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21 records · Page 2

Machine Learning Benchmarks for the Classification of Equivalent Circuit Models from Electrochemical Impedance Spectra

Analysis of Electrochemical Impedance Spectroscopy (EIS) data for electrochemical systems often consists of defining an Equivalent Circuit Model (ECM) using expert knowledge and then optimizing the model parameters to deconvolute various resistance, capacitive, inductive, or diffusion responses. For small data sets, this procedure can be conducted manually; however, it is not feasible to manually define a proper ECM for extensive data sets with a wide range of EIS responses. Automatic identification of an ECM would substantially accelerate the analysis of large sets of EIS data. We showcase machine learning methods to classify the ECMs of 9,300 impedance spectra provided by QuantumScape for the BatteryDEV hackathon. The best-performing approach is a gradient-boosted tree model utilizing a library to automatically generate features, followed by a random forest model using the raw spectral data. A convolutional neural network using boolean images of Nyquist representations is presented as an alternative, although it achieves a lower accuracy. We publish the data and open source the associated code. The approaches described in this article can serve as benchmarks for further studies. A key remaining challenge is the identifiability of the labels, underlined by the model performances and the comparison of misclassified spectra.

25 ENERGY STORAGE↗

Decision-Tree Formulation With Order-1 Lateral Execution

A compact symbolic formulation enables mapping of an arbitrarily complex decision tree of a certain type into a highly computationally efficient multidimensional software object. The type of decision trees to which this formulation applies is that known in the art as the Boolean class of balanced decision trees. Parallel lateral slices of an object created by means of this formulation can be executed in constant time considerably less time than would otherwise be required. Decision trees of various forms are incorporated into almost all large software systems. A decision tree is a way of hierarchically solving a problem, proceeding through a set of true/false responses to a conclusion. By definition, a decision tree has a tree-like structure, wherein each internal node denotes a test on an attribute, each branch from an internal node represents an outcome of a test, and leaf nodes represent classes or class distributions that, in turn represent possible conclusions. The drawback of decision trees is that execution of them can be computationally expensive (and, hence, time-consuming) because each non-leaf node must be examined to determine whether to progress deeper into a tree structure or to examine an alternative. The present formulation was conceived as an efficient means of representing a decision tree and executing it in as little time as possible. The formulation involves the use of a set of symbolic algorithms to transform a decision tree into a multi-dimensional object, the rank of which equals the number of lateral non-leaf nodes. The tree can then be executed in constant time by means of an order-one table lookup. The sequence of operations performed by the algorithms is summarized as follows: 1. Determination of whether the tree under consideration can be encoded by means of this formulation. 2. Extraction of decision variables. 3. Symbolic optimization of the decision tree to minimize its form. 4. Expansion and transformation of all nested conjunctive-disjunctive paths to a flattened conjunctive form composed only of equality checks when possible. If each reduced conjunctive form contains only equality checks and all of these forms use the same variables, then the decision tree can be reduced to an order-one operation through a table lookup. The speedup to order one is accomplished by distributing each decision variable over a surface of a multidimensional object by mapping the equality constant to an index

James, Mark↗

Structured adaptive grid generation using algebraic methods

The accuracy of the numerical algorithm depends not only on the formal order of approximation but also on the distribution of grid points in the computational domain. Grid adaptation is a procedure which allows optimal grid redistribution as the solution progresses. It offers the prospect of accurate flow field simulations without the use of an excessively timely, computationally expensive, grid. Grid adaptive schemes are divided into two basic categories: differential and algebraic. The differential method is based on a variational approach where a function which contains a measure of grid smoothness, orthogonality and volume variation is minimized by using a variational principle. This approach provided a solid mathematical basis for the adaptive method, but the Euler-Lagrange equations must be solved in addition to the original governing equations. On the other hand, the algebraic method requires much less computational effort, but the grid may not be smooth. The algebraic techniques are based on devising an algorithm where the grid movement is governed by estimates of the local error in the numerical solution. This is achieved by requiring the points in the large error regions to attract other points and points in the low error region to repel other points. The development of a fast, efficient, and robust algebraic adaptive algorithm for structured flow simulation applications is presented. This development is accomplished in a three step process. The first step is to define an adaptive weighting mesh (distribution mesh) on the basis of the equidistribution law applied to the flow field solution. The second, and probably the most crucial step, is to redistribute grid points in the computational domain according to the aforementioned weighting mesh. The third and the last step is to reevaluate the flow property by an appropriate search/interpolate scheme at the new grid locations. The adaptive weighting mesh provides the information on the desired concentration of points to the grid redistribution scheme. The evaluation of the weighting mesh is accomplished by utilizing the weight function representing the solution variation and the equidistribution law. The selection of the weight function plays a key role in grid adaptation. A new weight function utilizing a properly weighted boolean sum of various flowfield characteristics is defined. The redistribution scheme is developed utilizing Non-Uniform Rational B-Splines (NURBS) representation. The application of NURBS representation results in a well distributed smooth grid by maintaining the fidelity of the geometry associated with boundary curves. Several algebraic methods are applied to smooth and/or nearly orthogonalize the grid lines. An elliptic solver is utilized to smooth the grid lines if there are grid crossings. Various computational examples of practical interest are presented to demonstrate the success of these methods.

Yang, Jiann-Cherng↗