of liquid-to-gas mass flow rates (L/G), which together provide a non-dimensional number indicative of cooling tower performance, called the Merkel integral. Computing a 4-dimensional data structure that describes finite combinations of the Merkel integral, an inverse model is then generated using an ANN to determine the cell outlet water temperature from the other three model parameters along with the computed Merkel integral. Compared to traditional model inversion methods, the ANN reduces the computational time by approximately 4 orders of magnitude, with effectively no sacrifice to solution accuracy, and could be applied for different cooling towers in the event the performance curve is known. Finally, three use cases of the ANN are then reviewed: (1) determining the cell outlet water temperatures when gas flow at rated conditions (GFRC) is known, (2) performing the prior case without knowledge of the GRFC, and (3) assessing performance differences between the individual tower cells.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Methodologies for Adaptive Flight Envelope Estimation and Protection
This paper reports the latest development of several techniques for adaptive flight envelope estimation and protection system for aircraft under damage upset conditions. Through the integration of advanced fault detection algorithms, real-time system identification of the damage/faulted aircraft and flight envelop estimation, real-time decision support can be executed autonomously for improving damage tolerance and flight recoverability. Particularly, a bank of adaptive nonlinear fault detection and isolation estimators were developed for flight control actuator faults; a real-time system identification method was developed for assessing the dynamics and performance limitation of impaired aircraft; online learning neural networks were used to approximate selected aircraft dynamics which were then inverted to estimate command margins. As off-line training of network weights is not required, the method has the advantage of adapting to varying flight conditions and different vehicle configurations. The key benefit of the envelope estimation and protection system is that it allows the aircraft to fly close to its limit boundary by constantly updating the controller command limits during flight. The developed techniques were demonstrated on NASA s Generic Transport Model (GTM) simulation environments with simulated actuator faults. Simulation results and remarks on future work are presented.
Tang, Liang↗
Machine Learning-Driven Reliability Estimation of PV Inverters Considering Alert-Ambient Variability
Weather-induced spatio-temporal degradation limits outdoor PV inverter lifetime and reliability, necessitating advanced data analysis. This study employs a top-down, data-driven approach utilizing multiple machine learning (ML) algorithms to estimate inverter reliability in a 1.4 MW PV power plant, considering factors such as irradiance, humidity, temperature, time of day, and weather conditions. An extensive alert dataset from 17 identical inverters, including alert types, propagation, and frequency, reveals significant correlations with environmental factors and inverter output power, enabling the construction of a performance reliability model. Dual-stage supervised-ML models are evaluated for accuracy, with the ‘classification-regression’ model by an artificial neural network (ANN) tested on the averaged “Alert-Ambient” dataset, which is outperformed by ‘clustering-regression’ models using random forest (RF) and K-Nearest Neighbors (KNN) on individual inverter datasets. K-means clustering applies principal component analysis to reduce dimensions, achieving improved accuracy beyond the 80% achieved by ANN on the averaged dataset. Second-stage regression estimates inverter reliability with a mean square error of 0.0195 on the averaged dataset and as low as 0.002 on individual inverter datasets using RF. Furthermore, these findings highlight the method's suitability for estimating PV inverter output reliability under ambient conditions, essential for digital twin development and related applications.
14 SOLAR ENERGY↗
Adaptation of virtual synchronous generators to dynamic conditions in power grids
Virtual synchronous generators (VSGs) are widely adopted as grid-forming controls for inverter-based resources. However, when grid conditions vary significantly as characterized by changes in short-circuit ratio (SCR) and the reactance-to-resistance (X/R) ratio, fixed-gain designs and the commonly used P–Q decoupling assumption can become inaccurate. Such conditions can degrade transient power performance, leading to oscillations, prolonged settling, and overshoot, particularly in stiff-grid operating points. This paper quantifies how grid strength and impedance-dependent coupling affect the active–reactive power dynamics of a conventional VSG over a broad range of SCR and X/R values. An adaptive VSG tuning framework is then developed by combining (i) a coupling-explicit, impedance-parameterized state-space model to enable systematic controller synthesis, (ii) a full-state-feedback law designed via pole placement to meet prescribed damping and settling-time specifications, and (iii) a physics-informed neural network (PINN)–based online grid-impedance estimator that updates controller gains in real time as grid conditions vary. Offline simulations in MATLAB/Simulink and real-time validation on an OPAL-RT platform show that the proposed method preserves consistent damping and settling behavior with reduced overshoot across wide SCR and X/R ranges, compared with fixed-gain VSG baselines.
Adaptive control↗
Concept, Simulation, and Instrumentation for Radiometric Inflight Icing Detection
The multi-agency Flight in Icing Remote Sensing Team (FIRST), a consortium of the National Aeronautics and Space Administration (NASA), the Federal Aviation Administration (FAA), the National Center for Atmospheric Research (NCAR), the National Oceanographic and Atmospheric Administration (NOAA), and the Army Corps of Engineers (USACE), has developed technologies for remotely detecting hazardous inflight icing conditions. The USACE Cold Regions Research and Engineering Laboratory (CRREL) assessed the potential of onboard passive microwave radiometers for remotely detecting icing conditions ahead of aircraft. The dual wavelength system differences the brightness temperature of Space and clouds, with greater differences potentially indicating closer and higher magnitude cloud liquid water content (LWC). The Air Force RADiative TRANsfer model (RADTRAN) was enhanced to assess the flight track sensing concept, and a 'flying' RADTRAN was developed to simulate a radiometer system flying through simulated clouds. Neural network techniques were developed to invert brightness temperatures and obtain integrated cloud liquid water. In addition, a dual wavelength Direct-Detection Polarimeter Radiometer (DDPR) system was built for detecting hazardous drizzle drops. This paper reviews technology development to date and addresses initial polarimeter performance.
Ryerson, Charles↗
Voltage Probability Density Function Shaping Control Strategy Considering Grid Operational Uncertainties
It is well-known that power systems operation always affected by various uncertainties which make the bus voltage a random process that can be characterized by its probability density function (PDF) at any time instant. In this context, this paper presents a novel PDF-based voltage control framework for power systems. By modeling voltage as a stochastic process, we formulate a stochastic differential equationthat captures grid uncertainties. The associated Fokker-Planck-Kolmogorov equation is derived to describe the evolution of the voltage PDF, which enables the formulation of a PDF-shaping control strategy. To simplify the PDF control formulation, a B-spline neural network is introduced for real-time estimation and regulation of the voltage distribution. The proposed PDF control law updates voltage references for energy storage systems and synchronous generators using real-time PDF measurements and feedback signals. The proposed method is validated on a modified Kundur’s two-area system. Simulation results demonstrate that the controller can significantly improve the voltage stability under stochastic conditions, highlighting its effectiveness in modern inverter-rich grids.
Gui, Yonghao [ORNL] (ORCID:0000000250435534)↗
Reconstructing cosmological initial conditions from late-time structure with convolutional neural networks
ABSTRACT We present a method to reconstruct the initial linear-regime matter density field from the late-time non-linearly evolved density field in which we channel the output of standard first-order reconstruction to a convolutional neural network (CNN). Our method shows dramatic improvement over the reconstruction of either component alone. We show why CNNs are not well-suited for reconstructing the initial density directly from the late-time density: CNNs are local models, but the relationship between initial and late-time density is not local. Our method leverages standard reconstruction as a preprocessing step, which inverts bulk gravitational flows sourced over very large scales, transforming the residual reconstruction problem from long-range to local and making it ideally suited for a CNN. We develop additional techniques to account for redshift distortions, which warp the density fields measured by galaxy surveys. Our method improves the range of scales of high-fidelity reconstruction by a factor of 2 in wavenumber above standard reconstruction, corresponding to a factor of 8 increase in the number of well-reconstructed modes. In addition, our method almost completely eliminates the anisotropy caused by redshift distortions. As galaxy surveys continue to map the Universe in increasingly greater detail, our results demonstrate the opportunity offered by CNNs to untangle the non-linear clustering at intermediate scales more accurately than ever before.
Astronomy & Astrophysics↗
Using neural networks to assist in OPAD data analysis
The space shuttle main engine (SSME) became the subject of plume emission spectroscopy in 1986 when researchers from NASA-Marshall Space Flight Center (MSFC), Arnold Engineering Development Center (AEDC), and Rocketdyne went to the SSME test stands at the NASA-Stennis Space Center and at Rocketdyne's Santa Susan Field Laboratory to optically observe the plume. Since then, plume spectral acquisitions have recorded many nominal tests and the qualitative spectral features of the SSME plume are now well established. Significant discoveries made with both wide-band and narrow-band plume emission spectroscopy systems led MSFC to promote the Optical Plume Anomaly Detection (OPAD) program with a goal of instrumenting all SSME test stands with customized spectrometer systems. A prototype OPAD system is now installed on the SSME Technology Test Bed (TTB) at MSFC. The OPAD system instrumentation consists of a broad-band, optical multiple-channel analyzer (OMA) and a narrow-band device called a polychrometer. The OMA is a high-resolution (1.5-2.0 Angstroms) 'super-spectrometer' covering the near-ultraviolet to near-infrared waveband (2800-7400 Angstroms), providing two scans per second. The polychrometer consists of sixteen narrow-band radiometers: fourteen monitoring discrete wavelengths of health and condition monitoring elements and two dedicated to monitoring background emissions. All sixteen channels are capable of providing 500 samples per second. To date, the prototype OPAD system has been used during 43 SSME firings on the TTB, collecting well over 250 megabytes of plume spectral data. One goal of OPAD data analysis is to determine interatively with the help of a computer code, SPECTRA4, developed at AEDC. Experience has shown that iteration with SPECTRA4 is an incredibly labor intensive task and not one to be performed by band. What is really needed is the 'inverse' of SPECTRA4 but the mathematical model for this inverse mapping is tenuous at best. However, the robustness of PSECTRA4 run in the 'forward' direction means that accurate input/output mappings can be obtained. If the mappings were inverted (i.e., input becomes output and output becomes input) then an 'inverse' of SPECTRA4 would be at hand but the 'model' would be specific to the data utilized and would in no way be general. Building a generalized model based upon known input/output mappings while ignoring the details of the governing physical model is possible through the use of a neural network. The research investigation described involves the development of a neural network to provide a generalized 'inverse' of SPECTRA4. The objectives of the research were to design an appropriate neural network architecture, train the network, and then evaluate its performance.
Whitaker, Kevin W.↗
Optimized Gear Selection to Maximize Energy Savings in Electric Traction Drives for Medium and Heavy Duty Vehicles
Multi‑gear transmission systems are commonly used in electric traction drives for medium and heavy‑duty vehicles, while most passenger‑vehicle electric drivetrains rely on a single fixed ratio to reduce cost, weight, and complexity. Using multiple gear ratios can enable downsizing of the motor and inverter while still meeting performance requirements. Additionally, appropriately chosen ratios allow the motor to operate more frequently in high‑efficiency regions, improving overall energy usage and reducing operating costs over the drive cycle. This paper presents a systematic approach for selecting optimal gear ratios for electric drive systems. A neural‑network model is first developed to represent motor losses across the full torque–speed range using data generated from finite element analysis. This model enables fast, accurate evaluation of motor efficiency under varying operating conditions. A genetic‑algorithm‑based optimization framework is then applied to identify gear ratios that maximize energy cost savings over the drive cycle, with the resulting optimal ratios stored for real‑time implementation.
Gadiyar, Nishanth [ORNL] (ORCID:0000000348267524)↗
Comprehensive AI-based System for Control, Sensor Estimation, and Fault Detection of Cascaded Multilevel Inverters
In this paper, an Artificial Intelligence-based (AI) system is proposed for an 11-level cascaded H-bridge multilevel inverter (MLI) with the aims of harmonic suppression and reliability enhancement. The system consists of three seamlessly integrated Neural Networks (NNs). First, a multilayer perceptron is used to generalize the optimal switching angles for selective harmonic elimination under non-equal DC voltages. Next, an autoencoder NN estimates the voltage sensor readings to address potential drifting. Finally, a perceptron NN detects inverter faults based solely on the output voltage of the MLI. Simulation scenarios were evaluated, and the results show that the proposed system provides a comprehensive solution for the robust operation of the MLI. The proposed solution is capable of minimizing the targeted harmonics orders with minimal impact on the fundamental voltage, even when the voltage sensor drifts. Furthermore, the inverter under fault conditions was successfully identified.
Rezende da Costa Reis Kimpara, Renata↗
Adaptive critic design-based reinforcement learning approach in controlling virtual inertia-based grid-connected inverters
In this report, an adaptive critic design (ACD) approach is proposed to control the phase and voltage of a grid-connected virtual synchronous generator (VSG). The penetration of fast responding inertia-less power converters significantly affect the stability of the power system, especially weak systems such as micro grids. The concept of virtual inertia addresses this concern by virtually emulating the behavior of a synchronous generator. However, the conventional VSG is designed based on two conditions: (i) fixed operating point and (ii) inductive grid connections. The performance of VSGs in low-voltage semi-resistive microgrids is far from optimal. To overcome the aforementioned concerns, a heuristic dynamic programing (HDP) approach is proposed to optimally control grid-connected VSGs. The neural-network-based inherence of the HDP enables the proposed technique to adapt to any impedance angle. The HDP controller includes two subnetworks: (i) the action network that controls the system optimally and (ii) the critic network, which evaluates the effectiveness of the action network. The simulation and experimental results are provided to evaluate the effectiveness of the proposed technique. As shown, the HDP-based approach illustrates a better performance in comparison with the conventional PI-based VSG in various operating conditions.
24 POWER TRANSMISSION AND DISTRIBUTION↗
A Barrier-Certificated Reinforcement Learning Approach for Enhancing Power System Transient Stability
Increasing integration of renewable resources brings more flexibility and poses new challenges to modern power systems, leading to highly nonlinear and complex dynamics. Here, this paper aims to provide a general solution framework to traditional control problems, such as frequency control and voltage control, which attempt to maintain the stability of either synchronous generators-governed or inverter-governed systems when subjected to a disturbance and simultaneously guarantee operational constraints, providing a complete complement to existing works on control design. Building on reinforcement learning (RL) and control barrier functions, the framework includes two subsystems, i.e., a model-free controller and a barrier-certification system, which discover RL-based control actions and sequentially filter them using a barrier certificate to satisfy operational constraints. Calculating a barrier function is generally challenging for a complex power system. This is addressed by representing the barrier function using neural networks (NNs) and data-based approaches. An adaptive method is introduced to certify the neural barrier function that perseveres barrier conditions, which is more compatible with online implementation. The proposed framework synthesizes a stabilizing controller that satisfies predefined safety regions. The effectiveness of the proposed framework is demonstrated via several comparative case studies.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Self-organization via active exploration in robotic applications
We describe a neural network based robotic system. Unlike traditional robotic systems, our approach focussed on non-stationary problems. We indicate that self-organization capability is necessary for any system to operate successfully in a non-stationary environment. We suggest that self-organization should be based on an active exploration process. We investigated neural architectures having novelty sensitivity, selective attention, reinforcement learning, habit formation, flexible criteria categorization properties and analyzed the resulting behavior (consisting of an intelligent initiation of exploration) by computer simulations. While various computer vision researchers acknowledged recently the importance of active processes (Swain and Stricker, 1991), the proposed approaches within the new framework still suffer from a lack of self-organization (Aloimonos and Bandyopadhyay, 1987; Bajcsy, 1988). A self-organizing, neural network based robot (MAVIN) has been recently proposed (Baloch and Waxman, 1991). This robot has the capability of position, size rotation invariant pattern categorization, recognition and pavlovian conditioning. Our robot does not have initially invariant processing properties. The reason for this is the emphasis we put on active exploration. We maintain the point of view that such invariant properties emerge from an internalization of exploratory sensory-motor activity. Rather than coding the equilibria of such mental capabilities, we are seeking to capture its dynamics to understand on the one hand how the emergence of such invariances is possible and on the other hand the dynamics that lead to these invariances. The second point is crucial for an adaptive robot to acquire new invariances in non-stationary environments, as demonstrated by the inverting glass experiments of Helmholtz. We will introduce Pavlovian conditioning circuits in our future work for the precise objective of achieving the generation, coordination, and internalization of sequence of actions.
Ogmen, H.↗
A Machine Learning Framework to Predict Images of Edge-on Protoplanetary Disks
The physical structure and properties of protoplanetary disks are typically derived from spatially resolved disk images. Edge-on disks in particular provide an important view point on the vertical structure and degree of settling of disks. Such analyses rely on radiative transfer (RT) calculations that are generally computationally intensive due to the high optical depth of disks. Here we present a machine learning framework that has the potential to dramatically speed up the forward modeling process by approximating the results of RT calculations. This framework, trained on an initial set of RT calculations, utilizes an autoencoder neural network to enable the generation of synthetic scattered light images of edge-on disks directly from a set of physical parameters. We demonstrate that this framework generates synthetic images 2–3 orders of magnitude faster than using RT calculations. These machine learning-generated images appear to approximate the RT images well, in particular preserving their size and shape. We also find a strong correlation between the latent space representations of the generated disk images and several of their associated physical parameters. Finally, we discuss potential changes to the framework, such as methods to further improve the image quality, extending the framework to multiple wavelengths, and inverting the process to infer physical parameters from observed images. Overall, these new tools have the potential to enable a more efficient and uniform analysis of edge-on disk properties and the initial conditions of planet formation.
79 ASTRONOMY AND ASTROPHYSICS↗
Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks
One of the open problems in scientific computing is the long-time integration of nonlinear stochastic partial differential equations (SPDEs), especially with arbitrary initial data. We address this problem by taking advantage of recent advances in scientific machine learning and the spectral dynamically orthogonal (DO) and borthogonal (BO) methods for representing stochastic processes. The recently introduced DO/BO methods reduce the SPDE to solving a system of deterministic PDEs and a system of stochastic ordinary differential equations. Specifically, we propose two new physics-informed neural networks (PINNs) for solving time-dependent SPDEs, namely the neural network (NN)-DO/BO methods. The proposed methods incorporate the DO/BO constraints into the loss function (along with the modal decomposition of the SPDE) with an implicit form instead of generating explicit expressions for the temporal derivatives of the DO/BO modes. Hence, the NN-DO/BO methods can overcome some of the drawbacks of the original DO/BO methods. For example, we do not need the assumption that the covariance matrix of the random coefficients is invertible as in the original DO method, and we can remove the assumption of no eigenvalue crossing as in the original BO method. Moreover, the NN-DO/BO methods can be used to solve time-dependent stochastic inverse problems with the same formulation and same computational complexity as for forward problems. Furthermore, we demonstrate the capability of the proposed methods via several numerical examples, namely: (1) A linear stochastic advection equation with deterministic initial condition: we obtain good results with the proposed methods, while the original DO/BO methods cannot be applied directly in this case. (2) Long-time integration of the stochastic Burgers' equation: we show the good performance of NN-DO/BO methods, especially the effectiveness of the NN-BO approach for such problems with many eigenvalue crossings during the whole time evolution, while the original BO method fails. (3) Nonlinear reaction diffusion equation: we consider both the forward problem and the inverse problems, including very noisy initial point values, to investigate the flexibility of the NN-DO/BO methods in handling inverse and mixed type problems. Taken together, these simulation results demonstrate that the NN-DO/BO methods can be employed to effectively quantify uncertainty propagation in a wide range of physical problems, but future work should address the efficiency issue of PINNs for forward problems.
97 MATHEMATICS AND COMPUTING↗