{"id":10664,"date":"2026-05-18T10:47:42","date_gmt":"2026-05-18T08:47:42","guid":{"rendered":"https:\/\/ingenius.ecoledesponts.fr\/?p=10664"},"modified":"2026-05-18T10:47:42","modified_gmt":"2026-05-18T08:47:42","slug":"how-reduction-can-improve-prediction-a-conversation-with-sofiane-ezzehi","status":"publish","type":"post","link":"https:\/\/ingenius.ecoledesponts.fr\/en\/articles\/how-reduction-can-improve-prediction-a-conversation-with-sofiane-ezzehi\/","title":{"rendered":"How Reduction Can Improve Prediction: a Conversation With Sofiane Ezzehi"},"content":{"rendered":"\n\n\n
\"\"
Model reduction transforms a complex system into a much lower-dimensional representation, capable of faithfully approximating its behavior while significantly accelerating simulations.
Source: Image generated with ChatGPT (OpenAI, GPT-5.3 model), 2026, based on an illustration from the COMPAS project (Jade Hochschule)<\/a>.<\/figcaption><\/figure>\n\n\n\n

What is your research topic?<\/strong><\/p>\n\n\n\n

During the first year of my PhD, I explored two avenues of research. The first lies at the intersection of scientific computing and artificial intelligence, and concerns \u201cPINNs\u201d (Physics-Informed Neural Networks).The idea is to use neural networks to approximate as closely as possible the solution to equations describing physical phenomena. Although these methods have grown rapidly since 2019, they still raise important theoretical and numerical questions, which are central to my work.<\/p>\n\n\n\n

The second avenue concerns model reduction. The aim is to accelerate extremely costly numerical simulations which are used to study complex mechanical phenomena that depend on numerous parameters<\/a>. This applies, for example to the underground storage of CO\u2082<\/a>, which is injected into subsurface environments that already contain fractures or faults. This raises the question of determining what ground movements this injection may cause, and how these may interact with pre-existing geological structures. All of this requires the testing of multiple configurations, which can quickly become prohibitively expensive.<\/p>\n\n\n\n

My work consists in developing reduced models that retain the essential physical information while significantly decreasing computation time<\/a>, so that we can explore different scenarios more efficiently and better anticipate certain risks, such as ground deformation, microseismic activity, or \u2013 in extreme cases \u2013 CO\u2082 leakage.<\/p>\n\n\n\n

What led you to study mathematics?<\/strong><\/p>\n\n\n\n

My interest in mathematics developed somewhat unexpectedly during my final year of high school. By chance, I stumbled across the Monsieur Phi1<\/a><\/sup> YouTube channel, which presents popular philosophy content, and started to realize that certain aspects of contemporary philosophy maintain a close dialog with science.<\/p>\n\n\n\n

This discovery led me toward a community of French popular science communicators such as L\u00ea Nguy\u00ean Hoang from the Science4All channel and David Louapre at Science \u00c9tonnante. These videos sparked \u2013 and then reinforced \u2013 my interest in science, much to the surprise of everyone around me. I had initially planned to pursue literary studies, but I ultimately opted for a scientific preparatory program in Tunisia. I then entered the \u00c9cole nationale des ponts et chauss\u00e9es, completed the MVA master\u2019s program and then embarked on a PhD.<\/p>\n\n\n\n

\n
\"\"
The Two-Child Paradox is based on a simple premise: Mr. Smith has two children. One of them is a boy. What is the probability that the other child is also a boy? <\/em>What makes the problem interesting is its apparent simplicity: depending on how one interprets the given information, one can convincingly arrive at either 1\/3 or 1\/2. This apparent simplicity illustrates how our intuition about probabilities can lead us astray.\u00a0 To find out more, watch the video \u201cThe Two-Child Paradox\u201d by L\u00ea Nguy\u00ean Hoang from the Science 4Allchannel<\/a>.\u00a0 <\/figcaption><\/figure>\n\n\n\n
\"\"
Newcomb\u2019s paradox is another quite baffling thought experiment: an almost infallible predictor presents two boxes, one transparent containing \u201c\u20ac1,000\u201d, the other opaque containing either \u201c\u20ac1,000,000\u201d or \u201cnothing at all\u201d. If the predictor has predicted that you will take only the opaque box, it has placed the million euros inside it; if it has predicted that you would take both boxes, it has placed nothing inside. You must then choose between taking only the opaque box or taking both boxes. <\/em>This problem has generated a rich body of literature, because two rational lines of reasoning lead to different strategies. It raises questions about decision theory, causality, and \u2013 depending on the interpretation \u2013 free will. To find out more, watch the video: \u201cThis Paradox Will Drive You Mad\u201d by Monsieur Phi<\/a><\/figcaption><\/figure>\n<\/figure>\n\n\n\n

Which mathematicians have made the biggest impression on you so far?<\/strong><\/p>\n\n\n\n

Several figures have shaped the way I think about mathematics. I would particularly like to mention the British mathematician John Conway<\/a>, whom I discovered some time ago through his famous Game of Life, in which a cellular automaton evolves according to very simple rules, yet these are sufficient to give rise to unexpectedly complex behaviors.2<\/a><\/sup> It embodies a form of mathematical beauty that really speaks to me.<\/p>\n\n\n\n

In a very different vein, Alain Connes has also influenced me through the way he speaks about mathematical work. I remember a talk I discovered during my years in preparatory classes, in which he explained that mathematics is not simply about reading a sequence of statements and proofs, but about making the material one\u2019s own, reflecting on it, and coming back to it. I interpreted these words as a kind of process for developing genuine intuition by building one\u2019s own mental representation of mathematical objects. This intuition does not replace technical mastery, but it plays an essential role in making progress and in forging unexpected connections between seemingly unrelated fields.<\/p>\n\n\n\n

There is also a certain idealization of research, which consists in constantly pushing the boundaries of knowledge through sustained intellectual effort. I am thinking in particular of Albert Einstein, who formalized several major theories within the space of a few months during his \u201cannus mirabilis\u201d in 1905, in the form of four articles that laid the foundations of modern physics. It seems that many of his ideas came to him following long periods of reflection and physical imagination, which often arose before the actual mathematical formalization. This somewhat idealized vision is often far removed from the day-to-day reality of research, but nevertheless continues to inspire me.<\/p>\n\n\n\n

Why is a conference like this important for young researchers in mathematics?<\/strong><\/p>\n\n\n\n

The Congress of Young Researchers in Applied Mathematics is primarily aimed at PhD students and postdoctoral researchers. Unlike more traditional conferences, which often cater to an audience of experienced researchers, this congress encourages discussion in a more accessible and perhaps less intimidating setting. It provides a valuable opportunity to connect with peers from a wide range of laboratories, in a context encouraging disciplinary, institutional, and geographical diversity. The wide range of topics presented also allows participants to explore new fields.<\/p>\n\n\n\n

For my part, I was a member of the logistics committee. The conference also featured plenary sessions led by experienced speakers, tasked with presenting more general topics. Although I did not present my work this year, I would like to do so at a future edition.<\/p>\n\n\n\n

Interview by Mahalia Blanchard-Martial, scientific communicator at \u00c9cole nationale des ponts et chauss\u00e9es.<\/em><\/p>\n\n\n

  1. The popular philosophy YouTube channel Monsieur Phi <\/a><\/a>, by Thibaut Giraud, a French philosopher, popular science communicator, web videographer and writer. \u21a9\ufe0e<\/a><\/li>
  2. The Science \u00c9tonnante channel has a video explaining how these elementary structures manage to produce surprising macroscopic phenomena. \u21a9\ufe0e<\/a><\/li><\/ol>\n\n\n

    <\/p>\n","protected":false},"excerpt":{"rendered":"

    What is your research topic? During the first year of my PhD, I explored two avenues of research. The first […]<\/p>\n","protected":false},"author":9,"featured_media":10658,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_related_content_post":[],"_related_content_subject":[690],"_related_content_author":[10719],"_related_content_category":[1720,1716],"_related_content_folder":[10721],"_excerpt":"From biology and physics to economics, engineering and many other fields, applied mathematics cuts across a wide range of disciplines, enabling us to model, understand, and solve complex problems. Yet far from the abstract image often associated with it, applied mathematics permeates everyday life and drives research at the heart of very concrete challenges. This feature gives voice to five young researchers in applied mathematics who took part in the Congress of Young Researchers in Applied Mathematics (CJC-MA)<\/a>. Drawing on their backgrounds and in their own words, they describe what led them to this field, the scientists who inspired them, and the importance of such a conference to them in their careers as young researchers.","_duration":5,"_manual_duration":false,"footnotes":"[{\"content\":\"The popular philosophy YouTube channel Monsieur Phi <\/a><\/a>, by Thibaut Giraud, a French philosopher, popular science communicator, web videographer and writer.\",\"id\":\"a98b3554-320a-49dd-ba66-8be43bae778c\"},{\"content\":\"The Science \u00c9tonnante channel has a video explaining how these elementary structures manage to produce surprising macroscopic phenomena.\",\"id\":\"70754459-99ef-4776-afb4-69140a744ab8\"}]"},"article-types":[13],"class_list":["post-10664","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","article-types-article"],"has_blocks":true,"block_data":[{"blockName":"enpc\/excerpt","attrs":{"lock":[],"metadata":[],"className":"","style":""},"innerBlocks":[],"innerHTML":"","innerContent":[],"rendered":""},{"blockName":"core\/image","attrs":{"id":10658,"sizeSlug":"large","linkDestination":"none","align":"wide","blob":"","url":"https:\/\/ingenius.ecoledesponts.fr\/wp-content\/uploads\/2026\/04\/ChatGPT-Image-Apr-27-2026-11_19_52-AM-1024x512.png","alt":"","caption":"Model reduction transforms a complex system into a much lower-dimensional representation, capable of faithfully approximating its behavior while significantly accelerating simulations.Source: Image generated with ChatGPT (OpenAI, GPT-5.3 model), 2026, based on an illustration from the COMPAS project (Jade Hochschule).","lightbox":[],"title":"","href":"","rel":"","linkClass":"","width":"","height":"","aspectRatio":"","scale":"","linkTarget":"","lock":[],"metadata":[],"className":"wp-block-image alignwide size-large","style":"","borderColor":"","anchor":""},"innerBlocks":[],"innerHTML":"\n

    \"\"
    Model reduction transforms a complex system into a much lower-dimensional representation, capable of faithfully approximating its behavior while significantly accelerating simulations.
    Source: Image generated with ChatGPT (OpenAI, GPT-5.3 model), 2026, based on an illustration from the     COMPAS project (Jade Hochschule)<\/a>.<\/figcaption><\/figure>\n","innerContent":["\n
    \"\"
    Model reduction transforms a complex system into a much lower-dimensional representation, capable of faithfully approximating its behavior while significantly accelerating simulations.
    Source: Image generated with ChatGPT (OpenAI, GPT-5.3 model), 2026, based on an illustration from the     COMPAS project (Jade Hochschule)<\/a>.<\/figcaption><\/figure>\n"],"rendered":"\n
    \"\"
    Model reduction transforms a complex system into a much lower-dimensional representation, capable of faithfully approximating its behavior while significantly accelerating simulations.
    Source: Image generated with ChatGPT (OpenAI, GPT-5.3 model), 2026, based on an illustration from the     COMPAS project (Jade Hochschule)<\/a>.<\/figcaption><\/figure>\n"},{"blockName":"core\/paragraph","attrs":{"align":"","content":"What is your research topic?","dropCap":false,"placeholder":"","direction":"","lock":[],"metadata":[],"className":"","style":"","backgroundColor":"","textColor":"","gradient":"","fontSize":"","fontFamily":"","borderColor":"","anchor":""},"innerBlocks":[],"innerHTML":"\n

    What is your research topic?<\/strong><\/p>\n","innerContent":["\n

    What is your research topic?<\/strong><\/p>\n"],"rendered":"\n

    What is your research topic?<\/strong><\/p>\n"},{"blockName":"core\/paragraph","attrs":{"align":"","content":"During the first year of my PhD, I explored two avenues of research. The first lies at the intersection of scientific computing and artificial intelligence, and concerns \u201cPINNs\u201d (Physics-Informed Neural Networks).The idea is to use neural networks to approximate as closely as possible the solution to equations describing physical phenomena. Although these methods have grown rapidly since 2019, they still raise important theoretical and numerical questions, which are central to my work.","dropCap":false,"placeholder":"","direction":"","lock":[],"metadata":[],"className":"","style":"","backgroundColor":"","textColor":"","gradient":"","fontSize":"","fontFamily":"","borderColor":"","anchor":""},"innerBlocks":[],"innerHTML":"\n

    During the first year of my PhD, I explored two avenues of research. The first lies at the intersection of scientific computing and artificial intelligence, and concerns \u201cPINNs\u201d (Physics-Informed Neural Networks).The idea is to use neural networks to approximate as closely as possible the solution to equations describing physical phenomena. Although these methods have grown rapidly since 2019, they still raise important theoretical and numerical questions, which are central to my work.<\/p>\n","innerContent":["\n

    During the first year of my PhD, I explored two avenues of research. The first lies at the intersection of scientific computing and artificial intelligence, and concerns \u201cPINNs\u201d (Physics-Informed Neural Networks).The idea is to use neural networks to approximate as closely as possible the solution to equations describing physical phenomena. Although these methods have grown rapidly since 2019, they still raise important theoretical and numerical questions, which are central to my work.<\/p>\n"],"rendered":"\n

    During the first year of my PhD, I explored two avenues of research. The first lies at the intersection of scientific computing and artificial intelligence, and concerns \u201cPINNs\u201d (Physics-Informed Neural Networks).The idea is to use neural networks to approximate as closely as possible the solution to equations describing physical phenomena. Although these methods have grown rapidly since 2019, they still raise important theoretical and numerical questions, which are central to my work.<\/p>\n"},{"blockName":"core\/paragraph","attrs":{"align":"","content":"The second avenue concerns model reduction. The aim is to accelerate extremely costly numerical simulations which are used to study complex mechanical phenomena that depend on numerous parameters. This applies, for example to the underground storage of CO\u2082, which is injected into subsurface environments that already contain fractures or faults. This raises the question of determining what ground movements this injection may cause, and how these may interact with pre-existing geological structures. All of this requires the testing of multiple configurations, which can quickly become prohibitively expensive.","dropCap":false,"placeholder":"","direction":"","lock":[],"metadata":[],"className":"","style":"","backgroundColor":"","textColor":"","gradient":"","fontSize":"","fontFamily":"","borderColor":"","anchor":""},"innerBlocks":[],"innerHTML":"\n

    The second avenue concerns model reduction. The aim is to accelerate extremely costly numerical simulations which are used to study complex mechanical phenomena that depend on numerous parameters<\/a>. This applies, for example to the underground storage of CO\u2082<\/a>, which is injected into subsurface environments that already contain fractures or faults. This raises the question of determining what ground movements this injection may cause, and how these may interact with pre-existing geological structures. All of this requires the testing of multiple configurations, which can quickly become prohibitively expensive.<\/p>\n","innerContent":["\n

    The second avenue concerns model reduction. The aim is to accelerate extremely costly numerical simulations which are used to study complex mechanical phenomena that depend on numerous parameters<\/a>. This applies, for example to the underground storage of CO\u2082<\/a>, which is injected into subsurface environments that already contain fractures or faults. This raises the question of determining what ground movements this injection may cause, and how these may interact with pre-existing geological structures. All of this requires the testing of multiple configurations, which can quickly become prohibitively expensive.<\/p>\n"],"rendered":"\n

    The second avenue concerns model reduction. The aim is to accelerate extremely costly numerical simulations which are used to study complex mechanical phenomena that depend on numerous parameters<\/a>. This applies, for example to the underground storage of CO\u2082<\/a>, which is injected into subsurface environments that already contain fractures or faults. This raises the question of determining what ground movements this injection may cause, and how these may interact with pre-existing geological structures. All of this requires the testing of multiple configurations, which can quickly become prohibitively expensive.<\/p>\n"},{"blockName":"core\/paragraph","attrs":{"align":"","content":"My work consists in developing reduced models that retain the essential physical information while significantly decreasing computation time, so that we can explore different scenarios more efficiently and better anticipate certain risks, such as ground deformation, microseismic activity, or \u2013 in extreme cases \u2013 CO\u2082 leakage.","dropCap":false,"placeholder":"","direction":"","lock":[],"metadata":[],"className":"","style":"","backgroundColor":"","textColor":"","gradient":"","fontSize":"","fontFamily":"","borderColor":"","anchor":""},"innerBlocks":[],"innerHTML":"\n

    My work consists in developing reduced models that retain the essential physical information while significantly decreasing computation time<\/a>, so that we can explore different scenarios more efficiently and better anticipate certain risks, such as ground deformation, microseismic activity, or \u2013 in extreme cases \u2013 CO\u2082 leakage.<\/p>\n","innerContent":["\n

    My work consists in developing reduced models that retain the essential physical information while significantly decreasing computation time<\/a>, so that we can explore different scenarios more efficiently and better anticipate certain risks, such as ground deformation, microseismic activity, or \u2013 in extreme cases \u2013 CO\u2082 leakage.<\/p>\n"],"rendered":"\n

    My work consists in developing reduced models that retain the essential physical information while significantly decreasing computation time<\/a>, so that we can explore different scenarios more efficiently and better anticipate certain risks, such as ground deformation, microseismic activity, or \u2013 in extreme cases \u2013 CO\u2082 leakage.<\/p>\n"},{"blockName":"core\/paragraph","attrs":{"style":{"elements":{"link":{"color":{"text":"var:preset|color|red"}}}},"textColor":"red","align":"","content":"What led you to study mathematics?","dropCap":false,"placeholder":"","direction":"","lock":[],"metadata":[],"className":"has-red-color has-text-color has-link-color","backgroundColor":"","gradient":"","fontSize":"","fontFamily":"","borderColor":"","anchor":""},"innerBlocks":[],"innerHTML":"\n

    What led you to study mathematics?<\/strong><\/p>\n","innerContent":["\n

    What led you to study mathematics?<\/strong><\/p>\n"],"rendered":"\n

    What led you to study mathematics?<\/strong><\/p>\n"},{"blockName":"core\/paragraph","attrs":{"align":"","content":"My interest in mathematics developed somewhat unexpectedly during my final year of high school. By chance, I stumbled across the Monsieur Phi1 YouTube channel, which presents popular philosophy content, and started to realize that certain aspects of contemporary philosophy maintain a close dialog with science.","dropCap":false,"placeholder":"","direction":"","lock":[],"metadata":[],"className":"","style":"","backgroundColor":"","textColor":"","gradient":"","fontSize":"","fontFamily":"","borderColor":"","anchor":""},"innerBlocks":[],"innerHTML":"\n

    My interest in mathematics developed somewhat unexpectedly during my final year of high school. By chance, I stumbled across the Monsieur Phi1<\/a><\/sup> YouTube channel, which presents popular philosophy content, and started to realize that certain aspects of contemporary philosophy maintain a close dialog with science.<\/p>\n","innerContent":["\n

    My interest in mathematics developed somewhat unexpectedly during my final year of high school. By chance, I stumbled across the Monsieur Phi1<\/a><\/sup> YouTube channel, which presents popular philosophy content, and started to realize that certain aspects of contemporary philosophy maintain a close dialog with science.<\/p>\n"],"rendered":"\n

    My interest in mathematics developed somewhat unexpectedly during my final year of high school. By chance, I stumbled across the Monsieur Phi1<\/a><\/sup> YouTube channel, which presents popular philosophy content, and started to realize that certain aspects of contemporary philosophy maintain a close dialog with science.<\/p>\n"},{"blockName":"core\/paragraph","attrs":{"align":"","content":"This discovery led me toward a community of French popular science communicators such as L\u00ea Nguy\u00ean Hoang from the Science4All channel and David Louapre at Science \u00c9tonnante. These videos sparked \u2013 and then reinforced \u2013 my interest in science, much to the surprise of everyone around me. I had initially planned to pursue literary studies, but I ultimately opted for a scientific preparatory program in Tunisia. I then entered the \u00c9cole nationale des ponts et chauss\u00e9es, completed the MVA master\u2019s program and then embarked on a PhD.","dropCap":false,"placeholder":"","direction":"","lock":[],"metadata":[],"className":"","style":"","backgroundColor":"","textColor":"","gradient":"","fontSize":"","fontFamily":"","borderColor":"","anchor":""},"innerBlocks":[],"innerHTML":"\n

    This discovery led me toward a community of French popular science communicators such as L\u00ea Nguy\u00ean Hoang from the Science4All channel and David Louapre at Science \u00c9tonnante. These videos sparked \u2013 and then reinforced \u2013 my interest in science, much to the surprise of everyone around me. I had initially planned to pursue literary studies, but I ultimately opted for a scientific preparatory program in Tunisia. I then entered the \u00c9cole nationale des ponts et chauss\u00e9es, completed the MVA master\u2019s program and then embarked on a PhD.<\/p>\n","innerContent":["\n

    This discovery led me toward a community of French popular science communicators such as L\u00ea Nguy\u00ean Hoang from the Science4All channel and David Louapre at Science \u00c9tonnante. These videos sparked \u2013 and then reinforced \u2013 my interest in science, much to the surprise of everyone around me. I had initially planned to pursue literary studies, but I ultimately opted for a scientific preparatory program in Tunisia. I then entered the \u00c9cole nationale des ponts et chauss\u00e9es, completed the MVA master\u2019s program and then embarked on a PhD.<\/p>\n"],"rendered":"\n

    This discovery led me toward a community of French popular science communicators such as L\u00ea Nguy\u00ean Hoang from the Science4All channel and David Louapre at Science \u00c9tonnante. These videos sparked \u2013 and then reinforced \u2013 my interest in science, much to the surprise of everyone around me. I had initially planned to pursue literary studies, but I ultimately opted for a scientific preparatory program in Tunisia. I then entered the \u00c9cole nationale des ponts et chauss\u00e9es, completed the MVA master\u2019s program and then embarked on a PhD.<\/p>\n"},{"blockName":"core\/gallery","attrs":{"columns":1,"linkTo":"none","isSlideshow":true,"images":[],"ids":[],"shortCodeTransforms":[],"caption":"","imageCrop":true,"randomOrder":false,"fixedHeight":true,"linkTarget":"","sizeSlug":"large","allowResize":false,"aspectRatio":"auto","lock":[],"metadata":[],"align":"","className":"wp-block-gallery has-nested-images columns-1 is-cropped","style":"","backgroundColor":"","gradient":"","borderColor":"","layout":[],"anchor":""},"innerBlocks":[{"blockName":"core\/image","attrs":{"id":10573,"sizeSlug":"large","linkDestination":"none","blob":"","url":"https:\/\/ingenius.ecoledesponts.fr\/wp-content\/uploads\/2026\/04\/Paradoxe_2_enfants_Canva-1024x551.png","alt":"","caption":"The Two-Child Paradox is based on a simple premise: Mr. Smith has two children. One of them is a boy. What is the probability that the other child is also a boy? What makes the problem interesting is its apparent simplicity: depending on how one interprets the given information, one can convincingly arrive at either 1\/3 or 1\/2. This apparent simplicity illustrates how our intuition about probabilities can lead us astray.\u00a0 To find out more, watch the video \u201cThe Two-Child Paradox\u201d by L\u00ea Nguy\u00ean Hoang from the Science 4Allchannel.\u00a0 ","lightbox":[],"title":"","href":"","rel":"","linkClass":"","width":"","height":"","aspectRatio":"","scale":"","linkTarget":"","lock":[],"metadata":[],"align":"","className":"wp-block-image size-large","style":"","borderColor":"","anchor":""},"innerBlocks":[],"innerHTML":"\n

    \"\"
    The Two-Child Paradox is based on a simple premise: Mr. Smith has two children. One of them is a boy. What is the probability that the other child is also a boy? <\/em>What makes the problem interesting is its apparent simplicity: depending on how one interprets the given information, one can convincingly arrive at either 1\/3 or 1\/2. This apparent simplicity illustrates how our intuition about probabilities can lead us astray.\u00a0 To find out more, watch the video \u201cThe Two-Child Paradox\u201d by L\u00ea Nguy\u00ean Hoang from the Science 4Allchannel<\/a>.\u00a0 <\/figcaption><\/figure>\n","innerContent":["\n
    \"\"
    The Two-Child Paradox is based on a simple premise: Mr. Smith has two children. One of them is a boy. What is the probability that the other child is also a boy? <\/em>What makes the problem interesting is its apparent simplicity: depending on how one interprets the given information, one can convincingly arrive at either 1\/3 or 1\/2. This apparent simplicity illustrates how our intuition about probabilities can lead us astray.\u00a0 To find out more, watch the video \u201cThe Two-Child Paradox\u201d by L\u00ea Nguy\u00ean Hoang from the Science 4Allchannel<\/a>.\u00a0 <\/figcaption><\/figure>\n"],"rendered":"\n
    \"\"
    The Two-Child Paradox is based on a simple premise: Mr. Smith has two children. One of them is a boy. What is the probability that the other child is also a boy? <\/em>What makes the problem interesting is its apparent simplicity: depending on how one interprets the given information, one can convincingly arrive at either 1\/3 or 1\/2. This apparent simplicity illustrates how our intuition about probabilities can lead us astray.\u00a0 To find out more, watch the video \u201cThe Two-Child Paradox\u201d by L\u00ea Nguy\u00ean Hoang from the Science 4Allchannel<\/a>.\u00a0 <\/figcaption><\/figure>\n"},{"blockName":"core\/image","attrs":{"id":10572,"sizeSlug":"large","linkDestination":"none","blob":"","url":"https:\/\/ingenius.ecoledesponts.fr\/wp-content\/uploads\/2026\/04\/paradoxe-de-newcomb-1024x576.png","alt":"","caption":"Newcomb\u2019s paradox is another quite baffling thought experiment: an almost infallible predictor presents two boxes, one transparent containing \u201c\u20ac1,000\u201d, the other opaque containing either \u201c\u20ac1,000,000\u201d or \u201cnothing at all\u201d. If the predictor has predicted that you will take only the opaque box, it has placed the million euros inside it; if it has predicted that you would take both boxes, it has placed nothing inside. You must then choose between taking only the opaque box or taking both boxes. This problem has generated a rich body of literature, because two rational lines of reasoning lead to different strategies. It raises questions about decision theory, causality, and \u2013 depending on the interpretation \u2013 free will. To find out more, watch the video: \u201cThis Paradox Will Drive You Mad\u201d by Monsieur Phi","lightbox":[],"title":"","href":"","rel":"","linkClass":"","width":"","height":"","aspectRatio":"","scale":"","linkTarget":"","lock":[],"metadata":[],"align":"","className":"wp-block-image size-large","style":"","borderColor":"","anchor":""},"innerBlocks":[],"innerHTML":"\n
    \"\"
    Newcomb\u2019s paradox is another quite baffling thought experiment: an almost infallible predictor presents two boxes, one transparent containing \u201c\u20ac1,000\u201d, the other opaque containing either \u201c\u20ac1,000,000\u201d or \u201cnothing at all\u201d. If the predictor has predicted that you will take only the opaque box, it has placed the million euros inside it; if it has predicted that you would take both boxes, it has placed nothing inside. You must then choose between taking only the opaque box or taking both boxes. <\/em>This problem has generated a rich body of literature, because two rational lines of reasoning lead to different strategies. It raises questions about decision theory, causality, and \u2013 depending on the interpretation \u2013 free will. To find out more, watch the video: \u201cThis Paradox Will Drive You Mad\u201d by Monsieur Phi<\/a><\/figcaption><\/figure>\n","innerContent":["\n
    \"\"
    Newcomb\u2019s paradox is another quite baffling thought experiment: an almost infallible predictor presents two boxes, one transparent containing \u201c\u20ac1,000\u201d, the other opaque containing either \u201c\u20ac1,000,000\u201d or \u201cnothing at all\u201d. If the predictor has predicted that you will take only the opaque box, it has placed the million euros inside it; if it has predicted that you would take both boxes, it has placed nothing inside. You must then choose between taking only the opaque box or taking both boxes. <\/em>This problem has generated a rich body of literature, because two rational lines of reasoning lead to different strategies. It raises questions about decision theory, causality, and \u2013 depending on the interpretation \u2013 free will. To find out more, watch the video: \u201cThis Paradox Will Drive You Mad\u201d by Monsieur Phi<\/a><\/figcaption><\/figure>\n"],"rendered":"\n
    \"\"
    Newcomb\u2019s paradox is another quite baffling thought experiment: an almost infallible predictor presents two boxes, one transparent containing \u201c\u20ac1,000\u201d, the other opaque containing either \u201c\u20ac1,000,000\u201d or \u201cnothing at all\u201d. If the predictor has predicted that you will take only the opaque box, it has placed the million euros inside it; if it has predicted that you would take both boxes, it has placed nothing inside. You must then choose between taking only the opaque box or taking both boxes. <\/em>This problem has generated a rich body of literature, because two rational lines of reasoning lead to different strategies. It raises questions about decision theory, causality, and \u2013 depending on the interpretation \u2013 free will. To find out more, watch the video: \u201cThis Paradox Will Drive You Mad\u201d by Monsieur Phi<\/a><\/figcaption><\/figure>\n"}],"innerHTML":"\n
    \n\n<\/figure>\n","innerContent":["\n
    ",null,"\n\n",null,"<\/figure>\n"],"rendered":"\n
    \n
    \"\"
    The Two-Child Paradox is based on a simple premise: Mr. Smith has two children. One of them is a boy. What is the probability that the other child is also a boy? <\/em>What makes the problem interesting is its apparent simplicity: depending on how one interprets the given information, one can convincingly arrive at either 1\/3 or 1\/2. This apparent simplicity illustrates how our intuition about probabilities can lead us astray.\u00a0 To find out more, watch the video \u201cThe Two-Child Paradox\u201d by L\u00ea Nguy\u00ean Hoang from the Science 4Allchannel<\/a>.\u00a0 <\/figcaption><\/figure>\n\n\n\n
    \"\"
    Newcomb\u2019s paradox is another quite baffling thought experiment: an almost infallible predictor presents two boxes, one transparent containing \u201c\u20ac1,000\u201d, the other opaque containing either \u201c\u20ac1,000,000\u201d or \u201cnothing at all\u201d. If the predictor has predicted that you will take only the opaque box, it has placed the million euros inside it; if it has predicted that you would take both boxes, it has placed nothing inside. You must then choose between taking only the opaque box or taking both boxes. <\/em>This problem has generated a rich body of literature, because two rational lines of reasoning lead to different strategies. It raises questions about decision theory, causality, and \u2013 depending on the interpretation \u2013 free will. To find out more, watch the video: \u201cThis Paradox Will Drive You Mad\u201d by Monsieur Phi<\/a><\/figcaption><\/figure>\n<\/figure>\n"},{"blockName":"core\/paragraph","attrs":{"style":{"elements":{"link":{"color":{"text":"var:preset|color|red"}}}},"textColor":"red","align":"","content":"Which mathematicians have made the biggest impression on you so far?","dropCap":false,"placeholder":"","direction":"","lock":[],"metadata":[],"className":"has-red-color has-text-color has-link-color","backgroundColor":"","gradient":"","fontSize":"","fontFamily":"","borderColor":"","anchor":""},"innerBlocks":[],"innerHTML":"\n

    Which mathematicians have made the biggest impression on you so far?<\/strong><\/p>\n","innerContent":["\n

    Which mathematicians have made the biggest impression on you so far?<\/strong><\/p>\n"],"rendered":"\n

    Which mathematicians have made the biggest impression on you so far?<\/strong><\/p>\n"},{"blockName":"core\/paragraph","attrs":{"align":"","content":"Several figures have shaped the way I think about mathematics. I would particularly like to mention the British mathematician John Conway, whom I discovered some time ago through his famous Game of Life, in which a cellular automaton evolves according to very simple rules, yet these are sufficient to give rise to unexpectedly complex behaviors.2 It embodies a form of mathematical beauty that really speaks to me.","dropCap":false,"placeholder":"","direction":"","lock":[],"metadata":[],"className":"","style":"","backgroundColor":"","textColor":"","gradient":"","fontSize":"","fontFamily":"","borderColor":"","anchor":""},"innerBlocks":[],"innerHTML":"\n

    Several figures have shaped the way I think about mathematics. I would particularly like to mention the British mathematician John Conway<\/a>, whom I discovered some time ago through his famous Game of Life, in which a cellular automaton evolves according to very simple rules, yet these are sufficient to give rise to unexpectedly complex behaviors.2<\/a><\/sup> It embodies a form of mathematical beauty that really speaks to me.<\/p>\n","innerContent":["\n

    Several figures have shaped the way I think about mathematics. I would particularly like to mention the British mathematician John Conway<\/a>, whom I discovered some time ago through his famous Game of Life, in which a cellular automaton evolves according to very simple rules, yet these are sufficient to give rise to unexpectedly complex behaviors.2<\/a><\/sup> It embodies a form of mathematical beauty that really speaks to me.<\/p>\n"],"rendered":"\n

    Several figures have shaped the way I think about mathematics. I would particularly like to mention the British mathematician John Conway<\/a>, whom I discovered some time ago through his famous Game of Life, in which a cellular automaton evolves according to very simple rules, yet these are sufficient to give rise to unexpectedly complex behaviors.2<\/a><\/sup> It embodies a form of mathematical beauty that really speaks to me.<\/p>\n"},{"blockName":"core\/paragraph","attrs":{"align":"","content":"In a very different vein, Alain Connes has also influenced me through the way he speaks about mathematical work. I remember a talk I discovered during my years in preparatory classes, in which he explained that mathematics is not simply about reading a sequence of statements and proofs, but about making the material one\u2019s own, reflecting on it, and coming back to it. I interpreted these words as a kind of process for developing genuine intuition by building one\u2019s own mental representation of mathematical objects. This intuition does not replace technical mastery, but it plays an essential role in making progress and in forging unexpected connections between seemingly unrelated fields.","dropCap":false,"placeholder":"","direction":"","lock":[],"metadata":[],"className":"","style":"","backgroundColor":"","textColor":"","gradient":"","fontSize":"","fontFamily":"","borderColor":"","anchor":""},"innerBlocks":[],"innerHTML":"\n

    In a very different vein, Alain Connes has also influenced me through the way he speaks about mathematical work. I remember a talk I discovered during my years in preparatory classes, in which he explained that mathematics is not simply about reading a sequence of statements and proofs, but about making the material one\u2019s own, reflecting on it, and coming back to it. I interpreted these words as a kind of process for developing genuine intuition by building one\u2019s own mental representation of mathematical objects. This intuition does not replace technical mastery, but it plays an essential role in making progress and in forging unexpected connections between seemingly unrelated fields.<\/p>\n","innerContent":["\n

    In a very different vein, Alain Connes has also influenced me through the way he speaks about mathematical work. I remember a talk I discovered during my years in preparatory classes, in which he explained that mathematics is not simply about reading a sequence of statements and proofs, but about making the material one\u2019s own, reflecting on it, and coming back to it. I interpreted these words as a kind of process for developing genuine intuition by building one\u2019s own mental representation of mathematical objects. This intuition does not replace technical mastery, but it plays an essential role in making progress and in forging unexpected connections between seemingly unrelated fields.<\/p>\n"],"rendered":"\n

    In a very different vein, Alain Connes has also influenced me through the way he speaks about mathematical work. I remember a talk I discovered during my years in preparatory classes, in which he explained that mathematics is not simply about reading a sequence of statements and proofs, but about making the material one\u2019s own, reflecting on it, and coming back to it. I interpreted these words as a kind of process for developing genuine intuition by building one\u2019s own mental representation of mathematical objects. This intuition does not replace technical mastery, but it plays an essential role in making progress and in forging unexpected connections between seemingly unrelated fields.<\/p>\n"},{"blockName":"core\/paragraph","attrs":{"align":"","content":"There is also a certain idealization of research, which consists in constantly pushing the boundaries of knowledge through sustained intellectual effort. I am thinking in particular of Albert Einstein, who formalized several major theories within the space of a few months during his \u201cannus mirabilis\u201d in 1905, in the form of four articles that laid the foundations of modern physics. It seems that many of his ideas came to him following long periods of reflection and physical imagination, which often arose before the actual mathematical formalization. This somewhat idealized vision is often far removed from the day-to-day reality of research, but nevertheless continues to inspire me.","dropCap":false,"placeholder":"","direction":"","lock":[],"metadata":[],"className":"","style":"","backgroundColor":"","textColor":"","gradient":"","fontSize":"","fontFamily":"","borderColor":"","anchor":""},"innerBlocks":[],"innerHTML":"\n

    There is also a certain idealization of research, which consists in constantly pushing the boundaries of knowledge through sustained intellectual effort. I am thinking in particular of Albert Einstein, who formalized several major theories within the space of a few months during his \u201cannus mirabilis\u201d in 1905, in the form of four articles that laid the foundations of modern physics. It seems that many of his ideas came to him following long periods of reflection and physical imagination, which often arose before the actual mathematical formalization. This somewhat idealized vision is often far removed from the day-to-day reality of research, but nevertheless continues to inspire me.<\/p>\n","innerContent":["\n

    There is also a certain idealization of research, which consists in constantly pushing the boundaries of knowledge through sustained intellectual effort. I am thinking in particular of Albert Einstein, who formalized several major theories within the space of a few months during his \u201cannus mirabilis\u201d in 1905, in the form of four articles that laid the foundations of modern physics. It seems that many of his ideas came to him following long periods of reflection and physical imagination, which often arose before the actual mathematical formalization. This somewhat idealized vision is often far removed from the day-to-day reality of research, but nevertheless continues to inspire me.<\/p>\n"],"rendered":"\n

    There is also a certain idealization of research, which consists in constantly pushing the boundaries of knowledge through sustained intellectual effort. I am thinking in particular of Albert Einstein, who formalized several major theories within the space of a few months during his \u201cannus mirabilis\u201d in 1905, in the form of four articles that laid the foundations of modern physics. It seems that many of his ideas came to him following long periods of reflection and physical imagination, which often arose before the actual mathematical formalization. This somewhat idealized vision is often far removed from the day-to-day reality of research, but nevertheless continues to inspire me.<\/p>\n"},{"blockName":"core\/paragraph","attrs":{"style":{"elements":{"link":{"color":{"text":"var:preset|color|red"}}}},"textColor":"red","align":"","content":"Why is a conference like this important for young researchers in mathematics?","dropCap":false,"placeholder":"","direction":"","lock":[],"metadata":[],"className":"has-red-color has-text-color has-link-color","backgroundColor":"","gradient":"","fontSize":"","fontFamily":"","borderColor":"","anchor":""},"innerBlocks":[],"innerHTML":"\n

    Why is a conference like this important for young researchers in mathematics?<\/strong><\/p>\n","innerContent":["\n

    Why is a conference like this important for young researchers in mathematics?<\/strong><\/p>\n"],"rendered":"\n

    Why is a conference like this important for young researchers in mathematics?<\/strong><\/p>\n"},{"blockName":"core\/paragraph","attrs":{"align":"","content":"The Congress of Young Researchers in Applied Mathematics is primarily aimed at PhD students and postdoctoral researchers. Unlike more traditional conferences, which often cater to an audience of experienced researchers, this congress encourages discussion in a more accessible and perhaps less intimidating setting. It provides a valuable opportunity to connect with peers from a wide range of laboratories, in a context encouraging disciplinary, institutional, and geographical diversity. The wide range of topics presented also allows participants to explore new fields.","dropCap":false,"placeholder":"","direction":"","lock":[],"metadata":[],"className":"","style":"","backgroundColor":"","textColor":"","gradient":"","fontSize":"","fontFamily":"","borderColor":"","anchor":""},"innerBlocks":[],"innerHTML":"\n

    The Congress of Young Researchers in Applied Mathematics is primarily aimed at PhD students and postdoctoral researchers. Unlike more traditional conferences, which often cater to an audience of experienced researchers, this congress encourages discussion in a more accessible and perhaps less intimidating setting. It provides a valuable opportunity to connect with peers from a wide range of laboratories, in a context encouraging disciplinary, institutional, and geographical diversity. The wide range of topics presented also allows participants to explore new fields.<\/p>\n","innerContent":["\n

    The Congress of Young Researchers in Applied Mathematics is primarily aimed at PhD students and postdoctoral researchers. Unlike more traditional conferences, which often cater to an audience of experienced researchers, this congress encourages discussion in a more accessible and perhaps less intimidating setting. It provides a valuable opportunity to connect with peers from a wide range of laboratories, in a context encouraging disciplinary, institutional, and geographical diversity. The wide range of topics presented also allows participants to explore new fields.<\/p>\n"],"rendered":"\n

    The Congress of Young Researchers in Applied Mathematics is primarily aimed at PhD students and postdoctoral researchers. Unlike more traditional conferences, which often cater to an audience of experienced researchers, this congress encourages discussion in a more accessible and perhaps less intimidating setting. It provides a valuable opportunity to connect with peers from a wide range of laboratories, in a context encouraging disciplinary, institutional, and geographical diversity. The wide range of topics presented also allows participants to explore new fields.<\/p>\n"},{"blockName":"core\/paragraph","attrs":{"align":"","content":"For my part, I was a member of the logistics committee. The conference also featured plenary sessions led by experienced speakers, tasked with presenting more general topics. Although I did not present my work this year, I would like to do so at a future edition.","dropCap":false,"placeholder":"","direction":"","lock":[],"metadata":[],"className":"","style":"","backgroundColor":"","textColor":"","gradient":"","fontSize":"","fontFamily":"","borderColor":"","anchor":""},"innerBlocks":[],"innerHTML":"\n

    For my part, I was a member of the logistics committee. The conference also featured plenary sessions led by experienced speakers, tasked with presenting more general topics. Although I did not present my work this year, I would like to do so at a future edition.<\/p>\n","innerContent":["\n

    For my part, I was a member of the logistics committee. The conference also featured plenary sessions led by experienced speakers, tasked with presenting more general topics. Although I did not present my work this year, I would like to do so at a future edition.<\/p>\n"],"rendered":"\n

    For my part, I was a member of the logistics committee. The conference also featured plenary sessions led by experienced speakers, tasked with presenting more general topics. Although I did not present my work this year, I would like to do so at a future edition.<\/p>\n"},{"blockName":"core\/paragraph","attrs":{"align":"","content":"Interview by Mahalia Blanchard-Martial, scientific communicator at \u00c9cole nationale des ponts et chauss\u00e9es.","dropCap":false,"placeholder":"","direction":"","lock":[],"metadata":[],"className":"","style":"","backgroundColor":"","textColor":"","gradient":"","fontSize":"","fontFamily":"","borderColor":"","anchor":""},"innerBlocks":[],"innerHTML":"\n

    Interview by Mahalia Blanchard-Martial, scientific communicator at \u00c9cole nationale des ponts et chauss\u00e9es.<\/em><\/p>\n","innerContent":["\n

    Interview by Mahalia Blanchard-Martial, scientific communicator at \u00c9cole nationale des ponts et chauss\u00e9es.<\/em><\/p>\n"],"rendered":"\n

    Interview by Mahalia Blanchard-Martial, scientific communicator at \u00c9cole nationale des ponts et chauss\u00e9es.<\/em><\/p>\n"},{"blockName":"core\/footnotes","attrs":{"lock":[],"metadata":[],"className":"","style":"","backgroundColor":"","textColor":"","fontSize":"","fontFamily":"","borderColor":""},"innerBlocks":[],"innerHTML":"","innerContent":[],"rendered":""},{"blockName":"core\/paragraph","attrs":{"align":"","content":"","dropCap":false,"placeholder":"","direction":"","lock":[],"metadata":[],"className":"","style":"","backgroundColor":"","textColor":"","gradient":"","fontSize":"","fontFamily":"","borderColor":"","anchor":""},"innerBlocks":[],"innerHTML":"\n

    <\/p>\n","innerContent":["\n

    <\/p>\n"],"rendered":"\n

    <\/p>\n"}],"seo":{"title":"How Reduction Can Improve Prediction: a Conversation With Sofiane Ezzehi"},"media":{"img":"\"\"","src":"https:\/\/ingenius.ecoledesponts.fr\/wp-content\/uploads\/2026\/04\/ChatGPT-Image-Apr-27-2026-11_19_52-AM.png"},"url":"\/en\/articles\/how-reduction-can-improve-prediction-a-conversation-with-sofiane-ezzehi\/","related":{"post":[],"author":[{"title":"Sofiane Ezzehi","url":"\/en\/authors\/sofiane-ezzehi\/","id":"10719","media":"\"unknown\"","slug":"sofiane-ezzehi"}],"subject":[{"title":"Digital Technology, Modeling & Artificial Intelligence","url":"\/en\/subjects\/digital-technology-modeling-artificial-intelligence\/","id":"690","media":"\"\"","slug":"digital-technology-modeling-artificial-intelligence"}],"category":[{"title":"Article collection","url":"\/en\/articles\/category\/dossier\/","id":"1720","media":"","slug":"dossier","_related_post_type":"folder"},{"title":"Articles","url":"\/en\/articles\/category\/articles\/","id":"1716","media":"","slug":"articles","_related_post_type":""}],"folder":[{"title":"Applied Mathematics: pathways for young researchers","url":"\/en\/folders\/applied-mathematics-pathways-for-young-researchers\/","id":"10721","media":"\"\"","slug":"applied-mathematics-pathways-for-young-researchers"}]},"translated":"https:\/\/ingenius.ecoledesponts.fr\/articles\/comment-reduire-pour-mieux-predire-rencontre-avec-sofiane-ezzehi\/","icon":"icon-article","duration":"5","custom_excerpt":"From biology and physics to economics, engineering and many other fields, applied mathematics cuts across a wide range of disciplines, enabling us to model, understand, and solve complex problems. Yet far from the abstract image often associated with it, applied mathematics permeates everyday life and drives research at the heart of very concrete challenges. This feature gives voice to five young researchers in applied mathematics who took part in the Congress of Young Researchers in Applied Mathematics (CJC-MA)<\/a>. Drawing on their backgrounds and in their own words, they describe what led them to this field, the scientists who inspired them, and the importance of such a conference to them in their careers as young researchers.","duration_type":"","_links":{"self":[{"href":"https:\/\/ingenius.ecoledesponts.fr\/en\/wp-json\/wp\/v2\/posts\/10664","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ingenius.ecoledesponts.fr\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ingenius.ecoledesponts.fr\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ingenius.ecoledesponts.fr\/en\/wp-json\/wp\/v2\/users\/9"}],"replies":[{"embeddable":true,"href":"https:\/\/ingenius.ecoledesponts.fr\/en\/wp-json\/wp\/v2\/comments?post=10664"}],"version-history":[{"count":2,"href":"https:\/\/ingenius.ecoledesponts.fr\/en\/wp-json\/wp\/v2\/posts\/10664\/revisions"}],"predecessor-version":[{"id":10729,"href":"https:\/\/ingenius.ecoledesponts.fr\/en\/wp-json\/wp\/v2\/posts\/10664\/revisions\/10729"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/ingenius.ecoledesponts.fr\/en\/wp-json\/wp\/v2\/media\/10658"}],"wp:attachment":[{"href":"https:\/\/ingenius.ecoledesponts.fr\/en\/wp-json\/wp\/v2\/media?parent=10664"}],"wp:term":[{"taxonomy":"article-types","embeddable":true,"href":"https:\/\/ingenius.ecoledesponts.fr\/en\/wp-json\/wp\/v2\/article-types?post=10664"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}