Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “deep learning method”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 703 records · Page 39
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Explainable and Differentiable Reinforcement Learning for Multi-objective Optimization in Particle Accelerators

Operating particle accelerators involves optimizing multiple goals simultaneously, which can be challenging due to trade-offs among objectives. While evolutionary algorithms like the genetic algorithm (GA) have been used for various Multi-Objective Optimization (MOO) tasks, they are not inherently suited for complex control problems. This talk highlights two variations of Reinforcement Learning (RL) for concurrently optimizing heat load and trip rates at the Continuous Electron Beam Accelerator Facility (CEBAF). The problem involves strict constraints on individual states, actions, and overall energy requirements of the beam. First, this talk highlights how differentiability can be harnessed through a Deep Differentiable Reinforcement Learning (DDRL) approach to address MOO issues within particle accelerators. We examine the DDRL method alongside Model Free Reinforcement Learning (MFRL), GA, and Bayesian Optimization (BO). The performance of these methods is assessed by generating a Pareto-front for two objectives. Our findings indicate that DDRL excels in handling high-dimensional problems more effectively than MFRL, BO, and GA. Next, we will show integration of explainable physics-based constraints into RL algorithms to enhance trans- parency and trust in decision-making processes by enabling users to verify that agents adhere to established physical principles. This surrogate function can be modeled using neural networks or sparse dictionary mod- els. By examining the mathematical form of the learned constraint function, we are able to confirm the agent has learned to use the established physics of each environment provided but the surrogate model. In addi- tion, we find that the introduction of a mathematical functional dictionary based surrogate model enables our reinforcement learning algorithms to reliably converge for difficult high-dimensional accelerator controls environments.

Rajput, Kishansingh [Thomas Jefferson National Acc↗
DOE OSTI2025

Protein-ligand binding affinity prediction using multi-instance learning with docking structures

Recent advances in 3D structure-based deep learning approaches demonstrate improved accuracy in predicting protein-ligand binding affinity in drug discovery. These methods complement physics-based computational modeling such as molecular docking for virtual high-throughput screening. Despite recent advances and improved predictive performance, most methods in this category primarily rely on utilizing co-crystal complex structures and experimentally measured binding affinities as both input and output data for model training. Nevertheless, co-crystal complex structures are not readily available and the inaccurate predicted structures from molecular docking can degrade the accuracy of the machine learning methods. We introduce a novel structure-based inference method utilizing multiple molecular docking poses for each complex entity. Our proposed method employs multi-instance learning with an attention network to predict binding affinity from a collection of docking poses. We validate our method using multiple datasets, including PDBbind and compounds targeting the main protease of SARS-CoV-2. The results demonstrate that our method leveraging docking poses is competitive with other state-of-the-art inference models that depend on co-crystal structures. This method offers binding affinity prediction without requiring co-crystal structures, thereby increasing its applicability to protein targets lacking such data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Physics-constrained Deep Recurrent Neural Models of Building Thermal Dynamics

We develop physics-constrained and control-oriented predictive deep learning models for the thermal dynamics of a real-world commercial office building. The proposed method is based on the systematic encoding of physics-based prior knowledge into a structured recurrent neural architecture. Specifically, our model mimics the structure of the building thermal dynamics model and leverages penalty methods to model inequality constraints. Additionally, we use constrained matrix parameterization based on the Perron-Frobenius theorem to bound the eigenvalues of the learned network weights. We interpret the stable eigenvalues as dissipativeness of the learned building thermal model. We demonstrate the effectiveness of the proposed approach on a dataset obtained from an office building with $20$ thermal zones.

Building Energy, structured neural networks↗
NASA NTRSDate not supplied

Segmentation of Lightweight Ablator Micro-Tomography Using Deep Learning

Ablative thermal protection systems (TPS) are essential for high speed entry of planetary atmospheres, such as those of Earth and Mars. Upon entry the kinetic energy of the spacecraft is converted into thermal energy, leading to high heat fluxes at the wall of the craft. Because of this extreme heating, a robust ablative TPS material must be selected. A common material selection today is phenolic-impregnated carbon ablator (PICA), which is a low-density carbon material known for producing dust that is not suitable to a cleanroom environment. To mitigate dust created by a PICA heatshield, a silicone-based spray called NuSil is applied to the surface of the TPS, creating PICA-NuSil (PICA-N). PICA-N has been observed to have a different material response from regular PICA during high enthalpy flow testing, producing surface temperatures up to 200K less than those seen for PICA [1]. To better understand this phenomenon, it is critical that robust methods of PICA-N material characterization are developed. The purpose of this project is to investigate Object Research Systems’ (ORS) Dragonfly deep learning tools as a means of accurately segmenting and characterizing PICA-N. Systematic testing of this software has shown that Dragonfly deep learning tools have strong potential for accurate segmentation/ characterization of PICA-N and other TPS materials.

Micro-tomography↗
DOE OSTI2023

Strictly Enforcing Invertibility and Conservation in CNN-Based Super Resolution for Scientific Datasets

Abstract Recently, deep convolutional neural networks (CNNs) have revolutionized image “super resolution” (SR), dramatically outperforming past methods for enhancing image resolution. They could be a boon for the many scientific fields that involve imaging or any regularly gridded datasets: satellite remote sensing, radar meteorology, medical imaging, numerical modeling, and so on. Unfortunately, while SR-CNNs produce visually compelling results, they do not necessarily conserve physical quantities between their low-resolution inputs and high-resolution outputs when applied to scientific datasets. Here, a method for “downsampling enforcement” in SR-CNNs is proposed. A differentiable operator is derived that, when applied as the final transfer function of a CNN, ensures the high-resolution outputs exactly reproduce the low-resolution inputs under 2D-average downsampling while improving performance of the SR schemes. The method is demonstrated across seven modern CNN-based SR schemes on several benchmark image datasets, and applications to weather radar, satellite imager, and climate model data are shown. The approach improves training time and performance while ensuring physical consistency between the super-resolved and low-resolution data. Significance Statement Recent advancements in using deep learning to increase the resolution of images have substantial potential across the many scientific fields that use images and image-like data. Most image super-resolution research has focused on the visual quality of outputs, however, and is not necessarily well suited for use with scientific data where known physics constraints may need to be enforced. Here, we introduce a method to modify existing deep neural network architectures so that they strictly conserve physical quantities in the input field when “super resolving” scientific data and find that the method can improve performance across a wide range of datasets and neural networks. Integration of known physics and adherence to established physical constraints into deep neural networks will be a critical step before their potential can be fully realized in the physical sciences.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

DeepSZ: identification of Sunyaev–Zel’dovich galaxy clusters using deep learning

Galaxy clusters identified via the Sunyaev–Zel’dovich (SZ) effect are a key ingredient in multiwavelength cluster cosmology. In this paper, we present and compare three methods of cluster identification: the standard matched filter (MF) method in SZ cluster finding, a convolutional neural networks (CNN), and a ‘combined’ identifier. We apply the methods to simulated millimeter maps for several observing frequencies for a survey similar to SPT-3G, the third-generation camera for the South Pole Telescope. The MF requires image pre-processing to remove point sources and a model for the noise, while the CNN requires very little pre-processing of images. Additionally, the CNN requires tuning of hyperparameters in the model and takes cut-out images of the sky as input, identifying the cut-out as cluster-containing or not. We compare differences in purity and completeness. The MF signal-to-noise ratio depends on both mass and redshift. Our CNN, trained for a given mass threshold, captures a different set of clusters than the MF, some with signal-to-noise-ratio below the MF detection threshold. However, the CNN tends to mis-classify cut-out whose clusters are located near the edge of the cut-out, which can be mitigated with staggered cut-out. We leverage the complementarity of the two methods, combining the scores from each method for identification. The purity and completeness are both 0.61 for MF, and 0.59 and 0.61 for CNN. The combined method yields 0.60 and 0.77, a significant increase for completeness with a modest decrease in purity. We advocate for combined methods that increase the confidence of many low signal-to-noise clusters.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Quantum computing based hybrid deep learning for fault diagnosis in electrical power systems

Quantum computing (QC) and deep learning have shown promise of supporting transformative advances and have recently gained popularity in a wide range of areas. Here, this paper proposes a hybrid QC-based deep learning framework for fault diagnosis of electrical power systems that combine the feature extraction capabilities of conditional restricted Boltzmann machine with an efficient classification of deep networks. Computational challenges stemming from the complexities of such deep learning models are overcome by QC-based training methodologies that effectively leverage the complementary strengths of quantum assisted learning and classical training techniques. The proposed hybrid QC-based deep learning framework is tested on a simulated electrical power system with 30 buses and wide variations of substation and transmission line faults, to demonstrate the framework’s applicability, efficiency, and generalization capabilities. High computational efficiency is enjoyed by the proposed hybrid approach in terms of computational effort required and quality of diagnosis performance over classical training methods. In addition, superior and reliable fault diagnosis performance with faster response time is achieved over state-of-the-art pattern recognition methods based on artificial neural networks (ANN) and decision trees (DT).

42 ENGINEERING↗
DOE OSTI2022

Risk-Informed Operations and Maintenance Decision Making Using Deep Reinforcement Learning

A challenge for operating nuclear power plants is the significant cost of operations and maintenance, at times consuming up to 66% of annual operating costs. This project aims to build a framework for a risk-informed asset-management tool that integrates inspections, repairs, spare-part inventory, supply chain, and business choices to lower overall O&M costs. Our approach uses a combination of data-driven modeling and deep reinforcement learning to create and implement optimal maintenance policies for the existing nuclear fleet, as well as new advanced reactors. The creation of an asset management tool that uses these advanced methods will give operators new capabilities to help reduce the burden of O&M spending in nuclear power plants.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Branching Dueling Q-Network Based Online Scheduling of a Microgrid With Distributed Energy Storage Systems

This letter investigates a Branching Dueling Q-Network (BDQ) based online operation strategy for a microgrid with distributed battery energy storage systems (BESSs) operating under uncertainties. Additionally, the developed deep reinforcement learning (DRL) based microgrid online optimization strategy can achieve a linear increase in the number of neural network outputs with the number of distributed BESSs, which overcomes the curse of dimensionality caused by the charge and discharge decisions of multiple BESSs. Numerical simulations validate the effectiveness of the proposed method.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Grid-Connected Modular Soft-Switching Solid State Transformers (M-S4T)

The objective of this project is to develop and verify the concept of a flexible and modular soft-switching solid-state transformer (M-S4T) for direct grid-connected applications. The ability to directly connect power electronics converters to the medium voltage grid (4 kV – 13 kV), and to potentially replace the passive and bulky, but ubiquitous 60 hertz service transformer in the 25 kVA to 100 kVA range, with a more flexible and controllable device, has been regarded as the ‘holy grail’ in grid control. However, this has proven to be extremely difficult. This project has developed the solutions to several key challenges of the direct grid-connected power electronics and realized a 7.2 kV M-S4T prototype. First, a protection method to protect the M-S4T from the high voltages (110 kV for the 13 kV system) that occur on the grid due to transients and lightning strikes have been developed and experimentally verified. Second, the realization and the operation of the M-S4T based on high-voltage SiC devices (>3.3 kV) and a medium-frequency medium-voltage low-leakage transformer in a single-stage solid-state transformer with zero-voltage switching, low dv/dt, and low electromagnetic interference has been successfully demonstrated up to 7.5 kV peak. Third, an oil-cooling system and stable communication and distributed control system for converter module voltage sharing have been developed and experimentally verified. The developed M-S4T has realized a modular universal high-performance power conversion system. This conversion system is scalable to different voltage and power levels and adaptable to four-quadrant bidirectional operation. Moreover, the use of passive cooling techniques meets the equipment life requirements, and the lightning protection scheme fulfills the basic insulation level specifications for direct grid connection. Such power conversion system opens up near-term opportunities, including energy storage, solar PV, or electric vehicle charging with significant cost and footprint savings. In the longer term, the possibility of replacing the utility distribution transformer with an M-S4T will be transformative for future distribution grids with a compact footprint and full controllability to enable high renewable energy and storage penetration. In addition to the main project, this report expands on the Plus-Up projected including as part of the main award. This project developed and demonstrated the technology for autonomous collaborative inverters that can be connected in an ad hoc manner to the grid. The aim of the project was to: (1) evaluate the existing techniques for grid-connected inverters and find their limitations; (2) develop detailed requirements for grid-connected inverters in the modern grid with millions of active nodes; (3) design a unified control strategy that brings more autonomy and intelligence to grid-connected inverters, and addresses parts of the issues with the existing techniques. The proposed technique, called UniCon, enables inverters to 1) connect/disconnect to/from the grid in an ad hoc manner; (2) work based on local sensing. Slow communication could be used for a more optimized behavior; (3) work automatically in both grid-forming/grid-following mode; (4) handle large disturbances, e.g., big load step and fault, in an oscillation-free manner; (5) work collaboratively with other inverters in steady-state and during transients. UniCon can be implemented in the middle-level control; hence it is agnostic to the vendor and to the implementation of the inner voltage/current and protection loops. Furthermore, a new synchronization scheme, based on deep learning, was developed that can extract the grid voltage phase and amplitude in a stable manner. The method is cheap to implement can improve the dynamic performance of the grid-connected inverters during fast transients, e.g., fault. The proposed control scheme was validated by (1) MATLAB/Simulink; (2) hardware-in-the-loop results, and; (3) experimental results using three inverters that form a microgrid in a down-scaled feeder. Lastly, both the M-S4T and UniCon have achieved promising tangible paths to markets. In the case of the M-S4T, the underlying technology — the Soft Switching Solid State Transformer (S4T) developed at the Georgia Tech Center for Distributed Energy (GT-CDE) has been licensed by GridBlock from the Georgia Tech Research Corporation, and GridBlock has been working with manufacturing partner Jabil (one of the largest US-based contract manufacturers) and system integrator Power Secure (largest deployer of microgrids in the US with 4.7 GW under management), to meet the strong initial demand. Similarly, GridBlock has an exclusive license to the UniCon technology, developed under this award by GT-CDE. The UniCon provides an intermediate control layer that enables the implementation of the higher-level ‘transactive’ control commands for the system. The architecture of the system - slow communications with the cloud for system optimization and setpoints, and the use of locally measured quantities for real-time control, provide a very robust and secure way of implementing a real-time must-run grid that is also secure and stable. This is a brand-new functionality that is critical for the future grid and key to GridBlock’s business model.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2026

Machine learning approach for vibronically renormalized electronic band structures

Here, we present a machine learning (ML) method for efficient computation of vibrational thermal expectation values of physical properties from first principles. Our approach is based on the nonperturbative frozen phonon formulation in which stochastic Monte Carlo algorithm is employed to sample configurations of nuclei in a supercell at finite temperatures based on a first-principles phonon model. A deep-learning neural network is trained to accurately predict physical properties associated with sampled phonon configurations, thus bypassing the time-consuming ab initio calculations. To incorporate the point-group symmetry of the electronic system into the ML model, group-theoretical methods are used to develop a symmetry-invariant descriptor for phonon configurations in the supercell. We apply our ML approach to compute the temperature dependent electronic energy gap of silicon based on density functional theory (DFT). We show that, with less than a hundred DFT calculations for training the neural network model, an order of magnitude larger number of sampling can be achieved for the computation of the vibrational thermal expectation values. Our work highlights the promising potential of ML techniques for finite temperature first-principles electronic structure methods.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Using Machine Learning to Understand Electric and Hybrid Vehicles Ownership in Burdened and Nonburdened Communities

Transitioning to electric and hybrid vehicles (EHVs) for all communities is a pivotal step toward sustainable transportation and environmental conservation. This paper aims to understand the adoption of EHVs, focusing on burdened communities (BCs) in the United States. The EHV ownership-based analysis combines two datasets—behavioral data from the Puget Sound Regional Travel Survey integrated with BCs (Justice40) data covering transportation insecurity, environmental burden, social vulnerability, health vulnerability, and climate and disaster risk burden. After creating this unique database, descriptive analysis and modeling are used to analyze the data and predict EHV ownership in the future. Specifically, we use a new method that combines particle swarm optimization (PSO) with a stacking model named PSO-Stacking, which incorporates heterogeneous base learners of machine learning and deep learning. PSO applies a customized objective function to select the optimal hyperparameters for heterogeneous learners within the stacking model, effectively addressing challenges such as multicollinearity, data imbalance, nonlinearity, and overfitting. The proposed solution covers more accurate results than standard benchmark models for EHV ownership in BCs and non-BCs. In addition, the results of the PSO-Stacking method are explained using the local interpretable model-agnostic explanations technique. Results show a negative correlation between the BCs indicators, that is, higher transportation insecurity associated with lower EHV ownership. Furthermore, BCs have higher future climate risk scores, diesel particulate matter levels, and PM2.5 in the air than non-BCs because of higher conventional vehicle ownership. These communities are at higher risk and can benefit from electrification, EV infrastructure, and EV policies to address environmental challenges.

Aslam, Zeeshan [ORNL]↗
DOE OSTI2024

Transfer learning for metamaterial design and simulation

Abstract We demonstrate transfer learning as a tool to improve the efficacy of training deep learning models based on residual neural networks (ResNets). Specifically, we examine its use for study of multi-scale electrically large metasurface arrays under open boundary conditions in electromagnetic metamaterials. Our aim is to assess the efficiency of transfer learning across a range of problem domains that vary in their resemblance to the original base problem for which the ResNet model was initially trained. We use a quasi-analytical discrete dipole approximation (DDA) method to simulate electrically large metasurface arrays to obtain ground truth data for training and testing of our deep neural network. Our approach can save significant time for examining novel metasurface designs by harnessing the power of transfer learning, as it effectively mitigates the pervasive data bottleneck issue commonly encountered in deep learning. We demonstrate that for the best case when the transfer task is sufficiently similar to the target task, a new task can be effectively trained using only a few data points yet still achieve a test mean absolute relative error of 3 % with a pre-trained neural network, realizing data reduction by a factor of 1000.

Peng, Rixi↗
DOE OSTI2022

Scaling Building Energy Audits through Machine Learning Methods on Novel Drone Image Data

Building energy audits are time-consuming and labor-intensive. This paper describes a new method using machine learning (ML) techniques on novel data sources (drone images) to improve the identification of building characteristics and retrofit opportunities, and thereby reduce the effort for audits. The new ML method includes: (1) Building footprint extraction using line extraction, polygonization, and polygon-merging, (2) Building envelope extraction using PIX4d modeling software to reconstruct a building 3D model, (3) Visualization tool for viewing images from the 3D model, (4) Window-to-wall ratio (WWR) using state-of-art deep neural network semantic segmentation, (5) Envelope thermal anomaly detection using an unsupervised machine learning clustering algorithm, and (6) Rooftop energy equipment detection based on an object detection algorithm. The testing of this method involved a comparison of additional ML-generated information overlaid on current ‘state-of-practice’ audit and remote assessment baselines using evaluation metrics: labor time and associated cost, marginal benefits of using ML-generated information in workflows for audits and remote assessments, integration potential with existing processes and tools, and replicability/scalability of the method. In two test buildings in California that had comprehensive drawings and meter data available, the ML method effectively generated a building footprint, envelope, rooftop equipment, WWR, and locations of envelope thermal anomalies. Projected target segments of the ML method are sites with minimal drawings and energy data, and underserved sectors such as multistoried housing, disadvantaged communities, and schools for which the ML method can enable identification of building asset characteristics and prioritization of envelope retrofits and decentralized energy equipment retrofits.

Singh, Reshma↗
DOE OSTI2021

Deep Learning Classification of Cheatgrass Invasion in the Western United States Using Biophysical and Remote Sensing Data

Cheatgrass (Bromus tectorum) invasion is driving an emerging cycle of increased fire frequency and irreversible loss of wildlife habitat in the western US. Yet, detailed spatial information about its occurrence is still lacking for much of its presumably invaded range. Deep learning (DL) has demonstrated success for remote sensing applications but is less tested on more challenging tasks like identifying biological invasions using sub-pixel phenomena. We compare two DL architectures and the more conventional Random Forest and Logistic Regression methods to improve upon a previous effort to map cheatgrass occurrence at >2% canopy cover. High-dimensional sets of biophysical, MODIS, and Landsat-7 ETM+ predictor variables are also compared to evaluate different multi-modal data strategies. All model configurations improved results relative to the case study and accuracy generally improved by combining data from both sensors with biophysical data. Cheatgrass occurrence is mapped at 30 m ground sample distance (GSD) with an estimated 78.1% accuracy, compared to 250-m GSD and 71% map accuracy in the case study. Furthermore, DL is shown to be competitive with well-established machine learning methods in a limited data regime, suggesting it can be an effective tool for mapping biological invasions and more broadly for multi-modal remote sensing applications.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2021

A Robust Hybrid Deep Learning Model for Spatiotemporal Image Fusion

Dense time-series remote sensing data with detailed spatial information are highly desired for the monitoring of dynamic earth systems. Due to the sensor tradeoff, most remote sensing systems cannot provide images with both high spatial and temporal resolutions. Spatiotemporal image fusion models provide a feasible solution to generate such a type of satellite imagery, yet existing fusion methods are limited in predicting rapid and/or transient phenological changes. Additionally, a systematic approach to assessing and understanding how varying levels of temporal phenological changes affect fusion results is lacking in spatiotemporal fusion research. The objective of this study is to develop an innovative hybrid deep learning model that can effectively and robustly fuse the satellite imagery of various spatial and temporal resolutions. The proposed model integrates two types of network models: super-resolution convolutional neural network (SRCNN) and long short-term memory (LSTM). SRCNN can enhance the coarse images by restoring degraded spatial details, while LSTM can learn and extract the temporal changing patterns from the time-series images. To systematically assess the effects of varying levels of phenological changes, we identify image phenological transition dates and design three temporal phenological change scenarios representing rapid, moderate, and minimal phenological changes. The hybrid deep learning model, alongside three benchmark fusion models, is assessed in different scenarios of phenological changes. Results indicate the hybrid deep learning model yields significantly better results when rapid or moderate phenological changes are present. It holds great potential in generating high-quality time-series datasets of both high spatial and temporal resolutions, which can further benefit terrestrial system dynamic studies. The innovative approach to understanding phenological changes’ effect will help us better comprehend the strengths and weaknesses of current and future fusion models.

spatiotemporal fusion↗
DOE OSTI2021

Single-shot x-ray phase-contrast and dark-field imaging based on coded binary phase mask

We introduce a coded-mask-based multi-contrast imaging method for high-resolution phase-contrast and dark-field imaging. The method uses a binary phase mask designed to provide an ultra-high-contrast pattern and reference-free single-shot measurement and an algorithm based on maximum-likelihood optimization and automatic differentiation to perform simultaneous reconstruction of absorption, phase, and dark-field object images. Further, we demonstrate that the method has great potential for real-time quantitative phase imaging and wavefront sensing when combined with deep learning.

Qiao, Zhi (ORCID:0000000286285320)↗
DOE OSTI2025

Data-Driven Closures and Assimilation for Stiff Multiscale Random Dynamics

Here, we introduce a data-driven and physics-informed framework for propagating uncertainty in stiff, multiscale random ordinary differential equations (RODEs) driven by correlated (colored) noise. Unlike systems subjected to Gaussian white noise, a deterministic equation for the joint probability density function (PDF) of RODE state variables does not exist in closed form. Moreover, such an equation would require as many phase-space variables as there are states in the RODE system. To alleviate this curse of dimensionality, we instead derive exact, albeit unclosed, reduced-order PDF (RoPDF) equations for low-dimensional observables/quantities of interest. The unclosed terms take the form of state-dependent conditional expectations, which are directly estimated from data at sparse observation times. However, for systems exhibiting stiff, multiscale dynamics, data sparsity introduces regression discrepancies that compound during RoPDF evolution. This is overcome by introducing a kinetic-like defect term to the RoPDF equation, which is learned by assimilating in sparse, low-fidelity RoPDF estimates. Two assimilation methods are considered, namely nudging and deep neural networks, which are successfully tested against Monte Carlo simulations.

97 MATHEMATICS AND COMPUTING↗