Patent Publication Number: US-11035227-B2

Title: Generating spectral responses of materials

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims priority to U.S. provisional patent application No. 62/532,803 filed on Jul. 14, 2017 by The Board of Regents of the University of Oklahoma and titled “Generating Spectral Responses of Materials,” U.S. provisional patent application No. 62/554,352 filed on Sep. 5, 2017 by The Board of Regents of the University of Oklahoma and titled “Generating Spectral Responses of Materials,” and U.S. provisional patent application No. 62/598,182 filed on Dec. 13, 2017 by The Board of Regents of the University of Oklahoma and titled “Generating Spectral Responses of Materials,” all of which are incorporated by reference. 
    
    
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
     Not applicable. 
     BACKGROUND 
     Material analyses are important tools in many industries. Material analyses help determine types, characterizations, properties, and positions of those materials, as well as what substances and how much of those substances are in those materials. The properties include spatial features, internal arrangements, compositions, structures, distributions, and temporal changes. It is desirable to conduct material analyses in a cost-effective and operationally-convenient manner in the absence of the infrastructure needed to directly perform those material analyses. As a result, significant research is directed to reducing costs of material analyses, as well as improving materials analyses with an emphasis on reducing operational challenges. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a more complete understanding of this disclosure, reference is now made to the following brief description, taken in connection with the accompanying drawings and detailed description, wherein like reference numerals represent like parts. 
         FIG. 1  is a schematic diagram of a system for generating spectral responses of materials. 
         FIG. 2  is a flowchart illustrating a method of generating a spectral response of a material according to an embodiment of the disclosure. 
         FIG. 3  is a schematic diagram of the trainer in  FIG. 1 . 
         FIG. 4  is a 2D latent space according to an embodiment of the disclosure. 
         FIG. 5  is a 3D latent space according to an embodiment of the disclosure. 
         FIG. 6  is a schematic diagram of mathematical operations performed in a VAE according to an embodiment of the disclosure. 
         FIG. 7  is a schematic diagram of the tester in  FIG. 1 . 
         FIG. 8  is a schematic diagram of the generator in  FIG. 1 . 
         FIG. 9  is a flowchart illustrating a method of generating a generated spectral response of a material according to another embodiment of the disclosure. 
         FIG. 10  is a schematic diagram of a device according to an embodiment of the disclosure. 
         FIG. 11  is a plot comparing historical spectral responses to tested spectral responses for the 2D latent space. 
         FIG. 12  is a plot of R-squared for the generated spectral responses for the 2D latent space. 
         FIG. 13  is a plot comparing historical spectral responses to tested spectral responses for the 3D latent space. 
         FIG. 14  is a plot of R-squared for the generated spectral responses for the 3D latent space. 
         FIG. 15  is a series of plots comparing original dielectric spectra to generated dielectric spectra. 
         FIG. 16  is a GUI for implementing the system in  FIG. 1  according to an embodiment of the disclosure. 
         FIG. 17  is a schematic diagram of a generator based on a VAE-CNN model according to an embodiment of the disclosure. 
         FIG. 18  is a schematic diagram of a generator based on an LSTM/RNN model according to an embodiment of the disclosure. 
         FIG. 19  is a schematic diagram of a generator based on a GAN model according to an embodiment of the disclosure. 
         FIG. 20  is a flowchart illustrating a method of using a stacked ANN model for generating dielectric spectra according to an embodiment of the disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     In at least one non-limiting embodiment, the present disclosure is directed to a controller having a memory, and a processor coupled to the memory and configured to cause a neural network to (1) receive current measurements of a current material, (2) instruct the neural network to determine dominant features of the current measurements, (3) instruct the neural network to provide the dominant features to a decoder, and (4) instruct the decoder to generate a specific spectral response of the current material based on the dominant features. 
     In another non-limiting embodiment, the disclosure is directed to a method including the steps of (1) receiving current measurements of a current material, (2) determining dominant features of the current measurements, (3) providing the dominant features, and (4) generating a spectral response of the current material based on the dominant features. 
     In another non-limiting embodiment, the present disclosure is directed to a system having (1) a trainer including a deep neural network model having an encoder, a latent space database coupled to the encoder, and a first decoder; (2) a neural network system having a first neural network, and a second decoder associated with the first decoder; (3) a tester having a second neural network associated with the first neural network; (4) a third decoder associated with the second decoder; (5) a generator having a third neural network associated with the second neural network; and (6) a fourth decoder associated with the third decoder. In non-limiting embodiments, the deep neural network model can be a VAE, a GAN, an LSTM, an RNN, or a CNN for generating the specific spectral response. 
     The spectral response generated by the controllers, systems, and methods of the present disclosure may be used to instruct an operation such as, but not limited to, a drilling operation and/or a well completion operation. 
     It should be understood at the outset that, although an illustrative implementation of one or more embodiments are provided below, the disclosed systems and/or methods may be implemented using any number of techniques, whether currently known or in existence. The disclosure should in no way be limited to the illustrative implementations, drawings, and techniques illustrated below, including the exemplary designs and implementations illustrated and described herein, but may be modified in accordance with the presently disclosed inventive concepts. 
     Features of any of the embodiments described herein may be combined with any of the other embodiments to create a new embodiment. These and other features will be more clearly understood from the following detailed description taken in conjunction with the accompanying drawings and exemplary claims. 
     Before describing various embodiments of the present disclosure in more detail by way of exemplary description, examples, and results, it is to be understood as noted above that the present disclosure is not limited in application to the details of methods and apparatus as set forth in the following description. The present disclosure is capable of other embodiments or of being practiced or carried out in various ways. As such, the language used herein is intended to be given the broadest possible scope and meaning; and the embodiments are meant to be exemplary, not exhaustive. Also, it is to be understood that the phraseology and terminology employed herein is for the purpose of description and should not be regarded as limiting unless otherwise indicated as so. Moreover, in the following detailed description, numerous specific details are set forth in order to provide a more thorough understanding of the disclosure. However, it will be apparent to a person having ordinary skill in the art that the embodiments of the present disclosure may be practiced without these specific details. In other instances, features which are well known to persons of ordinary skill in the art have not been described in detail to avoid unnecessary complication of the description. 
     Unless otherwise defined herein, scientific and technical terms used in connection with the present disclosure shall have the meanings that are commonly understood by those having ordinary skill in the art. Further, unless otherwise required by context, singular terms shall include pluralities and plural terms shall include the singular. 
     All patents, published patent applications, and non-patent publications mentioned in the specification are indicative of the level of skill of those skilled in the art to which the present disclosure pertains. All patents, published patent applications, and non-patent publications referenced in any portion of this application are herein expressly incorporated by reference in their entirety to the same extent as if each individual patent or publication was specifically and individually indicated to be incorporated by reference. 
     As utilized in accordance with the methods and apparatus of the present disclosure, the following terms, unless otherwise indicated, shall be understood to have the following meanings: 
     The use of the word “a” or “an” when used in conjunction with the term “comprising” in the claims and/or the specification may mean “one,” but it is also consistent with the meaning of “one or more,” “at least one,” and “one or more than one.” The use of the term “or” in the claims is used to mean “and/or” unless explicitly indicated to refer to alternatives only or when the alternatives are mutually exclusive, although the disclosure supports a definition that refers to only alternatives and “and/or.” The use of the term “at least one” will be understood to include one as well as any quantity more than one, including but not limited to, 2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 20, 30, 40, 50, 100, or any integer inclusive therein. The term “at least one” may extend up to 100 or 1000 or more, depending on the term to which it is attached; in addition, the quantities of 100/1000 are not to be considered limiting, as higher limits may also produce satisfactory results. In addition, the use of the term “at least one of X, Y and Z” will be understood to include X alone, Y alone, and Z alone, as well as any combination of X, Y and Z. 
     As used herein, all numerical values or ranges include fractions of the values and integers within such ranges and fractions of the integers within such ranges unless the context clearly indicates otherwise. Thus, to illustrate, reference to a numerical range, such as 1-10 includes 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, as well as 1.1, 1.2, 1.3, 1.4, 1.5, etc., and so forth. Reference to a range of 1-50 therefore includes 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, etc., up to and including 50, as well as 1.1, 1.2, 1.3, 1.4, 1.5, etc., 2.1, 2.2, 2.3, 2.4, 2.5, etc., and so forth. Reference to a series of ranges includes ranges which combine the values of the boundaries of different ranges within the series. Thus, to illustrate reference to a series of ranges, for example, of 1-10, 10-20, 20-30, 30-40, 40-50, 50-60, 60-75, 75-100, 100-150, 150-200, 200-250, 250-300, 300-400, 400-500, 500-750, 750-1,000, includes ranges of 1-20, 10-50, 50-100, 100-500, and 500-1,000, for example. A reference to degrees such as 1 to 90 is intended to explicitly include all degrees in the range. 
     As used herein, the words “comprising” (and any form of comprising, such as “comprise” and “comprises”), “having” (and any form of having, such as “have” and “has”), “including” (and any form of including, such as “includes” and “include”) or “containing” (and any form of containing, such as “contains” and “contain”) are inclusive or open-ended and do not exclude additional, unrecited elements or method steps. 
     The term “or combinations thereof” as used herein refers to all permutations and combinations of the listed items preceding the term. For example, “A, B, C, or combinations thereof” is intended to include at least one of: A, B, C, AB, AC, BC, or ABC, and if order is important in a particular context, also BA, CA, CB, CBA, BCA, ACB, BAC, or CAB. Continuing with this example, expressly included are combinations that contain repeats of one or more item or term, such as BB, AAA, AAB, BBC, AAABCCCC, CBBAAA, CABABB, and so forth. The skilled artisan will understand that typically there is no limit on the number of items or terms in any combination, unless otherwise apparent from the context. 
     Throughout this application, the term “about” is used to indicate that a value includes the inherent variation of error. Further, in this detailed description, each numerical value (e.g., temperature or time) should be read once as modified by the term “about” (unless already expressly so modified), and then read again as not so modified unless otherwise indicated in context. As noted, any range listed or described herein is intended to include, implicitly or explicitly, any number within the range, particularly all integers, including the end points, and is to be considered as having been so stated. For example, “a range from 1 to 10” is to be read as indicating each possible number, particularly integers, along the continuum between about 1 and about 10. Thus, even if specific data points within the range, or even no data points within the range, are explicitly identified or specifically referred to, it is to be understood that any data points within the range are to be considered to have been specified, and that the inventors possessed knowledge of the entire range and the points within the range. The use of the term “about” may mean a range including ±10% of the subsequent number unless otherwise stated. 
     As used herein, the term “substantially” means that the subsequently described parameter, event, or circumstance completely occurs or that the subsequently described parameter, event, or circumstance occurs to a great extent or degree. For example, the term “substantially” means that the subsequently described parameter, event, or circumstance occurs at least 90% of the time, or at least 91%, or at least 92%, or at least 93%, or at least 94%, or at least 95%, or at least 96%, or at least 97%, or at least 98%, or at least 99%, of the time, or means that the dimension or measurement is within at least 90%, or at least 91%, or at least 92%, or at least 93%, or at least 94%, or at least 95%, or at least 96%, or at least 97%, or at least 98%, or at least 99%, of the referenced dimension or measurement (e.g., length). 
     As used herein any reference to “one embodiment” or “an embodiment” means that a particular element, feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment. The appearances of the phrase “in one embodiment” in various places in the specification are not necessarily all referring to the same embodiment. 
     The following abbreviations and initialisms apply: 
     ANN: artificial neural network 
     ASIC: application-specific integrated circuit 
     BPS: Bakken petroleum system 
     CNN: convolutional neural network 
     CPU: central processing unit 
     CT: computerized tomography 
     DSP: digital signal processor 
     EO: electrical-to-optical 
     FPGA: field-programmable gate array 
     ft: foot, feet 
     GAN: generative adversarial network 
     GHz: gigahertz 
     GR: gamma ray 
     GUI: graphical user interface 
     KL: Kullback-Leibler 
     LSTM: long short-term memory 
     MHz: megahertz 
     ML: machine learning 
     ms: millisecond(s) 
     mS/m: millisiemen(s) per meter 
     NMR: nuclear magnetic resonance 
     NN: neural network 
     OE: optical-to-electrical 
     RAM: random-access memory 
     RMS: root mean square 
     RNN: recurrent neural network 
     ROM: read-only memory 
     RX: receiver unit 
     SRAM: static RAM 
     TCAM: ternary content-addressable memory 
     TOC: total organic compound 
     TX: transmitter unit 
     VAE: variational auto-encoder 
     Vp: compressional velocity 
     Vs: shear velocity 
     wt %: percentage by weight 
     1D: one-dimensional 
     2D: two-dimensional 
     3D: three-dimensional 
     %: percentage. 
     The oil and gas industry is one industry that conducts material analyses of geological materials in laboratories and in the subsurface using wireline logging tools, logging while drilling tools, measurement while drilling tools and rate/pressure transient measurements. For instance, the oil and gas industry performs spectral analyses of porous materials such as shale or other hydrocarbon-bearing rocks that contain water, carbon, or other materials to determine what kind of rock is analyzed, how porous the rock is, how big the pores are, a pore size distribution, a depth below the surface where the rock exhibits a desired property, whether water or oil is in the rock, how much water or oil is in the rock, permeability, fluid mobility, bound fluid saturation, or other characteristics. The civil, mining, geoengineering, chemical, non-destructive testing, remote sensing, material science, analytical chemistry, semiconductor, medical sensing, polymer, and geophysical industries also perform such material analyses. One way to conduct such a material analysis is to perform spectroscopy. 
     Spectroscopy is a process in which a tool excites a material using radiative energy such as electromagnetic radiation, kinetic energy of particles, acoustic waves, or mechanical impact and an instrument measures a resulting spectral response or emission spectrum. The spectral response is a signal produced due to an interaction between the material and the radiative energy. The instrument measures or decomposes the signal as a function of a continuous variable such as energy in electron spectroscopy, mass-to-charge ratio in mass spectroscopy, frequency in dielectric spectroscopy, relaxation time in NMR spectroscopy, or time in rate/pressure transient measurements. 
     For instance, NMR spectroscopy is a process in which a magnetic source applies a magnetic field to a material and an instrument measures a resulting spectral response. Specifically, the magnetic source magnetizes hydrogen nuclei, carbon nuclei, or other nuclei that have magnetic poles. After application of the magnetic field, the material undergoes relaxation, which is the return of the nuclei to their original states. As the material does so, the material emits electromagnetic radiation in a specific manner. A device measures the electromagnetic radiation as a spectral response and may determine a T2 distribution from that spectral response. A T2 distribution indicates a relaxation time associated with broadening of a signal produced during the relaxation of the nuclei. 
     While spectroscopy is a helpful process, the cost of performing spectroscopy at a site of a material, such as a subsurface hydrocarbon reservoir, a groundwater aquifer, or deep mines, through a borehole may be prohibitively high, particularly when the spectroscopy is NMR spectroscopy, dielectric spectroscopy, or elemental spectroscopy. Mohammad Mandi Labani, et al., “Estimation of NMR log parameters from conventional well log data using a committee machine with intelligent systems: A case study from the Iranian part of the South Pars gas field, Persian Gulf Basin,” Journal of Petroleum Science and Engineering, Vol. 72, Issues 1-2, May 2010, which is incorporated by reference, describes a model that estimates NMR permeability from conventional logs. The model estimates NMR permeability, but not bound, free fluid, or other key data. Reza Farzi, et al., “Simulation of NMR response from micro-CT images using artificial neural networks,” Journal of Natural Gas Science and Engineering, Vol. 39, pages 54-61, March 2017, which is incorporated by reference, describes acquisition of micro-CT images through measurements of core samples, extraction of numerical features from the CT images, and simulation of an NMR relation time using the numerical features. However, the measurements of the core samples and the extraction of the numerical features are complex and applicable only in a laboratory. 
     Disclosed herein are embodiments for generating spectral responses of materials. The embodiments may be performed in the absence of some spectroscopy tools by processing current measurements acquired using available spectroscopy tools. The embodiments provide for training, testing, and generating steps based on machine learning and computation to produce generated, or synthetic or simulated, spectral responses of materials using historical measurements for purposes of material analyses in the absence of a spectroscopy tool. The generated spectral responses are not measured at a site, but are instead generated using a generator, historical spectral responses, and other historical measurements, thus greatly reducing the costs of analyzing materials. The embodiments dramatically reduce the dependency on spectroscopy tools when these tools are hard to find and deploy due to operational and logistical challenges. The generated spectral responses help determine what kind of materials are analyzed, how porous the materials are, how big the pores are, pore size distributions, a depth below the surface wherein the materials exhibit desired properties, whether water or oil is in the materials, how much water or oil is in the materials, permeabilities, fluid mobilities, bound fluid saturations, internal structures, compositions, concentrations, spatial variations, temporal changes, or other characteristics of the materials. The embodiments apply to generating spectral responses of subsurface geological formations such as shales, sandstones, carbonates, turbidites, and shaly sands for the oil and gas industry, as well as generating spectral responses of other materials for other industries. 
     A T2 distribution of a material is calculated as follows: 
                       1     T   2       =       1     T     2   ,   bulk         +     1     T     2   ,   surface         +     1     T     2   ,   diffusion             ,           (   1   )               
where T 2  is a T2 distribution of a material, T 2,bulk  is a bulk fluid relaxation indicating how much fluid is present in the material, T 2,surface  is a surface relaxation indicating characteristics of a surface of the material, and T 2,diffusion  is a diffusion relaxation indicating how excited nuclei diffuse within the material. A fluid type, a hydrogen content, and fluid mobility affect the bulk fluid relaxation. Surface relaxation occurs at a fluid-solid interface. A pore shape, pore network characteristics, and mineralogy affect surface relaxation. Diffusion relaxation occurs due to a non-zero gradient of a magnetic field exciting the material. Thus, both fluid saturations and chemical compositions of materials affect T2 distributions. By first determining complex relationships between the fluid saturations and the chemical compositions on one hand and the T2 distributions on the other hand, as well as identifying complex patterns and features in the spectra and measurements, one can then determine T2 distributions when receiving only the fluid saturations and the chemical compositions as input data. Together, the fluid saturations, the chemical compositions, or other characteristics may be referred to as material measurements, historical measurements, current measurements, real-time measurements, or simply measurements.
 
       FIG. 1  is a schematic diagram of a system  100  for generating spectral responses of materials. The system  100  comprises a controller  110 , a trainer  120 , a tester  130 , a generator  140 , and a database  150 . The controller  110  is a hardware computer server. The controller  110  controls or instructs the trainer  120 , the tester  130 , and the generator  140 , so it may be understood that the controller  110  controls, instructs, or otherwise causes the functions of those components as described below. Alternatively, the trainer  120 , the tester  130 , or the generator  140  act independently of the controller  110  for any of the functions of those components as described below. The controller  110  may comprise a GUI or another interface in order for a user to instruct the controller  110  as to how to control the trainer  120 , the tester  130 , and the generator  140 . In addition, the user views or otherwise receives data from, or the user supplies data to, the trainer  120 , the tester  130 , and the generator  140  via the GUI or other interface. The trainer  120 , the tester  130 , and the generator  140  are described further below. The database  150  is a memory or a portion of a memory. The database  150  stores data and supplies that data to the trainer  120 , the tester  130 , and the generator  140 . Alternatively, the database  150  is separated into a historical database storage coupled to the trainer  120  and the tester  130 , a current measurement storage coupled to the generator  140 , and a generated spectral response visualization and storage unit coupled to the generator  140 . 
       FIG. 2  is a flowchart illustrating a method  200  of generating a spectral response of a material according to an embodiment of the disclosure. The system  100  performs the method  200 . At step  210 , training is performed. For instance, the trainer  120  performs the training in response to instructions from the controller  110  to create a decoder and a neural network for step  220 . The decoder is based on an iterative processing of a historical spectral response of a historical material, and the neural network is based on an iterative processing of historical measurements of the historical material. At step  220 , testing is performed. For instance, the tester  130  performs the testing in response to instructions from the controller  110  in order to assess a performance of the decoder and the neural network. The neural network and the decoder are based on a processing of testing measurements of the historical material. Finally, at step  230 , generating is performed. For instance, the generator  140  performs the generating in response to instructions from the controller  110  to produce a generated spectral response based on a processing of current measurements of a current material for which no measured spectral response is available, but for which a generated spectral response is desired. The current material is the same material as the historical material or is similar to the historical material. The steps  210 ,  220 ,  230  are described further below. 
       FIG. 3  is a schematic diagram of the trainer  120  in  FIG. 1 . The trainer  120  generally comprises a deep neural network model  310  and a neural network system  360 . As mentioned above, the trainer  120  performs step  210  in  FIG. 2 . 
     The deep neural network model  310  may be a VAE, an LSTM, a CNN, an RNN, or a GAN. A VAE is a type of auto-encoder. The deep neural network model  310  trains to reproduce its input data as its output data as described in Ian Goodfellow, et al., “Deep Learning,” Nov. 10, 2016, which is incorporated by reference. Specifically, the deep neural network model  310  trains to reproduce a historical spectral response as a reproduced spectral response. The deep neural network model  310  comprises an encoder  320 , a latent space database  330 , a decoder  340 , and a comparer  350 . The encoder  320 , the decoder  340 , and the comparer  350  are software components, and the latent space database  330  is a memory or a portion of a memory. The latent space database  330  may be a part of the database  150 . 
     The encoder  320  receives a historical spectral response from the database  150 , determines dominant features of the historical spectral response, encodes a latent space based on the dominant features, and provides the latent space to the latent space database  330 . Alternatively, the historical spectral response is a real-time spectral response, and the encoder  320  receives the real-time spectral response from a real-time source of data. The historical spectral response is an NMR T2 distribution, an electromagnetic spectrum, a particle concentration/energy spectrum, a natural or induced radiation spectrum such as a gamma-ray spectrum, or another suitable spectral response of the historical material. The historical spectral response originates from a laboratory, subsurface, surface, or atmospheric environment. The dominant features of the historical spectral response may be referred to as latent variables. The dominant features include heights of peaks, variances around the peaks, distances between the peaks, relative features of the peaks, rates of change or other higher-order derivatives of magnitudes and phases with respect to time or other independent variables, numbers of peaks, or other identifying features of the historical spectral response. The word “latent” connotes that the dominant features are not physical features of the historical spectral response with well-defined physical significance. The encoder  320  constrains the latent variables to follow a Gaussian distribution as described in Diederik Kingma, et al., “Auto-Encoding Variational Bayes,” May 1, 2014, which is incorporated by reference. The Gaussian distribution adds uncertainty to the latent variables. The latent space is a collection of the latent variables organized in a manner that indicates the latent variables and is therefore usable by the decoder  340 . Because the encoder  320  projects data from a relatively higher dimension in the historical spectral response to a relatively lower dimension in the latent space, the encoder  320  narrows from left to right. Alternatively, the encoder acts as a creator or an extractor. 
     The latent space database  330  receives the latent space from the encoder  320  and stores the latent space. In the latent space, data with similar dominant features are close to each other in order to reduce a loss when the decoder  340  attempts to reproduce the historical spectral response.  FIGS. 4 and 5  illustrate such a latent space. 
       FIG. 4  is a 2D latent space  400  according to an embodiment of the disclosure. The 2D latent space  400  indicates latent variables. As a first example, a top-left corner of the 2D latent space  400  comprises curves with single peaks. As the curves shift to a top-middle portion of the 2D latent space  400 , the peaks shift to the middle. As a second example, a top-right corner of the 2D latent space  400  comprises curves with two peaks of similar amplitude. As the curves shift to a bottom-right corner of the 2D latent space  400 , left peaks lower in amplitude and right peaks increase in amplitude. The 2D latent space  400  indicates other latent variables as well. These variations are indicative of the learning accomplished during the training the trainer  120  performs at step  210 . 
       FIG. 5  is a 3D latent space  500  according to an embodiment of the disclosure. The 3D latent space  500  is similar to the 2D latent space  400  in  FIG. 4 , but the 3D latent space  500  provides a third dimension of latent variables in addition to the two dimensions of the 2D latent space  400 . 
     Returning to  FIG. 3 , the latent space in the latent space database  330  is the 2D latent space  400 , the 3D latent space  500 , or another suitable latent space. The latent space database  330  may store the 3D latent space  500  or a higher-dimension latent space when there are many historical spectral responses or when those historical responses have a large range of latent variables. 
     The decoder  340  receives the latent space from the latent space database  330  and decodes a reproduced spectral response based on the encoder&#39;s projection of the historical spectral response on the latent space. Because the decoder  340  projects data from a relatively lower dimension in the latent space to a relatively higher dimension in the initial spectral response, the decoder  340  widens from left to right. Alternatively, the decoder  340  acts as a comparator or a reconstructor. 
     The comparer  350  compares the reproduced spectral response from the decoder  340  to the historical spectral response at the encoder  320  to determine a similarity between the reproduced spectral response and the historical spectral response. If the similarity is below an initial threshold, then the comparer  350  instructs the encoder  320 , the latent space database  330 , and the decoder  340  to repeat their functions, and the comparer  350  reassigns weights and biases in the encoder  320  and the decoder  340  until the similarity is at or above the initial threshold. Once the similarity is at or above the initial threshold, the comparer  350  instructs the decoder  340  to freeze, and thus become a frozen decoder. The comparer  350  stores the decoder  340  for further use in the neural network system  360  in the trainer  120  and for further use in the tester  130 . 
     The neural network system  360  comprises a neural network  370 , a decoder  380 , and a comparer  390 . The neural network  370  is a software component or software components comprising various functions that train to produce complex relationships between the historical spectral response and the historical measurements. The neural network  370  may be distributed among multiple hardware computers. The decoder  380  and the comparer  390  are software components. The decoder  380  is the frozen decoder described above and remains frozen in the neural network system  360 . Thus, between the neural network  370  and the decoder  380 , only the neural network  370  trains. 
     The neural network  370  receives historical measurements from the database  150 , determines dominant features of the historical measurements, learns to relate the dominant features to the historical spectral response, and provides the dominant features to the decoder  380 , thereby associating the historical measurements to the historical spectral response. Alternatively, the historical measurements are real-time measurements, and the neural network  370  receives the real-time measurements from a real-time source of data. If the historical spectral response is an NMR T2 distribution, then the historical measurements comprise fluid saturation data; mineral composition data; raw subsurface logs such as gamma ray logs, resistivity logs, anisotropy logs, neutron porosity logs, density porosity logs, or photoelectric factor logs; or other suitable data from a subsurface, a surface, the atmosphere, or a laboratory. If the spectral historical spectral response is a dielectric spectrum, then the historical measurements comprise natural radiation data, induced radiation data, density data, porosity data, nuclear radiation data, photoelectric factor logs, sonic data, sonic logs, resistivity data, or other suitable data from a subsurface, a surface, the atmosphere, or a laboratory. The historical measurements are for the historical material. The dominant features of the historical measurements are heights of peaks, variances around the peaks, distances between the peaks, relative features of the peaks, rates of change or other higher-order derivatives of magnitudes and phases with respect to time or other independent variables, numbers of peaks, or other identifying features of the historical measurements. 
     The decoder  380  begins as the frozen decoder described above. The decoder  380  decodes a trained spectral response based on a projection of the historical measurements on the dominant features in the historical measurements with respect to the historical spectral response. Because the decoder  380  projects data from a relatively lower dimension in the dominant features to a relatively higher dimension in the trained spectral response, the decoder  380  widens from left to right. Alternatively, the decoder  340  is a comparator or a reconstructor. 
     The comparer  390  compares the trained spectral response from the decoder  380  to the historical spectral response at the encoder  320  to determine a similarity between the trained spectral response and the historical spectral response. If the similarity is below a final threshold, then the comparer  390  instructs the neural network  370  to repeat its functions, and the comparer  390  reassigns weights and biases in the neural network  370  until the similarity is at or above the final threshold. Once the similarity is at or above the final threshold, the comparer  390  instructs the neural network  370  to freeze, and thus become a frozen neural network. The comparer  390  stores the neural network  370  for further use in the tester  130 . 
       FIG. 6  is a schematic diagram of mathematical operations performed in a VAE  600  according to an embodiment of the disclosure. The VAE  600  is an embodiment of the deep neural network model  310  in  FIG. 3 . The VAE  600  comprises an input x  605 , an encoder  610 , function  615 , a function  620 , a loss function  625 , a sample ε  630 , a multiplier  635 , an adder  640 , a latent space z  645 , a decoder  650 , a function  655 , and a loss function  660 . 
     The input x  605 , the encoder  610 , the latent space z  645 , and the decoder  650  are similar to the historical spectral response, the encoder  320 , the latent space in the latent space database  330 , and the decoder  340  in  FIG. 3 , respectively. The function  615  is an deterministic function that defines a mean of a probability distribution function of a projection generated by the encoder  610 . The function  620  is an deterministic function that defines a covariance the probability distribution function. The function  655  is a deterministic function that is a reproduction of the input x  605 . 
     The loss functions  625 ,  660  guide the VAE  600  to generate an output, for instance the reproduced spectral response in  FIG. 3 , that matches the input x  605 . The VAE  600  alters weights to minimize the loss functions  625 ,  660 . The loss function  660  enables the VAE  600  to learn to minimize a difference between inputs and outputs. A KL divergence of the loss function  625  forces the encoder  610  to generate the latent space z  645  so that the latent space z  645  follows a Gaussian distribution. As described in Carl Doersch, “Tutorial on Variational Autoencoders,” Aug. 13, 2016, which is incorporated by reference, a KL divergence between two multivariate Gaussian distributions is expressed as follows: 
                   KL   =     [         N   (       μ   ⁡     (   X   )       ,       ∑     (   x   )       ||     N   ⁡     (     0   ,   I     )           ]     =       1   2     ⁢     (       tr   ⁡     (     ∑     (   X   )       )       +         (     μ   ⁡     (   X   )       )     2     ⁢     (     μ   ⁡     (   X   )       )       -   k   -     log   ⁢           ⁢     det   ⁡     (     ∑     (   X   )       )           )         ,               (   2   )               
where X is a historical spectral response and N(μ,Σ) represents the Gaussian distribution with a mean μ a covariance Σ, and a dimensionality k.
 
     The sample ε  630  represents a re-parameterization trick to reconstruct the latent space z  645 . A neural network such as the neural network  370  in  FIG. 3  trains through backpropagation and therefore calculates a contribution of each node to a final error, then learns to reduce an error. If latent variables sample randomly from the Gaussian distribution, then backpropagation may not be efficient for training the neural network. The representation process selects the sample ε  630  from the Gaussian distribution, which is N(0, I), and changes its mean and variance through a linear calculation. By this method, the latent space z  645  still follows the Gaussian distribution, but the neural network may train through backpropagation. 
       FIG. 7  is a schematic diagram of the tester  130  in  FIG. 1 . The tester  130  is similar to the neural network system  360  in  FIG. 3 . However, the tester  130  comprises a neural network  710 , which is the frozen neural network after the neural network system  360  completes training, and a decoder  720 , which is the frozen decoder after the deep neural network model  310  completes training. The tester  130  obtains the neural network  710  and the decoder  720  from the database  150 . As mentioned above, the tester  130  performs step  220  in  FIG. 2 . 
     The neural network  710  receives a testing spectral response and testing measurements from the database  150 , determines dominant features of the testing measurements that correspond to dominant features of the testing spectral response, and provides the dominant features of the testing measurements to the decoder  720 . The testing spectral response and the testing measurements are the same types of spectral response and measurements as the historical spectral response and historical measurements described with respect to  FIG. 3  and are therefore a spectral response and measurements of the historical material. For instance, the testing measurements may be measured at the same time as the historical measurements, but may be separated from the historical measurements randomly, arbitrarily, or based on specified criteria. Testing ensures limited or no overfitting. 
     The decoder  720  decodes a tested spectral response for testing based on the dominant features from the neural network  710 . The decoder  720  stores the tested spectral response in the database  150  and provides the tested spectral response to the controller  110  or another component for comparison to a spectral response corresponding to the testing measurements in order to determine the accuracy of the tester  130 . After the tester  130  completes testing, the tester  130  freezes the neural network  710  and the decoder  720  and stores them in the database  150  for further use in the generator  140 . Alternatively, the decoder  340  is a comparator or a reconstructor. 
       FIG. 8  is a schematic diagram of the generator  140  in  FIG. 1 . The generator  140  is similar to the tester  130  in  FIG. 7 . However, the generator  140  comprises a neural network  810 , which is the frozen neural network after the neural network system  360  completes training and the tester  130  completes testing, and a decoder  820 , which is the frozen decoder after the deep neural network model  310  completes training and the tester  130  completes testing. The tester  130  obtains the neural network  810  and the decoder  820  from the database  150 . As mentioned above, the generator  140  performs step  230  in  FIG. 2 . 
     The neural network  810  receives current measurements from the database  150 , determines dominant features of the current measurements, and provides the dominant features to the decoder  820 . The current measurements are of the current material. A tool or tools perform the current measurements at a site of the current material. In this context, the word “measurement” and its derivatives indicate an actual measurement of a material by a device contacting or otherwise directly observing the material, while the word “generated” and its derivatives indicate a calculation of a spectral response of a material by a device not contacting or otherwise directly observing the material, but remote from and independent of the material. The current measurements are of a fluid saturation, a gas saturation, a kerogen content, or a mineral composition. The fluid may be water or oil. 
     The decoder  820  decodes a generated spectral response based on the dominant features from the neural network  810 . The decoder  820  stores the generated spectral response in the database  150 . The neural network  810  and the decoder  820  need not perform their functions at the site of the current material, but may do so in a laboratory, a subsurface, or another location remote from the current material. Alternatively, the decoder  340  is a comparator or a reconstructor. 
     Though the components of the system  100  are described as being hardware components or software components, any suitable combination of hardware or software may implement the components. In addition, the components may exist on a single device, on multiple devices, or as distributed sensing and computing units. Furthermore, though the neural network system  360 , the tester  130 , and the generator  140  are described as three separate systems, they may be the same system, but at different stages such as training, testing, and simulating. Finally, though generated spectral responses that are NMR T2 distributions and dielectric spectral responses are described, the system  100  may generate other generated spectral responses relevant to industries that perform spectroscopy-based material analyses such as oil and gas, mining, material characterization, metallurgy, chemical, analytical chemistry, drug development, medical sensing, medical diagnostics, geophysical, remote sensing, semiconductor, construction, civil engineering, and other industries. 
       FIG. 9  is a flowchart illustrating a method  900  of generating a generated spectral response of a material according to another embodiment of the disclosure. The generator  140  may implement the method  900 . At step  910 , current measurements of a current material are received. For instance, the neural network  810  receives the current measurements. At step  920 , dominant features of the current measurements are determined. For instance, the neural network  810  determines the dominant features. At step  930 , the dominant features are provided. For instance, the neural network  810  provides the dominant features to the decoder  820 . Finally, at step  940 , a generated spectral response of the current material is generated based on the dominant features. For instance, the decoder  820  generates the generated spectral response. Based on the generated spectral response, one may determine what kind of material the current material is, how porous the current material is, how big the pores are, a pore size distribution, a depth below the surface wherein the current material exhibits desired properties, whether water or oil is in the current material, how much water or oil is in the current material, a permeability, a fluid mobility, a bound fluid saturation, an internal structure, a composition, a concentration, a spatial variation, a temporal change, or another characteristic of the current material. Based on that, one may determine whether to perform an operation of a material area containing the current material and, if so, at what depth. The operation may be a drilling operation or a well completion operation. The method  900  may implement other steps such as comparing the dominant features of the current measurements with dominant features of historical measurements and relating the dominant features of the current measurements to spectral responses in the database  150 . 
       FIG. 10  is a schematic diagram of a device  1000  according to an embodiment of the disclosure. The device  1000  may implement the disclosed embodiments. For instance, the device  1000  implements the controller  110 , the trainer  120 , the tester  130 , the generator  140 , or the database  150 . The device  1000  comprises ingress ports  1010  and an RX  1020  that receive data; a processor, logic unit, or CPU  1030  that processes the data; a TX  1040  and egress ports  1050  that transmit the data; and a memory  1060  that stores the data. The device  1000  may also comprise OE components and EO components coupled to the ingress ports  1010 , the RX  1020 , the TX  1040 , and the egress ports  1050  for ingress or egress of optical or electrical signals. 
     The processor  1030  is any suitable combination of hardware, middleware, firmware, or software. The processor  1030  comprises any combination of one or more CPU chips, cores, FPGAs, ASICs, or DSPs. The processor  1030  communicates with the ingress ports  1010 , RX  1020 , TX  1040 , egress ports  1050 , and memory  1060 . The processor  1030  comprises a spectral response component  1070 , which implements the disclosed embodiments. The inclusion of the spectral response component  1070  therefore provides a substantial improvement to the functionality of the device  1000  and effects a transformation of the device  1000  to a different state. Alternatively, the memory  1060  stores the spectral response component  1070  as instructions, and the processor  1030  executes those instructions. 
     The memory  1060  comprises one or more disks, tape drives, or solid-state drives. The device  1000  may use the memory  1060  as an over-flow data storage device to store programs when the device  1000  selects those programs for execution and to store instructions and data that the device  1000  reads during execution of those programs. The memory  1060  may be volatile or non-volatile and may be any combination of ROM, RAM, TCAM, or SRAM. 
     Example Training and Testing 
     The system  100  analyzed data from two formations in Bakken Formation shale. Specifically, the trainer  120  trained with the data and the tester  130  tested the data. Variations in mineral compositions changed pore structures, grain textures, and surface reflexivity of the formations. Those characteristics, as well as fluid saturations and pore network distribution, affected an NMR T2 distribution of the formations. 
     The data were randomly split into training data and testing data. The training data comprised historical spectral responses and historical measurements from 460 depths of the formations. The testing data comprised testing measurements from 100 depths of the formations. The historical spectral responses comprised 64 dimensions, and the encoder  320  created both a 2D latent space and a 3D latent space. 
     For the 2D latent space, 100 randomly-selected samples are shown as the 2D latent space  400  in  FIG. 4 .  FIG. 11  is a plot  1100  comparing historical spectral responses to tested spectral responses for the 2D latent space. As shown, the historical spectral responses and the tested spectral responses are similar.  FIG. 12  is a plot  1200  of R-squared for the generated spectral responses for the 2D latent space. As shown, as a number of data increased, the R-squared increased. For historical spectral responses with one peak, the R-squared was 0.8, and a normalized RMS deviation was 14%. For historical spectral responses with two peaks, accuracy decreased. However, less than one-third of the historical spectral responses were associated with two peaks. An average R-squared was 0.75, and an average normalized RMS deviation was 15%. 
     For the 3D latent space, the historical spectral responses and the trained spectral responses were more similar.  FIG. 13  is a plot  1300  comparing historical spectral responses to tested spectral responses for the 3D latent space.  FIG. 14  is a plot  1400  of R-squared for the generated spectral responses for the 3D latent space. As shown, as a number of data increased, the R-squared increased. An average R-squared was 0.77, which was better than for the 2D latent space, and an average normalized RMS deviation was 15%. However, the encoder  320  learned unrepresentative features when implementing the 3D latent space. For instance, the distributions in the lower-left corner of the graph  1300  exhibit second peaks, which are small, but unnatural features. 
       FIG. 15  is a series of plots  1500  comparing original dielectric spectra to generated dielectric spectra. The original dielectric spectra are shown with dashed lines, and the generated dielectric spectra are shown with solid lines. The dielectric spectra comprise both conductivity denoted as σ and relative permittivity denoted as ϵ r . The x-axes represent depth in ft, and the y-axes represent either conductivity in mS/m or relative permittivity without units. Both the conductivity and the relative permittivity are functions of operating frequency. The conductivity increases with an increase in operating frequency, and the relative permittivity decreases with an increase in operating frequency. The series of graphs  1500  comprises graphs of the conductivity and the relative permittivity acquired at operating frequencies f 0 , f 1 , f 2 , and f 3  of a subsurface formation along a 300 ft depth interval of an oil well drilled through a hydrocarbon-bearing shale formation, wherein 20 MHz&lt;f 0 &lt;f 1 &lt;f 2 &lt;f 3 ≅1 GHz. In the training phase, 3,434 depth points in the oil well were used to generate dielectric spectra using non-dielectric-spectra measurements such as gamma ray, density porosity, neutron porosity, formation photoelectric factor, bulk density, volume of clay, delta-T compressional sonic, delta-T shear sonic, and laterolog resistivity logs at various depths. In the testing phase, 300 depth points were used. Table 1 shows the accuracy of the tester  130  in generating dielectric spectra at f 0 , f 1 , f 2 , and f 3  for the 300 depth points. 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Tester Accuracy 
               
            
           
           
               
               
               
            
               
                   
                 R 2   
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 f0 
                 f1 
                 f2 
                 f3 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 Conductivity 
                 0.93 
                 0.92 
                 0.90 
                 0.86 
               
               
                   
                 Permittivity 
                 0.70 
                 0.71 
                 0.65 
                 0.62 
               
               
                   
                   
               
            
           
         
       
     
       FIG. 16  is a GUI  1600  for implementing the system  100  in  FIG. 1  according to an embodiment of the disclosure. Specifically, the GUI  1600  may implement the GUI described with respect to the controller  110  in  FIG. 1 . The GUI  1600  comprises a load inputs button  1610 , a selector generator button  1620 , and a generate spectral response button  1630 . A user clicks or otherwise selects the load inputs button  1610  to upload inputs like the current measurements in  FIG. 8 ; clicks or otherwise selects the select generator button  1620  to select a type of the trainer  120 , the tester  130 , and the generator  140  in  FIGS. 1, 3 and 7-8 ; and clicks or otherwise selects the generate spectral response button  1630  to obtain the generated spectral response in  FIG. 8 . The generated spectral response may be available in a subsequent GUI. The GUI  1600  and the generator  140  may communicate via the cloud. 
       FIG. 17  is a schematic diagram of a generator  1700  based on a VAE-CNN model according to an embodiment of the disclosure. The generator  1700  implements a VAE-CNN model. The generator  1700  comprises a first stage  1710  that performs VAE with a convolution layer and a second stage  1720  that is a VAE-based neural network. A VAE implements the CNN. The VAE is a neural network with a bottleneck architecture that compresses high-dimensional data into a low-dimensional space. The VAE comprises an intermediate layer with two or three neurons. The VAE is designed to reproduce its input data. The VAE moves a dataflow through a bottleneck following a Gaussian distribution in the intermediate layer. A VAEc combines the VAE and a CNN. The VAEc trains using a two-stage procedure. A normal NMR T2 distribution has a smooth multi-Gaussian shape. In the first stage  1710 , the VAEc trains to learn how to generate a typical NMR T2 from the training dataset. The VAEc processes NMR T2 data as a 1D datatype. A convolutional layer has 16 filters to transform the NMR T2 and extract generalized features. An encoder constructs a 3D latent layer after compressing the input T2 into the latent space, while preserving the relationship in a higher-dimensional space. A decoder generates a typical NMR T2 from the 3D latent space. In the second stage  1720 , the trained decoder is an NMR T2 generator and trains with a small neural network that processes a formation mineral composition and fluid saturation measurements. 
       FIG. 18  is a schematic diagram of a generator  1800  based on an LSTM-RNN model according to an embodiment of the disclosure. The generator  1800  implements an LSTM-RNN model. The generator  1800  comprises an encoder  1810  and a decoder  1820 . An LSTM is a recurrent neural network designed to handle long and short-term data dependencies such as those in language and stock market prediction. The LSTM uses a repeated data processing module to process data at each step. The LSTM memorizes the data by internal state and keeps a data flow in the repeated data processing module by gates, which are composed of sigmoid activation functions. The LSTM treats formation mineral content and fluid saturation measurements and a 64-dimensional NMR T2 as sequences. The LSTM mimics a language translation model, where an encoder uses input language to calculate an intermediate vector. A decoder decodes the intermediate vector into another language. The repeated data processing module solves a long-term data dependency in sequence-to-sequence mapping problems. The LSTM trained in one step as shown in  FIG. 17 . The encoder encodes formation composition logs into a 15-length intermediate vector v. The decoder decodes the vector v into the 64-dimensional NMR T2. 
       FIG. 19  is a schematic diagram of a generator  1900  based on a GAN model according to an embodiment of the disclosure. The generator  1900  implements a GAN model. The generator  1900  comprises a first stage  1910  and a second stage  1920 . The training process of the generator  1900  is similar to the training process of the generator  1700 . In the first stage  1910 , a GAN learns features in T2 distributions. A generator and a discriminator train alternatively until the generator can generate an NMR T2 that cannot be identified by the discriminator as generated data. After the GAN trains, a frozen generator connects to a neural network like in  FIG. 3  to learn to associate different mineral contents and fluid saturations measurements with learned features of T2 distributions. After the training, NMR T2 distributions are generated in a testing phase like in  FIG. 3 . T2 distributions generated by a GAN are not smooth. Therefore, a Gaussian fitting process fits a generated NMR T2 to make it smoother and more realistic. The generator is a 3-layer neural network that receives a six-dimensional noise vector as an input. The generator learns to generate the NMR T2 with different shapes with the aid of the discriminator. An output uses 64 dimensions to generate the T2 distribution. The discriminator contains 4 layers with 2 hidden layers that have 64 and 16 neurons each. 4,608 and 5,234 parameters train in the generator and discriminator, respectively. After the first stage  1910 , a third neural network comprises 4 layers having 2 hidden layers with 30 neurons each. A third neural network has 10-dimensional inputs and 6-dimensional outputs. The third NN trains with the frozen generator from the generator  1900  in a manner similar to the training in  FIG. 3 . 
       FIG. 20  is a flowchart illustrating a method  2000  of using a stacked ANN model for generating dielectric spectra according to an embodiment of the disclosure. The method  2000  may generate dielectric spectra, including conductivity spectra and relative permittivity spectra. 4 conductivity and 4 permittivity spectra measurements are ranked using a k-fold cross validation method. Ranking is done in order of the accuracy of their predictions using an ANN model. After ranking 8 DD logs, another ANN model sequentially generates 8 dispersion spectra one at a time, starting with predicting a spectrum having a highest prediction accuracy and ending with predicting a spectrum having a lowest prediction accuracy. During generation of each subsequent dispersion log, the ANN specific to that log is fed with previously predicted logs and the 15 current measurements of current material for which the dielectric spectra is desired to be generated. Physics of charge polarization gives rise to a dependence between conductivity and permittivity at each frequency and to a dependence of conductivity and permittivity dispersions on frequencies. The method  2000  mimics these physical trends. The 8 dielectric dispersion spectra are ranked in terms of prediction accuracy achieved when performing simultaneous generation using a single neural network, then sequential predictions of the 8 dielectric spectra are performed based on a predetermined rank, thereby honoring the dependence of conductivity and permittivity dispersions on frequencies. 
     While several embodiments have been provided in the present disclosure, it may be understood that the disclosed systems and methods might be embodied in many other specific forms without departing from the spirit or scope of the present disclosure. The present examples are to be considered as illustrative and not restrictive, and the intention is not to be limited to the details given herein. For example, the various elements or components may be combined or integrated in another system or certain features may be omitted, or not implemented. 
     In addition, techniques, systems, subsystems, and methods described and illustrated in the various embodiments as discrete or separate may be combined or integrated with other systems, components, techniques, or methods without departing from the scope of the present disclosure. Other items shown or discussed as coupled or directly coupled or communicating with each other may be indirectly coupled or communicating through some interface, device, or intermediate component whether electrically, mechanically, or otherwise. Other examples of changes, substitutions, and alterations are ascertainable by one skilled in the art and may be made without departing from the spirit and scope disclosed herein.