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Machine learning materials physics: Surrogate optimization and multi-fidelity algorithms predict precipitate morphology in an alternative to phase field dynamics
Machine learning has been effective at detecting patterns and predicting the response of systems that behave free of natural laws. Examples include learning crowd dynamics, recommender systems and autonomous mobility. There also have been applications to the search for new materials that draw upon big-data classification problems. Though, when it comes to physical systems governed by conservation laws, the role of machine learning has been more limited. Here, we present our recent work in exploring the role of machine learning methods in discovering, or aiding, the search for physics. Specifically, we focus on using machine learning algorithms to represent high-dimensional free energy surfaces with the goal of identifying precipitate morphologies in alloy systems. Traditionally, this problem has been approached by combining phase field models, which impose first-order dynamics, with elasticity, to traverse a free energy landscape in search of minima. Equilibrium precipitate morphologies occur at these minima. Here, we exploit the machine learning methods to represent high-dimensional data, combined with surrogate optimization, sensitivity analysis and multifidelity modeling as an alternate framework to explore phenomena controlled by energy extremization. This combination of data-driven methods offers an alternative to the imposition of first-order dynamics via phase field methods, and represents one aspect of applying machine learning to materials physics.
Sampling-based Sublinear Low-rank Matrix Arithmetic Framework for Dequantizing Quantum Machine Learning
We present an algorithmic framework for quantum-inspired classical algorithms on close-to-low-rank matrices, generalizing the series of results started by Tang’s breakthrough quantum-inspired algorithm for recommendation systems [STOC’19]. Motivated by quantum linear algebra algorithms and the quantum singular value transformation (SVT) framework of Gilyén et al. [STOC’19], we develop classical algorithms for SVT that run in time independent of input dimension, under suitable quantum-inspired sampling assumptions. Our results give compelling evidence that in the corresponding QRAM data structure input model, quantum SVT does not yield exponential quantum speedups. Since the quantum SVT framework generalizes essentially all known techniques for quantum linear algebra, our results, combined with sampling lemmas from previous work, suffice to generalize all prior results about dequantizing quantum machine learning algorithms. In particular, our classical SVT framework recovers and often improves the dequantization results on recommendation systems, principal component analysis, supervised clustering, support vector machines, low-rank regression, and semidefinite program solving. We also give additional dequantization results on low-rank Hamiltonian simulation and discriminant analysis. Our improvements come from identifying the key feature of the quantum-inspired input model that is at the core of all prior quantum-inspired results: ℓ 2 -norm sampling can approximate matrix products in time independent of their dimension. We reduce all our main results to this fact, making our exposition concise, self-contained, and intuitive.
Predicting nepheline precipitation in waste glasses using ternary submixture model and machine learning
Nepheline precipitation in nuclear waste glasses during vitrification can be detrimental due to its negative effect on chemical durability. Developing models to accurately predict nepheline precipitation from compositions is important to increase waste loading since existing models can be overly conservative. In this study, an expanded dataset containing 955 glasses was compiled from literature data, where 355 glasses are for high-level waste (HLW). Previously developed submixture models were refitted using the new dataset, where a misclassification rate of 7.8% was achieved. Nine machine learning (ML) algorithms (e.g., k-nearest neighbor, Gaussian process regression, artificial neural network, support vector machine, decision tree, etc.) were applied to evaluate their ability of predicting nepheline precipitation from compositions. Model accuracy, precision, recall/sensitivity, and F1 score were systemically compared between different ML algorithms and modeling protocols. Good model prediction with an accuracy ~0.9 (misclassification rate of ~10%) was observed with different algorithms under certain protocol. This study evaluated various ML models to predict nepheline precipitations in waste glasses, highlighting the importance of data preparation, modeling protocol, and their effect on model stability and reproducibility. The results provide insights into applying ML to predict glass properties and suggest areas for future research on modeling nepheline precipitations.
Design of lightweight BCC multi-principal element alloys with enhanced hydrogen storage using a machine learning-driven genetic algorithm
Body-centered cubic (BCC) based multi-principal element alloy (MPEA) hydrides have demonstrated significant potential for compact and efficient hydrogen storage. In this work, we first leverage machine learning (ML) models to predict the hydrogen affinity, storage capacity and phase stability of BCC MPEAs, creating a unique hydrogen-to-metal (H/M) predictor for materials with unprecedented performance. We developed a metaheuristic optimizer high-throughput framework by interfacing ML models with a genetic algorithm for the accelerated search of {Mg, Al, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Nb, Mo} based lightweight BCC MPEAs with improved hydrogen storage characteristics. We report five new MPEAs with a predicted gravimetric hydrogen storage capacity of around 3.5 wt% or more, including Cr 0.09 Mg 0.73 Ti 0.18 (4.25 wt% H) and Cr 0.21 Nb 0.11 Ti 0.35 V 0.33 (3.5 wt% H). The electronic structure of the top-performing composition, Cr 0.09 Mg 0.73 Ti 0.18 , was analyzed using density functional theory (DFT) to understand the reasons for its improved hydrogen storage properties compared to TiFe (1.90 wt% H), LaNi 5 (1.37 wt% H) or BCC MPEAs like TiVNbCr (3.70 wt% H). Temperature-dependent molecular dynamics (MD) studies were further performed on optimized BCC MPEAs to qualitatively study hydrogen mobility and analyze the effect of different elemental composition on bulk hydrogen diffusion. Our findings demonstrate how a ML assisted genetic algorithm framework can be used for efficient search of stable, lightweight and cost-effective MPEAs while minimizing the need for expensive ab initio calculations.
Genetic algorithms for computational materials discovery accelerated by machine learning
Materials discovery is increasingly being impelled by machine learning methods that rely on pre-existing datasets. Where datasets are lacking, unbiased data generation can be achieved with genetic algorithms. Here a machine learning model is trained on-the-fly as a computationally inexpensive energy predictor before analyzing how to augment convergence in genetic algorithm-based approaches by using the model as a surrogate. This leads to a machine learning accelerated genetic algorithm combining robust qualities of the genetic algorithm with rapid machine learning. The approach is used to search for stable, compositionally variant, geometrically similar nanoparticle alloys to illustrate its capability for accelerated materials discovery, e.g., nanoalloy catalysts. The machine learning accelerated approach, in this case, yields a 50-fold reduction in the number of required energy calculations compared to a traditional “brute force” genetic algorithm. This makes searching through the space of all homotops and compositions of a binary alloy particle in a given structure feasible, using density functional theory calculations.
An Approach to Bayesian Optimization for Design Feasibility Check on Discontinuous Black-Box Functions
The paper presents a novel approach to applying Bayesian Optimization (BO) in predicting an unknown constraint boundary, also representing the discontinuity of an unknown function, for a feasibility check on the design space, thereby representing a classification tool to discern between a feasible and infeasible region. Bayesian optimization is a low-cost black-box global optimization tool in the Sequential Design Methods where one learns and updates knowledge from prior evaluated designs, and proceeds to the selection of new designs for future evaluation. However, BO is best suited to problems with the assumption of a continuous objective function and does not guarantee true convergence when having a discontinuous design space. This is because of the insufficient knowledge of the BO about the nature of the discontinuity of the unknown true function. In this paper, we have proposed to predict the location of the discontinuity using a BO algorithm on an artificially projected continuous design space from the original discontinuous design space. The proposed approach has been implemented in a thin tube design with the risk of creep-fatigue failure under constant loading of temperature and pressure. The stated risk depends on the location of the designs in terms of safe and unsafe regions, where the discontinuities lie at the transition between those regions; therefore, the discontinuity has also been treated as an unknown creep-fatigue failure constraint. The proposed BO algorithm has been trained to maximize sampling toward the unknown transition region, to act as a high accuracy classifier between safe and unsafe designs with minimal training cost. The converged solution has been validated for different design parameters with classification error rate and function evaluations at an average of <1% and ~150, respectively. Finally, the performance of our proposed approach in terms of training cost and classification accuracy of thin tube design is shown to be better than the existing machine learning (ML) algorithms such as Support Vector Machine (SVM), Random Forest (RF), and Boosting.
Application of Machine Learning and Data Augmentation Algorithms in the Discovery of Metal Hydrides for Hydrogen Storage
The development of efficient and sustainable hydrogen storage materials is a key challenge for realizing hydrogen as a clean and flexible energy carrier. Among various options, metal hydrides offer high volumetric storage density and operational safety, yet their application is limited by thermodynamic, kinetic, and compositional constraints. In this work, we investigate the potential of machine learning (ML) to predict key thermodynamic properties—equilibrium plateau pressure, enthalpy, and entropy of hydride formation—based solely on alloy composition using Magpie-generated descriptors. We significantly expand an existing experimental dataset from ~400 to 806 entries and assess the impact of dataset size and data augmentation, using the PADRE algorithm, on model performance. Models including Support Vector Machines and Gradient Boosted Random Forests were trained and optimized via grid search and cross-validation. Results show a marked improvement in predictive accuracy with increased dataset size, while data augmentation benefits are limited to smaller datasets and do not improve accuracy in underrepresented pressure regimes. Furthermore, clustering and cross-validation analyses highlight the limited generalizability of models across different material classes, though high accuracy is achieved when training and testing within a single hydride family (e.g., AB2). The study demonstrates the viability and limitations of ML for accelerating hydride discovery, emphasizing the importance of dataset diversity and representation for robust property prediction.
Using Machine Learning to Predict MCNP Bias
For many real-world applications in radiation transport where simulations are compared to experimental measurements, like in nuclear criticality safety, the bias (simulated - experimental k eff ) in the calculation is an extremely important quantity used for code validation. The objective of this project is to accurately predict the bias of MCNP6 [1] criticality calculations using machine learning (ML) algorithms, with the intention of creating a tool that can complement the current nuclear criticality safety methods. In the latest release of MCNP6, the Whisper tool is available for criticality safety analysts and includes a large catalogue of experimental benchmarks, sensitivity profiles, and nuclear data covariance matrices. This data, coming from 1100+ benchmark cases, is used in this study of ML algorithms for criticality safety bias predictions.
X-ray nano-imaging of defects in thin film catalysts via cluster analysis
Functional properties of transition-metal oxides strongly depend on crystallographic defects; crystallographic lattice deviations can affect ionic diffusion and adsorbate binding energies. Scanning x-ray nanodiffraction enables imaging of local structural distortions across an extended spatial region of thin samples. Yet, localized lattice distortions remain challenging to detect and localize using nanodiffraction, due to their weak diffuse scattering. Here, in this study, we apply an unsupervised machine learning clustering algorithm to isolate the low-intensity diffuse scattering in as-grown and alkaline-treated thin epitaxially strained SrIrO 3 films. We pinpoint the defect locations, find additional strain variation in the morphology of electrochemically cycled SrIrO 3 , and interpret the defect type by analyzing the diffraction profile through clustering. Our findings demonstrate the use of a machine learning clustering algorithm for identifying and characterizing hard-to-find crystallographic defects in thin films of electrocatalysts and highlight the potential to study electrochemical reactions at defect sites in operando experiments.
A generalizable machine learning-assisted fast Fourier transform algorithm to simulate the large strain phenomena in polycrystalline materials
Machine learning methods have shown initial promise in constitutive modeling for single crystals or homogenized polycrystals, delivering notable computational efficiency. However, existing machine learning-based constitutive models often lack generalizability, limiting their application across diverse boundary value problems. This study introduces a thermodynamics-informed artificial neural network model to accelerate rate-tangent crystal plasticity fast Fourier transform simulations for cross-scale deformation behaviors of polycrystals under complex loading. Our model integrates microstructural variability and local interactions effectively. To address local effects in each grain, we employ K-means clustering to group Gauss points within the microstructure into clusters assumed to be in similar mechanical states. This approach, based on self-clustering analysis, extends model scope from macroscopic stress response to the granular level, capturing mechanical responses and orientation evolution across grains. This reduces the number of nonlinear problems to solve, with cluster responses propagated throughout each group. The thermodynamics-based artificial neural network-extracted features are further processed using local material state clusters to account for history-dependent deformation and evolving microstructures. Additionally, representative volume element simulations with rate-tangent crystal plasticity fast Fourier transform provide reliable datasets for model training. The proposed model demonstrates high efficiency, accuracy, self-consistency, and enhanced generalizability in predicting strain–stress responses and orientation evolution at both individual grain and aggregate scales under complex loading conditions, such as biaxial tension and arbitrary loading scenarios.
Machine Learning Applications to Maintain the NuMI Neutrino Beam Quality at Fermilab
The NuMI target facility at Fermilab produces an intense muon neutrino beam for NOvA (NuMI Off-axis νe Appearance) long baseline neutrino experiment. Three arrays of muon monitors located in the downstream of the hadron absorber in the NuMI beamline provide the measurements of the primary beam and horn current quality. We have studied the response of muon monitors with the proton beam profile changes and focusing horn current variations. The responses of muon monitors are used to develop Machine Learning (ML) algorithms to monitor the beam quality. We present the development of the machine learning applications and the future plans. This effort is important for future applications such as beam quality assurance, anomaly detections, neutrino beam systematics studies and neutrino beam quality assurance. Our results demonstrate the advantages of developing useful ML applications that can be leveraged for future beamlines such as LBNF.
Key Questions for the Quantum Machine Learner to Ask Themselves
Within the last several years quantum machine learning (QML) has begun to mature; however, many open questions remain. Rather than review open questions, in this perspective piece I will discuss my view about how we should approach problems in QML. In particular I will list a series of questions that I think we should ask ourselves when developing quantum algorithms for machine learning. These questions focus on what the definition of quantum ML is, what is the proper quantum analogue of QML algorithms is, how one should compare QML to traditional ML and what fundamental limitations emerge when trying to build QML protocols. As an illustration of this process I also provide information theoretic arguments that show that amplitude encoding can require exponentially more queries to a quantum model to determine membership of a vector in a concept class than classical bit-encodings would require; however, if the correct analogue is chosen then both the quantum and classical complexities become polynomially equivalent. This example underscores the importance of asking ourselves the right questions when developing and benchmarking QML algorithms.
Towards provably efficient quantum algorithms for large-scale machine-learning models
Large machine learning models are revolutionary technologies of artificial intelligence whose bottlenecks include huge computational expenses, power, and time used both in the pre-training and fine-tuning process. In this work, we show that fault-tolerant quantum computing could possibly provide provably efficient resolutions for generic (stochastic) gradient descent algorithms, scaling as $\mathcal{O}$(T 2 x polylog($n$)), where n is the size of the models and T is the number of iterations in the training, as long as the models are both sufficiently dissipative and sparse, with small learning rates. Based on earlier efficient quantum algorithms for dissipative differential equations, we find and prove that similar algorithms work for (stochastic) gradient descent, the primary algorithm for machine learning. In practice, we benchmark instances of large machine learning models from 7 million to 103 million parameters. We find that, in the context of sparse training, a quantum enhancement is possible at the early stage of learning after model pruning, motivating a sparse parameter download and re-upload scheme. Our work shows solidly that fault-tolerant quantum algorithms could potentially contribute to most state-of-the-art, large-scale machine-learning problems.
Digital Assistance for System Requirement Discovery and Analysis using Machine Learning Natural Language Processing Algorithm
NASA’s Air Traffic Management-Exploration (ATM-X) Urban Air Mobility (UAM) Airspace Subproject is conducting research that evolves UAM airspace towards a highly automated and operationally flexible system of the future (see https://www.nasa.gov/uam-overview/ for more information). The complexity of UAM airspace, and its evolution through a series of transformative epochs, requires a planning tool to effectively organize, integrate, and communicate the research that will guide the evolution of UAM operations in the National Airspace System (NAS). The planning tool, called the UAM airspace research roadmap (or just roadmap), is being developed as a new system engineering methodology leveraging model based system engineering (MBSE) and machine learning natural language processing (ML NLP, or just NLP) capabilities. This presentation gives an overview of the NLP application within this system engineering methodology and will describe how it is being used to meet the ATM-X UAM Airspace Subproject’s overarching research goals.
Automated isotope identification algorithm using artificial neural networks
There is a need to develop an algorithm that can determine the relative activities of radio-isotopes in a large dataset of low-resolution gamma-ray spectra that contains a mixture of many radio-isotopes. Low-resolution gamma-ray spectra that contain mixtures of radio-isotopes often exhibit feature over-lap, requiring algorithms that can analyze these features when overlap occurs. While machine learning and pattern recognition algorithms have shown promise for the problem of radio-isotope identification, their ability to identify and quantify mixtures of radio-isotopes has not been studied. Because machine learning algorithms use abstract features of the spectrum, such as the shape of overlapping peaks and Compton continuum, they are a natural choice for analyzing radio-isotope mixtures. An artificial neural network (ANN) has be trained to calculate the relative activities of 32 radio-isotopes in a spectrum. Furthermore, the ANN is trained with simulated gamma-ray spectra, allowing easy expansion of the library of target radio-isotopes. In this paper we present our initial algorithms based on an ANN and evaluate them against a series measured and simulated spectra.
Complexity-calibrated benchmarks for machine learning reveal when prediction algorithms succeed and mislead
Abstract Recurrent neural networks are used to forecast time series in finance, climate, language, and from many other domains. Reservoir computers are a particularly easily trainable form of recurrent neural network. Recently, a “next-generation” reservoir computer was introduced in which the memory trace involves only a finite number of previous symbols. We explore the inherent limitations of finite-past memory traces in this intriguing proposal. A lower bound from Fano’s inequality shows that, on highly non-Markovian processes generated by large probabilistic state machines, next-generation reservoir computers with reasonably long memory traces have an error probability that is at least $$\sim 60\%$$ ∼ 60 % higher than the minimal attainable error probability in predicting the next observation. More generally, it appears that popular recurrent neural networks fall far short of optimally predicting such complex processes. These results highlight the need for a new generation of optimized recurrent neural network architectures. Alongside this finding, we present concentration-of-measure results for randomly-generated but complex processes. One conclusion is that large probabilistic state machines—specifically, large $$\epsilon$$ ϵ -machines—are key to generating challenging and structurally-unbiased stimuli for ground-truthing recurrent neural network architectures.
Water Across Synthetic Aperture Radar Data (WASARD): SAR Water Body Classification for the Open Data Cube
The detection of inland water bodies from Synthetic Aperture Radar (SAR) data provides a great advantage over water detection with optical data, since SAR imaging is not impeded by cloud cover. Traditional methods of detecting water from SAR data involves using thresholding methods that can be labor intensive and imprecise. This paper describes Water Across Synthetic Aperture Radar Data (WASARD): a method of water detection from SAR data which automates and simplifies the thresholding process using machine learning on training data created from Geoscience Australia’s WOFS algorithm. Of the machine learning models tested, the Linear Support Vector Machine was determined to be optimal, with the option of training using solely the VH polarization or a combination of the VH and VV polarizations. WASARD was able to identify water in the target area with a correlation of 97% with WOFS. Sentinel-1, Open Data Cube, Earth Observations, Machine Learning, Water Detection 1. INTRODUCTION Water classification is an important function of Earth imaging satellites, as accurate remote classification of land and water can assist in land use analysis, flood prediction, climate change research, as well as a variety of agricultural applications [2]. The ability to identify bodies of water remotely via satellite is immensely cheaper than contracting surveys of the areas in question, meaning that an application that can accurately use satellite data towards this function can make valuable information available to nations which would not be able to afford it otherwise. Highly reliable applications for the remote detection of water currently exist for use with optical satellite data such as that provided by LANDSAT. One such application, Geoscience Australia’s Water Observations from Space (WOFS) has already been ported for use with the Open Data Cube [6]. However, water detection using optical data from Landsat is constrained by its relatively long revisit cycle of 16 days [5], and water detection using any optical data is constrained in that it lacks the ability to make accurate classifications through cloud cover [2]. The alternative solution which solves these problems is water detection using SAR data, which images the Earth using cloud-penetrating microwaves. Because of its advantages over optical data, much research has been done into water detection using SAR data. Traditionally, this has been done using the thresholding method, which involves picking a polarization band and labeling all pixels for which this band’s value is below a certain threshold as containing water. The thresholding method works since water tends to return a much lower backscatter value to the satellite than land [1]. However, this method can be flawed since estimating the proper threshold is often imprecise, complicated, and labor intensive for the end user. Thresholding also tends to use data from only one SAR polarization, when a combination of polarizations can provide insight into whether water is present. [2] In order to alleviate these problems, this paper presents an application for the Open Data Cube to detect water from SAR data using support vector machine (SVM) classification. 2. PLATFORM WASARD is an application for the Open Data Cube, a mechanism which provides a simple yet efficient means of ingesting, storing, and retrieving remote sensing data. Data can be ingested and made analysis ready according to whatever specifications the researcher chooses, and easily resampled to artificially alter a scene’s resolution. Currently WASARD supports water detection on scenes from ESA’s Sentinel-1 and JAXA’s ALOS. When testing WASARD, Sentinel-1 was most commonly used due to its relatively high spatial resolution and its rapid 6 day revisit cycle [5]. With minor alterations to the application's code, however, it could support data from other satellites. 3. METHODOLOGY Using supervised classification, WASARD compares SAR data to a dataset pre-classified by WOFS in order to train an SVM classifier. This classifier is then used to detect water in other SAR scenes outside the training set. Accuracy was measured according to the following metrics: Precision: a measure of what percentage of the points WASARD labels as water are truly water Recall: a measure of what percentage of the total water cover WASARD was able to identify. F1 Score: a harmonic average of the precision and recall scores Both precision and recall are calculated at the end of the training phase, when the trained classifier is compared to a testing dataset. Because the WOFS algorithm’s classifications are used as the truth values when training a WASARD classifier, when precision and recall are mentioned in this paper, they are always with respect to the values produced by WOFS on a similar scene of Landsat data, which themselves have a classification accuracy of 97% [6]. Visual representations of water identified by WASARD in this paper were produced using the function wasard_plot(), which is included in WASARD. 3.1 Algorithm Selection The machine learning model used by WASARD is the Linear Support Vector Machine (SVM). This model uses a supervised learning algorithm to develop a classifier, meaning it creates a vector which can be multiplied by the vector formed by the relevant data bands to determine whether a pixel in a SAR scene contains water. This classifier is trained by comparing data points from selected bands in a SAR scene to their respective labels, which in this case are “water” or “not water” as given by the WOFS algorithm. The SVM was selected over the Random Forest model, which outperformed the SVM in training speed, but had a greater classification time and lower accuracy, and the Multilayer Perceptron Artificial Neural Network, which had a slightly higher average accuracy than the SVM, but much greater training and classification times. Figure 1: Visual representation of the SVM Classifier. Each white point represents a pixel in a SAR scene. In Figure 1, the diagonal line separating pixels determined to be water from those determined not to be water represents the actual classification vector produced by the SVM. It is worth noting that once the model has been trained, classification of pixels is done in a similar manner as in the thresholding method. This is especially true if only one band was used to train the model. 3.1 Feature Selection Sentinel-1 collects data from two bands: the Vertical/Vertical polarization (VV) and the Vertical/Horizontal polarization (VH). When 100 SVM classifiers were created for each polarization individually, and for the combination of the two, the following results were achieved: Figure 2: Accuracy of classifiers trained using different polarization bands. Precision and Recall were measured with respect to the values produced by WOFS. Figure 2 demonstrates that using both the VV and VH bands trades slightly lower recall for significantly greater precision when compared with the VH band alone, and that using the VV band alone is inferior in both metrics. WASARD therefore defaults to using both the VV and VH bands, and includes the option to use solely the VH band. The VV polarization’s lower precision compared to the VH polarization is in contrast to results from previous research and may merit further analysis [4]. 3.2 Training a Classifier The steps in training a classifier with WASARD are 1. Selecting two scenes (one SAR, one optical) with the same spatial extents, and acquired close to each other in time, with a preference that the scenes are taken on the same day. 2. Using the WOFS algorithm to produce an array of the detected water in the scene of optical data, to be used as the labels during supervised learning 3. Data points from the selected bands from the SAR acquisition are bundled together into an array with the corresponding labels gathered from WOFS. A random sample with an equal number of points labeled “Water” and “Not Water” is selected to be partitioned into a training and a testing dataset 4. Using Scikit-Learn’s LinearSVC object, the training dataset is used to produce a classifier, which is then tested against the testing dataset to determine its precision and recall The result is a wasard_classifier object, which has the following attributes: 1. f1, recall, and precision: 3 metrics used to determine the classifier’s accuracy 2. Coefficient: Vector which the SVM uses to make its predictions. The classifier detects water when the dot product of the coefficient and the vector formed by the SAR bands is positive 3. Save(): allows a user to save a classifier to the disk in order to use it without retraining 4. wasard_classify(): Classifies an entire xarray of SAR data using the SVM classifier All of the above steps are performed automatically when the user creates a wasard_classifier object. 3.3 Classifying a Dataset Once the classifier has been created, it can be used to detect water in an xarray of SAR data using wasard_classify(). By taking the dot product of the classifier’s coefficients and the vector formed by the selected bands of SAR data, an array of predictions is constructed. A classifier can effectively be used on the same spatial extents as the ones where it was trained, or on any area with a similar landscape. While