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 <!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.0 20120330//EN" "http://jats.nlm.nih.gov/publishing/1.0/JATS-journalpublishing1.dtd"> <article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" article-type="research-article" dtd-version="1.0" xml:lang="en">
  <front>
    <journal-meta>
      <journal-id journal-id-type="publisher-id">JBR</journal-id>
      <journal-title-group>
        <journal-title>Journal of Big Data Research</journal-title>
      </journal-title-group>
      <issn pub-type="epub">2768-0207</issn>
      <publisher>
        <publisher-name>Open Access Pub</publisher-name>
        <publisher-loc>United States</publisher-loc>
      </publisher>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="publisher-id">JBR-23-4753</article-id>
      <article-id pub-id-type="doi">10.14302/issn.2768-0207.jbr-23-4753</article-id>
      <article-categories>
        <subj-group>
          <subject>research-article</subject>
        </subj-group>
      </article-categories>
      <title-group>
        <article-title>Can Data-Driven Hypotheses Replace the Scientific Method?</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <name>
            <surname>Raúl</surname>
            <given-names>Isea</given-names>
          </name>
          <xref ref-type="aff" rid="idm1841170428">1</xref>
          <xref ref-type="aff" rid="idm1841168340">*</xref>
        </contrib>
      </contrib-group>
      <aff id="idm1841170428">
        <label>1</label>
        <addr-line>Fundación Instituto de Estudios Avanzados, Hoyo de la Puerta, Baruta, Venezuela.</addr-line>
      </aff>
      <aff id="idm1841168340">
        <label>*</label>
        <addr-line>Corresponding author</addr-line>
      </aff>
      <contrib-group>
        <contrib contrib-type="editor">
          <name>
            <surname>Jinpeng</surname>
            <given-names>Chen</given-names>
          </name>
          <xref ref-type="aff" rid="idm1841279500">1</xref>
        </contrib>
      </contrib-group>
      <aff id="idm1841279500">
        <label>1</label>
        <addr-line>Department of Computer Science and Technology, Beihang University (BUAA).</addr-line>
      </aff>
      <author-notes>
        <corresp>
    
    Raul Isea, <addr-line>Fundación Instituto de Estudios Avanzados IDEA, Hoyo de la Puerta, Baruta, Venezuela</addr-line>, <email>raul.isea@gmail.com</email></corresp>
        <fn fn-type="conflict" id="idm1841676748">
          <p>The authors have declared that no competing interests exist.</p>
        </fn>
      </author-notes>
      <pub-date pub-type="epub" iso-8601-date="2023-10-17">
        <day>17</day>
        <month>10</month>
        <year>2023</year>
      </pub-date>
      <volume>1</volume>
      <issue>3</issue>
      <fpage>12</fpage>
      <lpage>19</lpage>
      <history>
        <date date-type="received">
          <day>18</day>
          <month>09</month>
          <year>2023</year>
        </date>
        <date date-type="accepted">
          <day>13</day>
          <month>10</month>
          <year>2023</year>
        </date>
        <date date-type="online">
          <day>17</day>
          <month>10</month>
          <year>2023</year>
        </date>
      </history>
      <permissions>
        <copyright-statement>©</copyright-statement>
        <copyright-year>2023</copyright-year>
        <copyright-holder>Raul Isea</copyright-holder>
        <license xlink:href="http://creativecommons.org/licenses/by/4.0/" xlink:type="simple">
          <license-p>This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.</license-p>
        </license>
      </permissions>
      <self-uri xlink:href="http://openaccesspub.org/jbr/article/2017">This article is available from http://openaccesspub.org/jbr/article/2017</self-uri>
      <abstract>
        <p>The rapid growth of data and scientific journals has led to the promotion of                     data-based hypotheses. Data-driven hypotheses can also be used to establish new scientific laws or confirm existing ones, demonstrating the foundation of this                 philosophy. To introduce this idea, this article presents a Python-based                           computational algorithm that can generate system dynamics equations without using working hypotheses.</p>
      </abstract>
      <kwd-group>
        <kwd>Data driven Hypothesis</kwd>
        <kwd>Data</kwd>
        <kwd>Scientific method</kwd>
        <kwd>van der Pol</kwd>
        <kwd>Covid-19.</kwd>
      </kwd-group>
      <counts>
        <fig-count count="2"/>
        <table-count count="1"/>
        <page-count count="8"/>
      </counts>
    </article-meta>
  </front>
  <body>
    <sec id="idm1841033036" sec-type="intro">
      <title>Introduction</title>
      <p>A lot of scientific work is based on the scientific method, which includes several steps such as planning, gathering data, generating predictions using logical                   reasoning, testing, and eventually reporting the findings, where the data enables us to evaluate our research work.</p>
      <p>One of the first people to use the scientific method was the Arab and Muslim                   physicist Abu al-Hasan ibn al-Hasan ibn Al-Haytham  (965–1044), known as Alhazen, the father of modern optics <xref ref-type="bibr" rid="ridm1841525420">1</xref>, while Isaac Newton popularized the                          scientific method with the publication called <italic>Principia</italic><xref ref-type="bibr" rid="ridm1841529236">2</xref>.</p>
      <p>Today, advances in technology have made data available to people all over the world. The National Institute of Biotechnology Information (NCBI) repository is a part of the US National Library of Medicine <xref ref-type="bibr" rid="ridm1841536588">3</xref>. This database, which was created on November 4, 1988, includes a catalog of scholarly papers relating to                                 biotechnology and medicine, as well as DNA sequence data derived from genes and some other data. All information is freely available at www.ncbi.nlm.nih.gov.</p>
      <p>This database includes the nucleotide sequence record, which shows the growth of data from 1992 to August 2023, comprising over 246 million DNA sequences                       generated by scientists and over 400 million articles in the domains of bio                         technology and medicine <xref ref-type="bibr" rid="ridm1841536588">3</xref>.</p>
      <p>The publications also increased. A recent example is the statistics on the number of Covid-19 cases, responsible for more than six hundred ninety-five million cases worldwide, with less than seven million deaths by the beginning of September 2023. Daily information on cases and deaths is available on several portals, such as Johns Hopkins University (coronavirus.jhu.edu), Worldometers (worldometers.info), outworldindata (outworldindada.org), World Health Organization (covid19.who.int), to name just a few examples. As with many free-access repositories of                        scientific works, among the preprint servers we can indicate arXiv, bioRxiv, preprint, agriRxive,                      AfricArXiv, and so on.</p>
      <sec id="idm1841034692">
        <title>What has the Covid-19 pandemic revealed?</title>
        <p>The Covid-19 pandemic emphasizes the speed with which scientific publications are being published, as well as the spread of misleading information in blogs and even scientific papers, giving rise to the                                 problem known as fake news <xref ref-type="bibr" rid="ridm1841387140">4</xref>. Prashant Pradhan and his Indian partners released a paper on January 31, 2019 where they offered evidence of unusual parallels in the coronavirus sequence with HIV gp120 and Gag proteins, implying that it was a fabricated virus <xref ref-type="bibr" rid="ridm1841385340">5</xref>.</p>
        <p>Serge Horbach of Radboud University Nijmegen submitted a study titled "<italic>Article about the pandemic: medical journals are significantly accelerating their publication process on Covid-19</italic>" at the                                   pre-publication stage (keep in mind that this is a work that has not yet been peer-reviewed). After                reviewing 669 publications published in 14 medical journals, he stated that the time it takes for most articles associated with Covid-19 to be published in scientific journals has been reduced by half <xref ref-type="bibr" rid="ridm1841389948">6</xref>.</p>
      </sec>
      <sec id="idm1841032316">
        <title>But, all ideas come from the scientific method?</title>
        <p>We must keep in mind that not all ideas emerge through the scientific process. Let me recall a few                               classic non-scientific examples, such as the Archimedes bath incident (287–212 AD). It recalls the                         account of King Hiero II of Syracuse (306-215 BC), who wished to see if his crown was truly composed of gold. Archimedes attested to this and discovered a solution by bathing in a tin can after noticing a correlation between the amount of water displaced and the body mass.</p>
        <p>Another example is Alexander Fleming's (1881–1955) discovery of penicillin in 1928, which paved the way for the development of antibiotics while working with bacterial cultures. When he returned from his vacation, he discovered a petri plate that had been accidently contaminated by a green mold (<italic>Penicillium notatum</italic>), and with his scientific eye, he recognized the significance of this discovery. This type of chance finding is now known as serendipia.</p>
        <p>This was not an isolated occurrence. Other examples include the discovery of X-rays in 1895 by                       physicist Wilhelm Conrad Roentgen while experimenting with electrons in vacuum tubes, radioactivity in 1896 by Antoine Henri Becquerel, LSD by Albert Hofmann in 1943, aspirin by Felix Hoffman in 1894, and Isaac Newton deducing gravity after falling an apple on his head.</p>
        <p>In addition, early notions or ideas are frequently incorrect. Consider the instance of Albert Abraham          Michelson and Edward Morley <xref ref-type="bibr" rid="ridm1841380124">7</xref>, who prepared and carried out an experiment in 1887 to measure the relative speed of the earth with respect to the ether and discovered that their hypothesis was incorrect. Albert Einstein benefited from this observation.  Therefore, the data should be the guide to scientific publications. Therefore, the data should be the guide for scientific publications. This approach is not new, as discussed below.</p>
      </sec>
      <sec id="idm1841030444">
        <title>Francis Bacon's contribution</title>
        <p>The father of philosophical and scientific empiricism, Francis Bacon (1561–1626), pointed out in his work <italic>Novum Organum</italic> ("New Instruments") in 1620 that scientific knowledge should not be based on preconceived notions that must be based on empirical data <xref ref-type="bibr" rid="ridm1841378828">8</xref>, therefore inferences must be drawn from these data, i.e., Bacon argued that science should be technical rather than based on theory or speculation. Furthermore, he argued that knowledge should be constructed by observation and prioritization                          according to logical principles <xref ref-type="bibr" rid="ridm1841378828">8</xref>.</p>
        <p>Bacon advocated inductive reasoning, the process of drawing conclusions from observations. A notable example of this is Johannes Kepler's (1571–1630) work on planetary motion, until Isaac Newton (1642–1727) was able to publish the laws of universal motion in <italic>Principia</italic> in 1686 <xref ref-type="bibr" rid="ridm1841529236">2</xref>.</p>
        <p>Recently, Chris Anderson (former editor of <italic>Wired</italic> magazine from 2001 to 2012) published an article titled "<italic>The End of Theory: Data Deluge Makes the Scientific Method Obsolete</italic>" <xref ref-type="bibr" rid="ridm1841374508">9</xref>.  Basically claims that data and supercomputers will replace the conventional scientific approach, eliminating the need for new hypotheses and theories. In this context, the author believes that we have seen a tendency that may lead to a theoretical science, but this is a topic that has to be researched further in future study.</p>
        <p>Anderson emphasizes Craig Venter's case of genome sequencing, in which he effectively sequenced            entire ecosystems using ant knowledge gained by sequencing species by using supercomputers and                       sequencers to generate vast volumes of data <xref ref-type="bibr" rid="ridm1841374508">9</xref>.</p>
      </sec>
      <sec id="idm1841028212">
        <title>Algorithms to develop data-driven hypotheses</title>
        <p>Recently, the possibility of deriving mathematical equations capable of describing the dynamics of a          system without considering any operational hypotheses has emerged thanks to the large amount of                      information and advances in computational programming <xref ref-type="bibr" rid="ridm1841360612">10</xref>, i.e., a procedure that reverses the                              scientific method by not using an initial hypothesis.</p>
        <p>This initiative was led by Schmidth and Lipson, who used symbolic regression and genetic programming <xref ref-type="bibr" rid="ridm1841358380">11</xref>, and to date it has been applied to nuclear fusion <xref ref-type="bibr" rid="ridm1841365148">12</xref>, seismology <xref ref-type="bibr" rid="ridm1841349020">13</xref>, climate change <xref ref-type="bibr" rid="ridm1841348444">14</xref>, and recently drugs that can be used to fight Covid-19 <xref ref-type="bibr" rid="ridm1841345420">15</xref>.</p>
        <p>As a result, data management is driving the potential of data-driven hypothesis <xref ref-type="bibr" rid="ridm1841337428">16</xref> which is an approach that allows us to generate a dynamic solution without any theoretical basis; that is, the objective function capable of explaining the system's behavior is unknown. In other words, this concept is similar to a                         reverse scientific procedure, with the emphasis on data.</p>
      </sec>
    </sec>
    <sec id="idm1841029436">
      <title>Computational Methodology</title>
      <p>This research improves the ability to extract equations from a data-driven dynamic system, which can be broadly summarized in four parts (details <xref ref-type="bibr" rid="ridm1841324556">17</xref>). The first place arranges the data into a transposed matrix of the observed data. The next step is to create a coefficient library based on non-linear functions using the approach given by Rudy et al. <xref ref-type="bibr" rid="ridm1841323764">18</xref>. As a result, the system's dynamics are straightforward. </p>
      <p>The previous stage is a process of optimizing parameters determined using the LASSO (<italic>Least Absolute Shrinkage and Selection Operator</italic>) approach, until we eventually have the mathematical expressions that characterize the system.</p>
      <p>This method is applied in two examples. The first was to demonstrate that it could determine the                      dynamics of a system based on the van der Pol equation system, named after the Dutch engineer and physicist Balthasar van der pol (1889–1959) <xref ref-type="bibr" rid="ridm1841317788">19</xref>. These equations have been used to explain, for                 example, the potential of action in neurons, in seismology, in electrical circuits, etc.</p>
      <p>Remember that a system of equations describing a van der Pol oscillator is described as follows:</p>
      <graphic xlink:href="images/image1.png" mime-subtype="png"/>
      <p>where  is <bold>μ</bold>  a scalar parameter that governs nonlinearity and amortization.</p>
      <fig id="idm1840889708">
        <label>Figure 1.</label>
        <caption>
          <title> Numerical solution of the van der Pol equation for  μ  equal to 0.01 and 2 (text for more details).</title>
        </caption>
        <graphic xlink:href="images/image2.jpg" mime-subtype="jpg"/>
      </fig>
      <p><xref ref-type="fig" rid="idm1840889708">Figure 1</xref> depicts the numerical results for two alternative values (i.e., <bold>μ</bold> equal to 0.01 and 2.0) with         initial values 0 and 1, respectively. As a result, we proceed to build a solution to the system of equations with five hundred data points generated with it (represented by the orange solid line), and we can verify whether or not it really reproduces the system depicted above.</p>
      <p>The second example will derive differential equations that will allow the dynamics of Covid-19 spread to be reproduced based solely on daily records of illnesses and deaths in any country in the world, using the equations anticipated for Brazil and Venezuela from the start. From March 27, 2020, to June 14, 2021, 445 cases were reported in these countries as part of the outbreak.</p>
      <p> </p>
    </sec>
    <sec id="idm1840996748" sec-type="results">
      <title>Results</title>
      <p>Applying the methodology described in the previous section, the Python program obtained the following equations:</p>
      <graphic xlink:href="images/image3.png" mime-subtype="png"/>
      <p> </p>
      <p>The solution found actually describes the van der Pol equations obtained from the data without inferring any assumptions from the mathematical model. Also, the value of   <bold>μ</bold>  oscillates between 1.998 ± 0.004, i.e., an error of the order of is practically the same equation with which the data was generated. </p>
      <p>The second scenario consists of contagions (which will be presented in I) and deaths (D) in two distinct countries, Venezuela and Brazil. The found polynomial solution is represented as follows:</p>
      <p> <graphic xlink:href="images/image4.png" mime-subtype="png"/></p>
      <p>where the coefficients of the system of equations are presented in <xref ref-type="table" rid="idm1840890716">Table 1</xref>, where empty cells correspond to a value of 0.</p>
      <table-wrap id="idm1840890716">
        <label>Table 1.</label>
        <caption>
          <title>Coefficients obtained from the system of differential equations describing the dynamics of  contagion in Venezuela (VEN) and Brazil (B), corresponding to the equations dI/dt and dD/dt, respectively</title>
        </caption>
        <table rules="all" frame="box">
          <tbody>
            <tr>
              <td>
                <graphic xlink:href="images/image5.png" mime-subtype="png"/>
              </td>
              <td>
                <graphic xlink:href="images/image6.png" mime-subtype="png"/>
              </td>
              <td>
                <graphic xlink:href="images/image7.png" mime-subtype="png"/>
              </td>
              <td>
                <graphic xlink:href="images/image8.png" mime-subtype="png"/>
              </td>
              <td>
                <graphic xlink:href="images/image9.png" mime-subtype="png"/>
              </td>
              <td>
                <graphic xlink:href="images/image10.png" mime-subtype="png"/>
              </td>
              <td>
                <graphic xlink:href="images/image11.png" mime-subtype="png"/>
              </td>
              <td>
                <graphic xlink:href="images/image12.png" mime-subtype="png"/>
              </td>
              <td>
                <graphic xlink:href="images/image13.png" mime-subtype="png"/>
              </td>
              <td>
                <graphic xlink:href="images/image14.png" mime-subtype="png"/>
              </td>
              <td>
                <graphic xlink:href="images/image15.png" mime-subtype="png"/>
              </td>
            </tr>
            <tr>
              <td>VEN</td>
              <td> </td>
              <td>-3,66</td>
              <td>7,97</td>
              <td>-7,46</td>
              <td>13,3</td>
              <td>-8,73</td>
              <td>17,3</td>
              <td>-26,6</td>
              <td> </td>
              <td>9,90</td>
            </tr>
            <tr>
              <td>BRA</td>
              <td>0,15</td>
              <td>0,34</td>
              <td>0,04</td>
              <td>15,8</td>
              <td>14,0</td>
              <td>-29,8</td>
              <td>63,3</td>
              <td>-55,1</td>
              <td>-24,0</td>
              <td>15,8</td>
            </tr>
            <tr>
              <td> </td>
              <td> </td>
              <td> </td>
              <td> </td>
              <td> </td>
              <td> </td>
              <td> </td>
              <td> </td>
              <td> </td>
              <td> </td>
              <td> </td>
            </tr>
            <tr>
              <td>
                <graphic xlink:href="images/image16.png" mime-subtype="png"/>
              </td>
              <td>
                <graphic xlink:href="images/image17.png" mime-subtype="png"/>
              </td>
              <td>
                <graphic xlink:href="images/image18.png" mime-subtype="png"/>
              </td>
              <td>
                <graphic xlink:href="images/image19.png" mime-subtype="png"/>
              </td>
              <td>
                <graphic xlink:href="images/image20.png" mime-subtype="png"/>
              </td>
              <td>
                <graphic xlink:href="images/image21.png" mime-subtype="png"/>
              </td>
              <td>
                <graphic xlink:href="images/image22.png" mime-subtype="png"/>
              </td>
              <td>
                <graphic xlink:href="images/image23.png" mime-subtype="png"/>
              </td>
              <td>
                <graphic xlink:href="images/image24.png" mime-subtype="png"/>
              </td>
              <td>
                <graphic xlink:href="images/image25.png" mime-subtype="png"/>
              </td>
              <td>
                <graphic xlink:href="images/image26.png" mime-subtype="png"/>
              </td>
            </tr>
            <tr>
              <td>VEN</td>
              <td> </td>
              <td>-4,10</td>
              <td>7,17</td>
              <td>-1,82</td>
              <td>18,5</td>
              <td>-18,5</td>
              <td>15,8</td>
              <td>-24,0</td>
              <td> </td>
              <td>8,59</td>
            </tr>
            <tr>
              <td>BRA</td>
              <td>0,34</td>
              <td>1,64</td>
              <td>-2,52</td>
              <td>14,3</td>
              <td>13,3</td>
              <td>-26,7</td>
              <td>10,7</td>
              <td>-5,52</td>
              <td>-5,29</td>
              <td> </td>
            </tr>
          </tbody>
        </table>
      </table-wrap>
      <p><xref ref-type="fig" rid="idm1840777564">Figure 2</xref>(A) and  <xref ref-type="fig" rid="idm1840777564">Figure 2</xref>(B) repeat the solution obtained from the system of equations describing Covid-19 infection cases in Brazil and Venezuela from March 2020 to June 2021, respectively. This solution is polynomial. These graphs depict the daily cases of infection in blue and the equation predictions in red. It is worth noting that this process allows the data to be filtered in order to generate this forecast. This set of equations can lead to more generic equations, which will be proven in a subsequent scholarly publication.</p>
      <fig id="idm1840777564">
        <label>Figure 2.</label>
        <caption>
          <title> Daily case records in (A) Venezuela and (B) Brazil from March 2020 to June 2021. Daily case counts are indcated by blue dots, while forecasts are colored red. Normalized data is shown in black for easy visualization of cases.</title>
        </caption>
        <graphic xlink:href="images/image27.jpg" mime-subtype="jpg"/>
      </fig>
      <graphic xlink:href="images/image28.jpg" mime-subtype="jpg"/>
    </sec>
    <sec id="idm1840925468" sec-type="discussion">
      <title>Discussions and Conclusion</title>
      <p>The paper proposes a computational method based on data-based solutions in which system                        equations can be evaluated and generated only on data, with no bias introduced into the result. This method is a clear example of a data-driven hypothesis. </p>
      <p>The first example in the study was able to reproduce the dynamic equations of the van der Pol     oscillator, which are difficult to determine manually without making any assumptions, while in the second example, we gain a polynomial-type equation system that can describe the Covid-19               dissemination dynamics without any epidemiological basis, and we can even make predictions, albeit only in the short term.</p>
      <p>Therefore, scientific knowledge must have a strong component of inductive reasoning, which is more data-based than limited to confirming pre-established theories. That is why it is necessary to study how new a discovery is or whether it is simply the result of a theoretical verification.</p>
      <p>So it opens up the possibility of reinterpreting and validating scientific laws using data-driven   hypothesis, and it is to be hoped that with the rise of Intelligence Artificial, it will be possible to deduce and even revalidate scientific laws for the large volume of information that is being                generated around the world.</p>
      <p> </p>
    </sec>
  </body>
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