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At least 73 records · Page 4

Automating Bug Report Classification with Few Shot Learning

Orthogonal defect classification (ODC) is a method used to categorize software defects, providing valuable insights into the development process. This study focuses on automating the classification of software bug reports into different ODC defect types using few shot learning, a machine learning approach that requires minimal labeled data. Previous research has manually classified bug reports or used traditional machine learning algorithms like linear support vector machine, achieving limited success. Our approach uses few shot learning to improve classification accuracy and efficiency. The results show a harmonic mean of recall and precision (i.e., the F1 score) of around 0.6 which is a performance improvement over previous methods. The results highlight the potential benefit of few shot learning techniques and their application in enhancing the safety and reliability of nuclear digital instrumentation and control (DI&C) systems. Future work will explore incorporating advanced techniques to supplement the model's training data and achieve better results.

42 - ENGINEERING

Ca X ML: Chemistry‐informed machine learning explains mutual changes between protein conformations and calcium ions in calcium‐binding proteins using structural and topological features

Proteins' flexibility is a feature in communicating changes in cell signaling instigated by binding with secondary messengers, such as calcium ions, associated with the coordination of muscle contraction, neurotransmitter release, and gene expression. When binding with the disordered parts of a protein, calcium ions must balance their charge states with the shape of calcium-binding proteins and their versatile pool of partners depending on the circumstances they transmit. Accurately determining the ionic charges of those ions is essential for understanding their role in such processes. However, it is unclear whether the limited experimental data available can be effectively used to train models to accurately predict the charges of calcium-binding protein variants. Here, we developed a chemistry-informed, machine-learning algorithm that implements a game theoretic approach to explain the output of a machine-learning model without the prerequisite of an excessively large database for high-performance prediction of atomic charges. We used the ab initio electronic structure data representing calcium ions and the structures of the disordered segments of calcium-binding peptides with surrounding water molecules to train several explainable models. Network theory was used to extract the topological features of atomic interactions in the structurally complex data dictated by the coordination chemistry of a calcium ion, a potent indicator of its charge state in protein. Our design created a computational tool of Ca X ML, which provided a framework of explainable machine learning model to annotate ionic charges of calcium ions in calcium-binding proteins in response to the chemical changes in an environment. Our framework will provide new insights into protein design for engineering functionality based on the limited size of scientific data in a genome space.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Optimization of an aerostructural machining process using physics-guided Bayesian stability modelling

Existing algorithms for predicting milling chatter have not been widely adopted in industry since they require specialized instruments to measure the stability inputs. This study describes how the machining process for a meter-scale aluminum aerostructure was optimized using a physics-guided Bayesian stability model. The study was performed in collaboration with an industrial partner on production machines to evaluate the practicality of the proposed method under real-world conditions. For each cutting tool, the Bayesian approach automatically selected a small number of cutting tests, which were monitored using a microphone to observe the chatter frequency. The algorithm learned the system dynamics, cutting forces, and stability map from these test results. A novel algorithm for predicting tool bending stress was incorporated into the test selection algorithm to avoid tool breakage. On average, each set of optimized cutting parameters required less than six tests to identify and were 97% more productive than baseline parameters from the cutting tool manufacturer. The machining program was then further optimized using commercial feedrate scheduling software to remove cutting force spikes and reduce air cutting time. Five components were machined using the optimized process. These results demonstrate the potential for physics-guided Bayesian models to improve productivity in industrial settings.

Cornelius, Aaron [UT Knoxville]

A Reinforcement Learning Approach to Augment Conventional PID Control in Nuclear Power Plant Transient Operation

The ability of nuclear reactors to operate their power conversion cycles more flexibly will enhance their value to energy grids with variable pricing. Current nuclear control systems are typically classical controllers that are often based on proportional-integral-derivative (PID) control. This paper presents a method of augmenting the existing PID control for difficult transient operations in nuclear power plants using a reinforcement learning–derived feedforward signal applied in real time. The agents, which are trained on a test thermal load-following problem, are designed to improve steam generator outlet temperature control for a range of fast load-following scenarios covering ramp rates from 9%/min to 15%/min. Several reinforcement learning algorithms were initially investigated for the training of the feedforward agents with deep Q-learning (DQN) and proximal policy optimization (PPO) networks, which were found to be the most promising. The DQN controllers utilize discrete actions, giving them a better disturbance rejection at steady state but inconsistent response to initial temperature deviations. In contrast, PPO-trained agents, which take continuous actions except for a dead zone around zero, were shown to have the best combination of high disturbance rejection at steady state and good tracking of the desired temperature value. The ability of the PPO agent was also examined, with the average time of decision making found to be on the order of 1 ms. The fault properties of the controller under the loss of the reinforcement learning agent feedforward signal were also examined. The controller showed strong performance in situations of “no-signal” faults. but was less good at handling “stuck-at” faults, where the feedforward signal remains at a set value. In both cases, however, the PID was able to successfully maintain stability, eventually returning the system to a steady state. It is hoped that this work will allow for the proposed control architecture to be examined for more difficult control problems such that it may eventually be used to adapt existing nuclear plants for more aggressive load-following on grids of the future.

22 GENERAL STUDIES OF NUCLEAR REACTORS

High-Throughput Discovery Illuminates Design Principles and Limits for Long-Lived Charged Species in Organic Electrolytes

The chemical stability of charged molecules in all-organic redox flow batteries (RFBs) is required for the prolonged operation of these devices. Molecular engineering and electrolyte optimization are used to mitigate parasitic reactions and extend the lifetimes of the charge carriers. However, how much can structural variation extend the lifetime? To probe this query, we designed a high-throughput kinetic study of the radical cation of N-methylphenothiazinium, guided by statistical sampling and learning algorithms. Using Argonne’s autonomous discovery facility, we conducted over 6,000 kinetic experiments with robotic sample preparation, parallel kinetic measurements, and machine learning inputs, testing 188 solvent molecules selected from a space of over 540 candidates from 11 chemical classes. Algorithmic selections guided us to stable solvent candidates, which were further tested in high concentration with and without supporting electrolyte. Our findings reveal the inherent difficulty of exceeding the current state of the art through solvent variation. The desired stability is statistically rare and poorly predictable. Among the many tested, only three solvents significantly outperformed our baseline, acetonitrile─and none by more than a factor of 3─suggesting a general challenge in achieving the necessary techno-economic targets. Furthermore, we suggest that self-discharge through solvent homolysis is the cause of the observed limitations. Several structural motifs contribute to >1,000 h half-life stability including molecular simplicity, symmetry, oxidation complement, and strategic fluorination. Importantly, this workflow establishes effective assays for diagnosing and predicting oxidative stress for highly stable liquid electrolytes in all batteries.

Batteries

Machine learning without a processor: Emergent learning in a nonlinear analog network

Standard deep learning algorithms require differentiating large nonlinear networks, a process that is slow and power-hungry. Electronic contrastive local learning networks (CLLNs) offer potentially fast, efficient, and fault-tolerant hardware for analog machine learning, but existing implementations are linear, severely limiting their capabilities. These systems differ significantly from artificial neural networks as well as the brain, so the feasibility and utility of incorporating nonlinear elements have not been explored. Here, we introduce a nonlinear CLLN—an analog electronic network made of self-adjusting nonlinear resistive elements based on transistors. We demonstrate that the system learns tasks unachievable in linear systems, including XOR (exclusive or) and nonlinear regression, without a computer. We find our decentralized system reduces modes of training error in order (mean, slope, curvature), similar to spectral bias in artificial neural networks. The circuitry is robust to damage, retrainable in seconds, and performs learned tasks in microseconds while dissipating only picojoules of energy across each transistor. This suggests enormous potential for fast, low-power computing in edge systems like sensors, robotic controllers, and medical devices, as well as manufacturability at scale for performing and studying emergent learning.

Science & Technology - Other Topics

Impurity gas detection for SNF canisters using probabilistic deep learning and acoustic sensing *

Abstract Monitoring impurity gases in spent nuclear fuel (SNF) canisters is a novel structural health monitoring approach for SNF in dry storage. The SNF canisters are sealed containers that do not facilitate visual access to the inside. Acoustic sensing can be deployed by taking advantage of the pathways unobstructed by internal hardware. Although the ultrasonic time-of-flight measurement can provide valuable information, it is limited in its ability to discern the concentration of only one impurity gas. As such, deep learning algorithms, particularly convolutional neural networks (CNNs), offer a promising solution. In this study, CNN-based probabilistic deep learning models were implemented to detect and quantify multiple impurity gases in helium. An experimental platform was established to simulate canister conditions, and ultrasonic test data were collected. The presence of argon and air in helium at concentrations ranging from 0% to 1.2% at increments of 0.05% was considered. The multi-layer perceptron, decision tree, and logistic regression classifiers achieved high accuracies when distinguishing pure helium from helium with impurities. CNN with dropout layers and CNN using maximum likelihood estimation showed a similar performance, indicating their ability to capture uncertainties. The ensemble CNN model exhibited improved predictions and the ability to balance individual gas concentration by integrating 1D- and 2D-CNN models. These findings contribute probabilistic deep learning solutions for impurity gas detection and analysis within SNF canisters, thus ensuring safe storage and management of SNFs.

47 OTHER INSTRUMENTATION

Enhancing segmentation fairness through curriculum learning and progressive loss: a centralized and federated perspective on radiograph analysis

Bias in medical image segmentation can lead to unequal performance across demographic subgroups, raising concerns about fairness and reliability in clinical AI systems. While deep learning models have achieved high segmentation accuracy, ensuring equitable performance across race and gender remains a significant challenge, particularly in privacy-sensitive healthcare environments. This study investigates fairness-aware medical image segmentation for hip and knee radiographs using deep learning models evaluated in both centralized and Federated Learning (FL) settings. We introduce Curriculum Learning (CL) strategies and Progressive Loss (PL) functions to regulate sample difficulty during training. In addition, we propose two novel fairness-oriented federated learning algorithms, Federated Intersection over Union (FedIoU) and Federated Intersection over Union with Outlier Analysis (FedIoUoutlier). Experiments are conducted using multiple segmentation backbones and simulated multi-site data partitions derived from the Osteoarthritis Initiative dataset. Model performance is evaluated using Intersection over Union (IoU), IoU standard deviation, Skewed Error Ratio (SER), and Min-Max Disparity across race and gender subgroups. Statistical significance was verified using paired t-tests to compare per-sample IoU performance against baseline configurations. Across both hip and knee segmentation tasks, curriculum learning and progressive loss strategies consistently improved segmentation accuracy and reduced demographic performance disparities in centralized training. In federated settings, fairness-aware aggregation further enhanced performance. Notably, FedIoUoutlier combined with balanced curriculum learning and tiered progressive loss achieved the highest mean IoU while yielding the lowest SER and Min-Max Disparity, indicating improved fairness without sacrificing accuracy. In several configurations, federated models matched or exceeded the performance of optimized centralized models, with statistically significant improvements in per-sample IoU over baseline configurations. The results demonstrate that structured training strategies and fairness-aware federated aggregation can jointly improve accuracy, stability, and demographic fairness in medical image segmentation. By integrating curriculum learning, progressive loss, and novel FL algorithms, this work provides a practical pathway toward equitable and privacy-preserving AI systems for medical imaging.

97 MATHEMATICS AND COMPUTING

Machine learning opportunities for nucleosynthesis studies

Nuclear astrophysics is an interdisciplinary field focused on exploring the impact of nuclear physics on the evolution and explosions of stars and the cosmic creation of the elements. While researchers in astrophysics and in nuclear physics are separately using machine learning approaches to advance studies in their fields, there is currently little use of machine learning in nuclear astrophysics. We briefly describe the most common types of machine learning algorithms, and then detail their numerous possible uses to advance nuclear astrophysics, with a focus on simulation-based nucleosynthesis studies. We show that machine learning offers novel, complementary, creative approaches to address many important nucleosynthesis puzzles, with the potential to initiate a new frontier in nuclear astrophysics research.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Gearbox bearing crack growth prognostics and uncertainty quantification with physics-informed machine learning

This paper introduces the extreme theory of functional connections (X-TFC), a physics-informed machine learning algorithm, and tailors it to estimate the remaining useful life (RUL) of wind turbine gearbox bearings experiencing fatigue crack growth. Unlike purely data-driven methods, X-TFC embeds a physics model, based on Head's theory in this work, into its training objective. The core of X-TFC is a random-projection single-layer neural network trained via an extreme learning machine, which requires only limited damage progression data and solves for output weights with a least-squares optimization algorithm. A composite loss function balances the network's fit to observed degradation data against the residuals of the governing crack growth differential equation, ensuring the learned damage trajectory remains physically plausible. When applied to a vibration-based health-index (HI) dataset measured during the growth of a crack on the inner ring of a high-speed bearing in a wind turbine gearbox (Bechhoefer and Dubé, 2020), X-TFC achieves near-zero prediction bias. Even when trained on only the first 10 %–20 % of the damage progression data, with sufficient physics weighting its predictions remain monotonic and smooth, delivering high prognosability and trendability. To quantify the epistemic uncertainty, we employ a Monte Carlo ensemble of independently initialized X-TFC models trained on noise-perturbed data, which yields confidence intervals around each RUL estimate and captures both model-parameter and epistemic uncertainty. In addition to a vibration-based HI, we demonstrate that the proposed framework can be directly applied to a supervisory control and data acquisition (SCADA) data-based HI (Eftekhari Milani et al., 2026) measured during similar wind turbine gearbox bearing crack faults, preserving its accuracy and interpretability. This extension shows the versatility of our approach, which is applicable to bearings of multiple gearbox manufacturers, models, and ratings using only SCADA data. By integrating domain knowledge with machine learning, X-TFC offers a rapid, reliable tool for crack prognostics. Its adaptability to other bearing failure modes, such as pitch bearing ring cracks, positions X-TFC as a powerful enabler of data-driven, physics-informed asset management in the wind energy sector and beyond.

17 WIND ENERGY

Mid-IR UAV-based sensing platform with deep learning to Identify and Quantify Gaseous Emission in Gas Flares

This report details the development and evaluation of a Mid-Infrared (Mid-IR) Unmanned Aerial Vehicle (UAV)-based sensing platform integrated with deep learning algorithms for the identification and quantification of gaseous emissions in gas flares. The project, spearheaded by Omega Optics, Inc., aimed to address environmental monitoring challenges by leveraging advanced photonic technologies and autonomous UAV operations. The research focused on designing, optimizing, and fabricating photonic crystal waveguides and grating couplers to enhance the sensitivity and accuracy of gas detection. A comprehensive drone-based system was developed, featuring a miniaturized sensor, GPS module, and microcontroller communication network for real-time gas concentration monitoring. The system's adaptive sampling algorithm, implemented using the Robot Operating System (ROS), enables autonomous detection and localization of gas emission sources. Preliminary results demonstrate the platform's capability to detect and monitor gas emissions with high precision, cost-effectiveness, and scalability. Future work will expand upon this foundation by introducing 3D wind model-based learning for dynamic environmental conditions and further enhancing the user interface and data processing algorithms to support broader environmental monitoring applications. Overall, this project represents a significant step forward in UAV-based environmental sensing technologies, offering robust solutions for detecting and mitigating the impacts of gaseous emissions on public health and safety.

47 OTHER INSTRUMENTATION

Sub-millisecond keyhole pore detection in laser powder bed fusion using sound and light sensors and machine learning

Laser powder bed fusion is a mainstream additive manufacturing technology widely used to manufacture complex parts in prominent sectors, including aerospace, biomedical, and automotive industries. However, during the printing process, the presence of an unstable vapor depression can lead to a type of defect called keyhole porosity, which is detrimental to the part quality. In this study, we developed an effective approach to locally detect the generation of keyhole pores during the printing process by leveraging machine learning and a suite of optical and acoustic sensors. Simultaneous synchrotron x-ray imaging allows the direct visualization of pore generation events inside the sample, offering high-fidelity ground truth. A neural network model adopting SqueezeNet architecture using single-sensor data was developed to evaluate the fidelity of each sensor for capturing keyhole pore generation events. Our comparative study shows that the near infrared images gave the highest prediction accuracy, followed by 100 kHz and 20 kHz microphones, and the photodiode sensitive to processing laser wavelength had the lowest accuracy. Using a single sensor, over 90% prediction accuracy can be achieved with a temporal resolution as short as 0.1 ms. A data fusion scheme was also developed with features extracted using SqueezeNet neural network architecture and classification using different machine learning algorithms. Our work demonstrates the correlation between the characteristic optical and acoustic emissions and the keyhole oscillation behavior, and thereby provides strong physics support for the machine learning approach.

36 MATERIALS SCIENCE

A Multi-Sensor Approach for Measuring Bird and Bat Collisions with Offshore Wind Turbines (Final Technical Report)

Collision of birds and bats with wind turbines is a conservation concern for both land-based and offshore wind projects. The fatality rates of birds and bats at land-based turbines are well documented. The measurement strategies on land focus on finding carcasses following collision, estimating the number of carcasses missed through searcher efficiency, carcass persistence trials and carcass fall distributions, and modeling statistically robust fatality rates. Few technologies have been developed to monitor offshore bird and bat collisions, and many that have been developed focused on detecting collisions with large birds. The few studies that have attempted to document collisions at offshore turbines do not account for smaller bodied animals or for collisions that might be missed, which prevents the calculation of statistically robust fatality rates. The overall goal of this report, A Multi-Sensor Approach for Measuring Bird and Bat Collisions with Offshore Wind Turbines (Project), was to develop an effective multi-sensor system for quantifying bird and bat collision rates, specifically for offshore wind facilities. The Project goal and resulting automated collision detection system was achieved through two major technological advancements: 1) refining The Netherlands Organisation for Applied Scientific Research’s (TNO’s) existing WT-Bird® vibration sensing system, that had successfully detected large bird collisions during daytime, to allow for improved detection of smaller birds and bats during both daytime and nighttime hours and 2) improving image processing systems and developing and integrating machine learning algorithms to automatically detect and classify small and large bird and bat collisions with offshore turbines. This final technical report (FTR) summarizes Methods , Results , Conclusions , and Lessons Learned during each of the five Tasks identified for this research and development effort. This FTR includes summaries of the following: Task 1. Initial Engineering Tests to Improve WT-Bird® Task 2. Installation of WT‐Bird® on a Utility-scale Turbine at the National Wind Technology Center – National Renewable Energy Laboratory Task 3. Field Tests and Refinement of the Object Detection System Task 4. Validation of WT-Bird® on a Land-based Turbine Task 5. Preparation for the Implementation of WT-Bird® on an Offshore Turbine. This research and development effort documented successful improvement of the WT Bird® collision detection system to detect small birds and bats, and WT-Bird® is the first collision detection system to validate results compared to land-based post-construction monitoring. The collision trials provide estimates of missed targets that can be used to estimate fatality rates, a significant improvement relative to other offshore collision monitoring systems. Advances were made in developing an edge-processing solution to reduce data storage requirements, which is important if the system is deployed for long periods of time at offshore turbines. The improved WT-Bird® system also provides an important option for wind operators on land or offshore who need to document specific details about when collisions occur, particularly efforts to further research on bat impact minimization, or when standard fatality searches are impractical (e.g. offshore) or inadequate (e.g. challenging locations on land).

17 WIND ENERGY

Deep probabilistic direction prediction in 3D with applications to directional dark matter detectors

Abstract We present the first method to probabilistically predict 3D direction in a deep neural network model. The probabilistic predictions are modeled as a heteroscedastic von Mises-Fisher distribution on the sphere S 2 , giving a simple way to quantify aleatoric uncertainty. This approach generalizes the cosine distance loss which is a special case of our loss function when the uncertainty is assumed to be uniform across samples. We develop approximations required to make the likelihood function and gradient calculations stable. The method is applied to the task of predicting the 3D directions of electrons, the most complex signal in a class of experimental particle physics detectors designed to demonstrate the particle nature of dark matter and study solar neutrinos. Using simulated Monte Carlo data, the initial direction of recoiling electrons is inferred from their tortuous trajectories, as captured by the 3D detectors. For 40 keV electrons in a 70% He 30% CO 2 gas mixture at STP, the new approach achieves a mean cosine distance of 0.104 (26 ∘ ) compared to 0.556 (64 ∘ ) achieved by a non-machine learning algorithm. We show that the model is well-calibrated and accuracy can be increased further by removing samples with high predicted uncertainty. This advancement in probabilistic 3D directional learning could increase the sensitivity of directional dark matter detectors.

Computer Science

Sensitive detection of structural dynamics using a statistical framework for comparative crystallography

Chemical and conformational changes are crucial to protein function and its pharmacological control. X-ray crystallography can reveal these changes in atomic detail, but standard analysis methods, which refine separate datasets, often overlook differences that are subtle or arise in only a subset of molecules. Direct comparison of crystallographic datasets is, in principle, more powerful, but systematic errors (“scales”) often mask changes in the crystallographic observables (“structure factors”). Machine learning algorithms that jointly estimate scales and structure factors can address this limitation. Here, we augment this approach with multivariate, structured priors derived from crystallographic theory, implemented in the variational deep learning framework Careless. Doing so strongly improves the detection of protein dynamics, element-specific anomalous signals, and the binding of drug candidates, offering a robust approach to comparative crystallography and, potentially, to detection of protein dynamics by other structure determination methods.

Hekstra, Doeke R. [Harvard Univ., Cambridge, MA (U

Universal Nuclear Accident Dosimeter

The Lawrence Livermore National Laboratory (LLNL) Universal Nuclear Accident Dosimetry (UNAD) project is a four-year initiative aimed at advancing nuclear accident dosimetry methods. This article presents an overview of the research, key findings, and the progress made throughout the project. The primary goals included a background into the history of nuclear accident dosimetry, consolidating current dosimetry techniques within the NNSA/DOE complex, fostering collaboration among subject matter experts, and exploring novel technologies for potential implementation. The technical focus centered on investigating new and novel technologies, instrumentation methods, and analysis methods to develop recommendations for a potential nuclear accident dosimeter (NAD) to be universally deployed through the DOE complex. A multilaboratory and multinational Usergroup was established, conducting periodic meetings to facilitate knowledge exchange. The UNAD team has participated in two international nuclear accident dosimetry intercomparison exercises and one characterization exercise, where the existing LLNL NAD and a prototype alanine electron paramagnetic dosimeter NAD were deployed. Ongoing improvements are being made to the prototype NAD based on results from the exercises, laboratory studies, and collaboration with other laboratories. A machine learning algorithm to optimize the geometry and conversion factors of the current LLNL NAD is being implemented, and the resulting design will be tested in the next exercise. In conclusion, key lessons learned and future directions for the project are discussed.

Electron paramagnetic resonance spectroscopy

Characterization and Quantification of Radiation-Induced Clusters/Precipitates in RPV Steels Using STEM-EDS and Machine Learning

Over the operational lifespan of a nuclear reactor, reactor pressure vessel (RPV) steels are subjected to significant neutron irradiation, resulting in complex microstructural changes and the consequent degradation of mechanical properties. Various physically motivated correlation models have been developed to predict neutron irradiation-induced embrittlement of RPVs under different irradiation conditions. However, the efficient and accurate characterizations and quantification of radiation-induced clusters in RPVs are still challenging, which will affect the precision of the predictive models for embrittlement of RPV components. In the DOE Visiting Faculty Program (VFP) research work at Oak Ridge National Lab (ORNL), I integrate machine learning to aid Scanning Transmission Electron Microscopy – Energy Dispersive X-ray Spectroscopy (STEM-EDS) analyses, which improve the characterization and quantification of radiation-induced clusters in RPV steels, thereby enabling more accurate predictions of material behavior under irradiation. The surveillance base- and welded- RPV steels were annealed at various temperatures of 340 °C, 450 °C and 500 °C for up to 168 hours, respectively. Afterwards, I have characterized radiation-induced clusters using advanced STEM-EDS techniques and subsequently applying machine learning algorithms to analyze and refine STEM-EDS datasets, enhancing the quantification of clusters compositions and distributions. In the end, an efficient workflow for integrating STEM-EDS data analysis with machine learning to address challenges including noise reduction has been developed. The completion of this VFP work will support bridge critical gaps in the accurate quantification of radiation-induced clusters in RPV steels using STEM-EDS and support the development of more precise models for predicting RPV embrittlement in the Light Water Reactor Sustainability program supported by Department of Energy and enhancing the collaboration between ORNL and Alred University. The outcome of the VFP project will leverage a few research papers submission to peer-reviewed journals in the relevant scientific field and a few oral presentations at national and international conferences.

22 GENERAL STUDIES OF NUCLEAR REACTORS

An adaptive and stability-promoting layerwise training approach for sparse deep neural network architecture

This work presents a two-stage adaptive framework for progressively developing deep neural network (DNN) architectures that generalize well for a given training data set. In the first stage, a layerwise training approach is adopted where a new layer is added each time and trained independently by freezing parameters in the previous layers. We impose desirable structures on the DNN by employing manifold regularization, sparsity regularization, and physics-informed terms. We introduce a ε – δ – stability-promoting concept as a desirable property for a learning algorithm and show that employing manifold regularization yields a ε – δ stability-promoting algorithm. Further, we also derive the necessary conditions for the trainability of a newly added layer and investigate the training saturation problem. In the second stage of the algorithm (post-processing), a sequence of shallow networks is employed to extract information from the residual produced in the first stage, thereby improving the prediction accuracy. Numerical investigations on prototype regression and classification problems demonstrate that the proposed approach can outperform fully connected DNNs of the same size. Moreover, by equipping the physics-informed neural network (PINN) with the proposed adaptive architecture strategy to solve partial differential equations, we numerically show that adaptive PINNs not only are superior to standard PINNs but also produce interpretable hidden layers with provable stability. As a result, we also apply our architecture design strategy to solve inverse problems governed by elliptic partial differential equations.

42 ENGINEERING