<html>
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
</head>
<body>
<h1 style="box-sizing: border-box; margin: 0px 0px 15px; padding:
0px; color: rgb(26, 26, 26); font-family: Arial; font-style:
normal; font-weight: 700; line-height: 1.5; text-rendering:
optimizelegibility; font-size: 26px; max-height: 1e+06px;
font-variant-ligatures: normal; font-variant-caps: normal;
letter-spacing: normal; orphans: 2; text-align: start;
text-indent: 0px; text-transform: none; white-space: normal;
widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px;
text-decoration-thickness: initial; text-decoration-style:
initial; text-decoration-color: initial;"><font size="2">Special
Issue "Physics-Based Machine and Deep Learning for PDE Models"</font></h1>
<p><a
href="https://www.mdpi.com/journal/entropy/special_issues/Physics-Based_Machine"
id="LPlnkOWALinkPreview" class="moz-txt-link-freetext">https://www.mdpi.com/journal/entropy/special_issues/Physics-Based_Machine</a></p>
<div class=" large-4 small-12 columns" style="box-sizing:
border-box; margin: 10px 0px 0px; padding: 0px 10px 10px;
max-height: 1e+06px; width: 230.326px; float: left; position:
relative; color: rgb(34, 34, 34); font-family: Arial; font-size:
12px; font-style: normal; font-variant-ligatures: normal;
font-variant-caps: normal; font-weight: 400; letter-spacing:
normal; orphans: 2; text-align: start; text-indent: 0px;
text-transform: none; white-space: normal; widows: 2;
word-spacing: 0px; -webkit-text-stroke-width: 0px;
text-decoration-thickness: initial; text-decoration-style:
initial; text-decoration-color: initial;"><span class="qlst"
style="box-sizing: border-box; max-height: 1e+06px;"></span>
<p style="box-sizing: border-box; margin: 0px 0px 10px; padding:
0px; font-family: inherit; font-size: 1rem; font-weight: 400;
line-height: 1.6; text-rendering: optimizelegibility;
max-height: 1e+06px;"><br>
</p>
<p style="box-sizing: border-box; margin: 0px 0px 10px; padding:
0.5em 0px; font-family: inherit; font-size: 1rem; font-weight:
400; line-height: 1.6; text-rendering: optimizelegibility;
max-height: 1e+06px;"><span class="si-deadline"
style="box-sizing: border-box; max-height: 1e+06px;"><font
size="2">Deadline for manuscript submissions:<span> </span><b
style="box-sizing: border-box; font-weight: 700;
line-height: inherit; max-height: 1e+06px;">30 June 2022</b></font><span>
</span></span><br style="box-sizing: border-box; max-height:
1e+06px;">
</p>
</div>
<div class="large-8 small-12 columns text-right" style="box-sizing:
border-box; margin: 10px 0px 0px; padding: 0px 10px 2em;
max-height: 1e+06px; width: 460.667px; float: left; position:
relative; text-align: right !important; color: rgb(34, 34, 34);
font-family: Arial; font-size: 12px; font-style: normal;
font-variant-ligatures: normal; font-variant-caps: normal;
font-weight: 400; letter-spacing: normal; orphans: 2; text-indent:
0px; text-transform: none; white-space: normal; widows: 2;
word-spacing: 0px; -webkit-text-stroke-width: 0px;
text-decoration-thickness: initial; text-decoration-style:
initial; text-decoration-color: initial;"><img
src="https://www.mdpi.com/files/special_issues_graphic_abstract/82723/GA%20Banner.png"
style="box-sizing: border-box; display: inline-block;
vertical-align: middle; max-height: 1e+06px; max-width: 400px;
height: auto; margin-bottom: 5px;"></div>
<div class="sharingLinks" style="box-sizing: border-box; margin:
0px; padding: 0px; max-height: 1e+06px; color: rgb(34, 34, 34);
font-family: Arial; font-size: 12px; font-style: normal;
font-variant-ligatures: normal; font-variant-caps: normal;
font-weight: 400; letter-spacing: normal; orphans: 2; text-align:
start; text-indent: 0px; text-transform: none; white-space:
normal; widows: 2; word-spacing: 0px; -webkit-text-stroke-width:
0px; text-decoration-thickness: initial; text-decoration-style:
initial; text-decoration-color: initial;">
<h2 style="box-sizing: border-box; margin: 30px 0px 10px; padding:
0px; color: rgba(0, 128, 128, 0.75); font-family: Arial;
font-style: normal; font-weight: 700; line-height: 1.5;
text-rendering: optimizelegibility; font-size: 20px; max-height:
1e+06px;"><br>
</h2>
<div class="social-media-links" style="box-sizing: border-box;
margin: 0px; padding: 0px; max-height: 1e+06px; text-align:
left;"><a
href="mailto:?&subject=From%20MDPI%3A%20%22Physics-Based%20Machine%20and%20Deep%20Learning%20for%20PDE%20Models%22&body=https://www.mdpi.com/si/82723%0A%0APhysics-Based%20Machine%20and%20Deep%20Learning%20for%20PDE%20ModelsMachine%20learning%20has%20been%20successfully%20used%20for%20over%20a%20decade%20for%20applications%20in%20engineering.%20It%20has%20recently%20started%20to%20attract%20attention%20for%20scientific%20computing%20in%20domains%20dominated%20up%20to%20now%20by%20the%20classical%20mechanistic%20modeling%20paradigm.%20It%20is%20particularly%20promising%20for%20domains%20involving%20complex%20processes%2C%20only%20partially%20known%20and%20understood%20or%20when%20existing%20solutions%20are%20computationally%20not%20feasible.%20This%20is%20the%20case%20for%20the%20modeling%20and%20simulation%20of%20complex%20dynamical%20physical%20systems.%20Classical%20modeling%20relies%20on%20PDEs%2C%20and%20simulation%20is%20central%20to%20engineering%20and%20physical%20science%20with%20applications%20in%20domains%20such%20as%20earth%20systems%2C%20biology%2C%20medicine%2C%20mechanics%20and%20robotics.%20Traditional%20simulation%20problems%20involve%20computational%20fluid%20dynamics%20and%20turbulence%20modeling%2C%20mechanistic%20design%20and%20many%20other%20domains.%20Such%20numerical%20models%20are%20also%20used%20intensively%20in%20industrial%20systems%20design%2C%20in%20simulation%20for%20decision%20support%2C%20or%20in%20safety%20studies.%20They%20are%20used%20for%20inversion%2C%20data%20assimilation%20and%20forecasting.%20Despite%20extensive%20developments%20and%20promising%20progress%2C%20this%20classical%20paradigm%20suffers%20from%20limitations.%20It%20is%20often%20impossible%20or%20too%20costly%20to%20carry%20out%20direct%20simulations%20at%20the%20scale%20required%20for%20natural%20or%20industrial%20problems.%20The%20physics%20may%20be%20too%20complex%20or%20unknown%2C%20leading%20to%20incomplete%20or[...]"
title="Email" style="box-sizing: border-box; color: rgb(26,
26, 26); line-height: inherit; text-decoration: none;
max-height: 1e+06px; font-weight: 700; margin: 2px;"><span> </span></a><a
href="https://twitter.com/intent/tweet?text=Physics-Based+Machine+and+Deep+Learning+for+PDE+Models&hashtags=mdpientropy&url=https%3A%2F%2Fwww.mdpi.com%2Fsi%2F82723&via=Entropy_MDPI"
title="Twitter" target="_blank" rel="noopener noreferrer"
style="box-sizing: border-box; color: rgb(26, 26, 26);
line-height: inherit; text-decoration: none; max-height:
1e+06px; font-weight: 700; margin: 2px;"><span> </span></a><a
href="http://www.linkedin.com/shareArticle?mini=true&url=https%3A%2F%2Fwww.mdpi.com%2Fsi%2F82723&title=Physics-Based%20Machine%20and%20Deep%20Learning%20for%20PDE%20Models%26source%3Dhttps%3A%2F%2Fwww.mdpi.com%26summary%3DMachine%20learning%20has%20been%20successfully%20used%20for%20over%20a%20decade%20for%20applications%20in%20engineering.%20It%20has%20recently%20started%20to%20attract%20attention%20for%20scientific%20computing%20in%20domains%20dominated%20up%20to%20now%20by%20the%20classical%20mechanistic%20modeling%20paradigm.%20It%20is%20%5B...%5D"
title="LinkedIn" target="_blank" rel="noopener noreferrer"
style="box-sizing: border-box; color: rgb(26, 26, 26);
line-height: inherit; text-decoration: none; max-height:
1e+06px; font-weight: 700; margin: 2px;"><span> </span></a><a
href="https://www.facebook.com/sharer.php?u=https://www.mdpi.com/si/82723"
title="facebook" target="_blank" rel="noopener noreferrer"
style="box-sizing: border-box; color: rgb(26, 26, 26);
line-height: inherit; text-decoration: none; max-height:
1e+06px; font-weight: 700; margin: 2px;"><span> </span></a></div>
</div>
<br>
<div class="no-margin" style="box-sizing: border-box; margin: 0px
!important; padding: 0px; max-height: 1e+06px; color: rgb(34, 34,
34); font-family: Arial; font-size: 12px; font-style: normal;
font-variant-ligatures: normal; font-variant-caps: normal;
font-weight: 400; letter-spacing: normal; orphans: 2; text-align:
start; text-indent: 0px; text-transform: none; white-space:
normal; widows: 2; word-spacing: 0px; -webkit-text-stroke-width:
0px; text-decoration-thickness: initial; text-decoration-style:
initial; text-decoration-color: initial;">
<div class="generic-item editor-div img-exists"
data-filter="nicolas bousquet bayesian modeling; treatment of
uncertainties; machine/deep learning; industrial risk;
simulation" style="box-sizing: border-box; margin: 15px 0px 0px;
padding: 0px; max-height: 1e+06px; position: relative;
min-height: 100px; font-family: Arial; font-weight: 400;
line-height: 1.5; border: 0px; font-size: 12px;">
<div class="editor-div__content img-exists" style="box-sizing:
border-box; margin: 0px 95px 0px 0px; padding: 0px;
max-height: 1e+06px;">
<h2 style="box-sizing: border-box; margin: 30px 0px 10px;
padding: 0px; color: rgba(0, 128, 128, 0.75); font-family:
Arial; font-style: normal; font-weight: 700; line-height:
1.5; text-rendering: optimizelegibility; font-size: 20px;
max-height: 1e+06px; font-variant-ligatures: normal;
font-variant-caps: normal; letter-spacing: normal; orphans:
2; text-align: start; text-indent: 0px; text-transform:
none; white-space: normal; widows: 2; word-spacing: 0px;
-webkit-text-stroke-width: 0px; text-decoration-thickness:
initial; text-decoration-style: initial;
text-decoration-color: initial;"><br>
</h2>
</div>
<div class="editor-div__content img-exists" style="box-sizing:
border-box; margin: 0px 95px 0px 0px; padding: 0px;
max-height: 1e+06px;"><br>
</div>
<div class="editor-div__content img-exists" style="box-sizing:
border-box; margin: 0px 95px 0px 0px; padding: 0px;
max-height: 1e+06px;"><br>
</div>
<div class="editor-div__content img-exists" style="box-sizing:
border-box; margin: 0px 95px 0px 0px; padding: 0px;
max-height: 1e+06px;"><br>
</div>
<div class="editor-div__content img-exists" style="box-sizing:
border-box; margin: 0px 95px 0px 0px; padding: 0px;
max-height: 1e+06px;"><br>
</div>
<div class="editor-div__content img-exists" style="box-sizing:
border-box; margin: 0px 95px 0px 0px; padding: 0px;
max-height: 1e+06px;"><br>
</div>
<div class="editor-div__content img-exists" style="box-sizing:
border-box; margin: 0px 95px 0px 0px; padding: 0px;
max-height: 1e+06px;"><br>
</div>
<div class="editor-div__content img-exists" style="box-sizing:
border-box; margin: 0px 95px 0px 0px; padding: 0px;
max-height: 1e+06px;">Guest Editors</div>
<div class="editor-div__content img-exists" style="box-sizing:
border-box; margin: 0px 95px 0px 0px; padding: 0px;
max-height: 1e+06px;"><b style="box-sizing: border-box;
font-weight: 700; line-height: inherit; max-height:
1e+06px;">Dr. Nicolas Bousquet</b><span> <br>
</span></div>
<div class="editor-div__content img-exists" style="box-sizing:
border-box; margin: 0px 95px 0px 0px; padding: 0px;
max-height: 1e+06px;">1. CNRS, LPSM, Sorbonne University,
75005 Paris, France<br style="box-sizing: border-box;
max-height: 1e+06px;">
2. EDF R&D, Industrial AI Lab SINCLAIR, Paris, France</div>
</div>
<div class="generic-item editor-div img-exists"
data-filter="patrick gallinari machine learning; deep learning;
dynamical systems; natural language processing"
style="box-sizing: border-box; margin: 15px 0px 0px; padding:
15px 0px 0px; max-height: 1e+06px; position: relative;
min-height: 100px; font-family: Arial; font-weight: 400;
line-height: 1.5; border-top: 1px solid rgb(237, 237, 237);
font-size: 12px;">
<div class="editor-div__img-container" style="box-sizing:
border-box; margin: 0px 0px 15px; padding: 0px; max-height:
1e+06px; position: absolute; display: block; right: 0px;"><br>
</div>
<div class="editor-div__content img-exists" style="box-sizing:
border-box; margin: 0px 95px 0px 0px; padding: 0px;
max-height: 1e+06px;"><b style="box-sizing: border-box;
font-weight: 700; line-height: inherit; max-height:
1e+06px;">Prof. Patrick Gallinari</b><span> </span><br
style="box-sizing: border-box; max-height: 1e+06px;">
</div>
<div class="editor-div__content img-exists" style="box-sizing:
border-box; margin: 0px 95px 0px 0px; padding: 0px;
max-height: 1e+06px;">1. CNRS, ISIR, Sorbonne University,
75005 Paris, France<br style="box-sizing: border-box;
max-height: 1e+06px;">
2. Criteo AI Lab, 75009 Paris, France</div>
</div>
</div>
<h2 style="box-sizing: border-box; margin: 30px 0px 10px; padding:
0px; color: rgba(0, 128, 128, 0.75); font-family: Arial;
font-style: normal; font-weight: 700; line-height: 1.5;
text-rendering: optimizelegibility; font-size: 20px; max-height:
1e+06px; font-variant-ligatures: normal; font-variant-caps:
normal; letter-spacing: normal; orphans: 2; text-align: start;
text-indent: 0px; text-transform: none; white-space: normal;
widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px;
text-decoration-thickness: initial; text-decoration-style:
initial; text-decoration-color: initial;"><font size="2">Special
Issue Information</font></h2>
<div style="box-sizing: border-box; margin: 0px; padding: 0px;
max-height: 1e+06px; color: rgb(34, 34, 34); font-family: Arial;
font-size: 12px; font-style: normal; font-variant-ligatures:
normal; font-variant-caps: normal; font-weight: 400;
letter-spacing: normal; orphans: 2; text-align: start;
text-indent: 0px; text-transform: none; white-space: normal;
widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px;
text-decoration-thickness: initial; text-decoration-style:
initial; text-decoration-color: initial;">
<p style="box-sizing: border-box; margin: 0px 0px 10px; padding:
0px; font-family: inherit; font-size: 1rem; font-weight: 400;
line-height: 1.6; text-rendering: optimizelegibility;
max-height: 1e+06px;"><font size="1">Machine learning has been
successfully used for over a decade for applications in
engineering. It has recently started to attract attention for
scientific computing in domains dominated up to now by the
classical mechanistic modeling paradigm. It is particularly
promising for domains involving complex processes, only
partially known and understood or when existing solutions are
computationally not feasible. This is the case for the
modeling and simulation of complex dynamical physical systems.
Classical modeling relies on PDEs, and simulation is central
to engineering and physical science with applications in
domains such as earth systems, biology, medicine, mechanics
and robotics. Traditional simulation problems involve
computational fluid dynamics and turbulence modeling,
mechanistic design and many other domains. Such numerical
models are also used intensively in industrial systems design,
in simulation for decision support, or in safety studies. They
are used for inversion, data assimilation and forecasting.
Despite extensive developments and promising progress, this
classical paradigm suffers from limitations. It is often
impossible or too costly to carry out direct simulations at
the scale required for natural or industrial problems. The
physics may be too complex or unknown, leading to incomplete
or inaccurate models.</font></p>
<p style="box-sizing: border-box; margin: 0px 0px 10px; padding:
0px; font-family: inherit; font-size: 1rem; font-weight: 400;
line-height: 1.6; text-rendering: optimizelegibility;
max-height: 1e+06px;"><font size="1">The availability of
increasingly large amounts of data, either from observations
or from simulations, and the successes witnessed by ML methods
on large size or large dimensional problems has opened the way
for exploring the data driven modeling of complex dynamical
physical phenomena. ML based techniques may accelerate
simulations, acting, for example, as reduced models. More
generally, a promising direction consists in integrating
physics-based models with machine learning. This raises
several challenges such as how to perform such decompositions,
how to train such combined systems, how to handle
discretization errors or guarantee numerical stability of the
solutions, how to handle out-of-sample scenarios, and how to
ensure physical consistency of the solutions.</font></p>
<p style="box-sizing: border-box; margin: 0px 0px 10px; padding:
0px; font-family: inherit; font-size: 1rem; font-weight: 400;
line-height: 1.6; text-rendering: optimizelegibility;
max-height: 1e+06px;"><font size="1">An additional challenge is
the shift from academic case studies to realistic problems
representing complex phenomena. Current solutions are most
often demonstrated on simulated problems and there is still a
large gap between academic and real-world developments.</font></p>
<p style="box-sizing: border-box; margin: 0px 0px 10px; padding:
0px; font-family: inherit; font-size: 1rem; font-weight: 400;
line-height: 1.6; text-rendering: optimizelegibility;
max-height: 1e+06px;"><font size="1">This Special Issue,
therefore, aims to gather specialists from different
disciplines and to enable the dissemination of their recent
research at the crossroad of model based and data based
dynamical physical system modeling and on “physically
inspired” ML models for dynamic systems.</font></p>
<p style="box-sizing: border-box; margin: 0px 0px 10px; padding:
0px; font-family: inherit; font-size: 1rem; font-weight: 400;
line-height: 1.6; text-rendering: optimizelegibility;
max-height: 1e+06px;"><font size="1">The topics of interest for
publication include but are not limited to:</font></p>
<ul style="box-sizing: border-box; margin: 10px 0px 1.25rem
1.1rem; padding: 0px; font-family: inherit; font-size: inherit;
line-height: inherit; list-style-position: outside; max-height:
1e+06px;">
<li style="box-sizing: border-box; margin: 0px 0px 10px;
padding: 0px; max-height: 1e+06px; break-inside: avoid;"><font
size="1">Deep learning;</font></li>
<li style="box-sizing: border-box; margin: 0px 0px 10px;
padding: 0px; max-height: 1e+06px; break-inside: avoid;"><font
size="1">Gaussian processes;</font></li>
<li style="box-sizing: border-box; margin: 0px 0px 10px;
padding: 0px; max-height: 1e+06px; break-inside: avoid;"><font
size="1">Uncertainty quantification;</font></li>
<li style="box-sizing: border-box; margin: 0px 0px 10px;
padding: 0px; max-height: 1e+06px; break-inside: avoid;"><font
size="1">Data-driven techniques;</font></li>
<li style="box-sizing: border-box; margin: 0px 0px 10px;
padding: 0px; max-height: 1e+06px; break-inside: avoid;"><font
size="1">PDE solving;</font></li>
<li style="box-sizing: border-box; margin: 0px 0px 10px;
padding: 0px; max-height: 1e+06px; break-inside: avoid;"><font
size="1">Spatio-temporal forecasting;</font></li>
<li style="box-sizing: border-box; margin: 0px 0px 10px;
padding: 0px; max-height: 1e+06px; break-inside: avoid;"><font
size="1">Simulation;</font></li>
<li style="box-sizing: border-box; margin: 0px 0px 10px;
padding: 0px; max-height: 1e+06px; break-inside: avoid;"><font
size="1">Computational fluid dynamics;</font></li>
<li style="box-sizing: border-box; margin: 0px 0px 10px;
padding: 0px; max-height: 1e+06px; break-inside: avoid;"><font
size="1">Graphics;</font></li>
<li style="box-sizing: border-box; margin: 0px 0px 10px;
padding: 0px; max-height: 1e+06px; break-inside: avoid;"><font
size="1">Robotics.</font></li>
</ul>
<p style="box-sizing: border-box; margin: 0px 0px 10px; padding:
0px; font-family: inherit; font-size: 1rem; font-weight: 400;
line-height: 1.6; text-rendering: optimizelegibility;
max-height: 1e+06px;"><strong style="box-sizing: border-box;
font-weight: 700; line-height: inherit; max-height: 1e+06px;">Manuscript
Submission Information</strong></p>
<p style="box-sizing: border-box; margin: 0px 0px 10px; padding:
0px; font-family: inherit; font-size: 1rem; font-weight: 400;
line-height: 1.6; text-rendering: optimizelegibility;
max-height: 1e+06px;"><font size="1">Manuscripts should be
submitted online at<span> </span><a
href="https://www.mdpi.com/" style="box-sizing: border-box;
color: rgba(0, 128, 128, 0.75); line-height: inherit;
text-decoration: none; max-height: 1e+06px; font-weight:
700;">www.mdpi.com</a><span> </span>by<span> </span><a
href="https://www.mdpi.com/user/register/"
style="box-sizing: border-box; color: rgba(0, 128, 128,
0.75); line-height: inherit; text-decoration: none;
max-height: 1e+06px; font-weight: 700;">registering</a><span> </span>and<span> </span><a
href="https://www.mdpi.com/user/login/" style="box-sizing:
border-box; color: rgba(0, 128, 128, 0.75); line-height:
inherit; text-decoration: none; max-height: 1e+06px;
font-weight: 700;">logging in to this website</a>. Once you
are registered,<span> </span><a
href="https://susy.mdpi.com/user/manuscripts/upload/?journal=entropy"
style="box-sizing: border-box; color: rgba(0, 128, 128,
0.75); line-height: inherit; text-decoration: none;
max-height: 1e+06px; font-weight: 700;">click here to go to
the submission form</a>. Manuscripts can be submitted until
the deadline. All submissions that pass pre-check are
peer-reviewed. Accepted papers will be published continuously
in the journal (as soon as accepted) and will be listed
together on the special issue website. Research articles,
review articles as well as short communications are invited.
For planned papers, a title and short abstract (about 100
words) can be sent to the Editorial Office for announcement on
this website.</font></p>
<p style="box-sizing: border-box; margin: 0px 0px 10px; padding:
0px; font-family: inherit; font-size: 1rem; font-weight: 400;
line-height: 1.6; text-rendering: optimizelegibility;
max-height: 1e+06px;"><font size="1">Submitted manuscripts
should not have been published previously, nor be under
consideration for publication elsewhere (except conference
proceedings papers). All manuscripts are thoroughly refereed
through a single-blind peer-review process. A guide for
authors and other relevant information for submission of
manuscripts is available on the<span> </span><a
href="https://www.mdpi.com/journal/entropy/instructions"
style="box-sizing: border-box; color: rgba(0, 128, 128,
0.75); line-height: inherit; text-decoration: none;
max-height: 1e+06px; font-weight: 700;">Instructions for
Authors</a><span> </span>page.<span> </span><a
href="https://www.mdpi.com/journal/entropy/"
style="box-sizing: border-box; color: rgba(0, 128, 128,
0.75); line-height: inherit; text-decoration: none;
max-height: 1e+06px; font-weight: 700;"><em
style="box-sizing: border-box; font-style: italic;
line-height: inherit; max-height: 1e+06px;">Entropy</em></a><span> </span>is
an international peer-reviewed open access monthly journal
published by MDPI.</font></p>
<p style="box-sizing: border-box; margin: 0px 0px 10px; padding:
0px; font-family: inherit; font-size: 1rem; font-weight: 400;
line-height: 1.6; text-rendering: optimizelegibility;
max-height: 1e+06px;"><font size="1">Please visit the<span> </span><a
href="https://www.mdpi.com/journal/entropy/instructions"
style="box-sizing: border-box; color: rgba(0, 128, 128,
0.75); line-height: inherit; text-decoration: none;
max-height: 1e+06px; font-weight: 700;">Instructions for
Authors</a><span> </span>page before submitting a
manuscript. The<span> </span><a
href="https://www.mdpi.com/about/apc/" style="box-sizing:
border-box; color: rgba(0, 128, 128, 0.75); line-height:
inherit; text-decoration: none; max-height: 1e+06px;
font-weight: 700;">Article Processing Charge (APC)</a><span> </span>for
publication in this<span> </span><a
href="https://www.mdpi.com/about/openaccess/"
style="box-sizing: border-box; color: rgba(0, 128, 128,
0.75); line-height: inherit; text-decoration: none;
max-height: 1e+06px; font-weight: 700;">open access</a><span> </span>journal
is 1800 CHF (Swiss Francs). Submitted papers should be well
formatted and use good English. Authors may use MDPI's<span> </span><a
href="https://www.mdpi.com/authors/english"
style="box-sizing: border-box; color: rgba(0, 128, 128,
0.75); line-height: inherit; text-decoration: none;
max-height: 1e+06px; font-weight: 700;">English editing
service</a><span> </span>prior to publication or during
author revisions.</font></p>
</div>
<h2 style="box-sizing: border-box; margin: 30px 0px 10px; padding:
0px; color: rgba(0, 128, 128, 0.75); font-family: Arial;
font-style: normal; font-weight: 700; line-height: 1.5;
text-rendering: optimizelegibility; font-size: 20px; max-height:
1e+06px; font-variant-ligatures: normal; font-variant-caps:
normal; letter-spacing: normal; orphans: 2; text-align: start;
text-indent: 0px; text-transform: none; white-space: normal;
widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px;
text-decoration-thickness: initial; text-decoration-style:
initial; text-decoration-color: initial;"><font size="2">Keywords</font></h2>
<div style="box-sizing: border-box; margin: 0px; padding: 0px;
max-height: 1e+06px; color: rgb(34, 34, 34); font-family: Arial;
font-size: 12px; font-style: normal; font-variant-ligatures:
normal; font-variant-caps: normal; font-weight: 400;
letter-spacing: normal; orphans: 2; text-align: start;
text-indent: 0px; text-transform: none; white-space: normal;
widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px;
text-decoration-thickness: initial; text-decoration-style:
initial; text-decoration-color: initial;">
<ul style="box-sizing: border-box; margin: 10px 0px 1.25rem
1.1rem; padding: 0px; font-family: inherit; font-size: inherit;
line-height: inherit; list-style-position: outside; max-height:
1e+06px;">
<li style="box-sizing: border-box; margin: 0px 0px 10px;
padding: 0px; max-height: 1e+06px; break-inside: avoid;">deep
learning</li>
<li style="box-sizing: border-box; margin: 0px 0px 10px;
padding: 0px; max-height: 1e+06px; break-inside: avoid;">machine
learning</li>
<li style="box-sizing: border-box; margin: 0px 0px 10px;
padding: 0px; max-height: 1e+06px; break-inside: avoid;">PDE</li>
<li style="box-sizing: border-box; margin: 0px 0px 10px;
padding: 0px; max-height: 1e+06px; break-inside: avoid;">neural
networks</li>
<li style="box-sizing: border-box; margin: 0px 0px 10px;
padding: 0px; max-height: 1e+06px; break-inside: avoid;">uncertainty
quantification</li>
<li style="box-sizing: border-box; margin: 0px 0px 10px;
padding: 0px; max-height: 1e+06px; break-inside: avoid;">physics-inspired
meta-models</li>
<li style="box-sizing: border-box; margin: 0px 0px 10px;
padding: 0px; max-height: 1e+06px; break-inside: avoid;">Gaussian
processes</li>
</ul>
</div>
<pre class="moz-signature" cols="72">--
Prof. Patrick Gallinari
Sorbonne Universite - ISIR
4 place Jussieu, 75252 Paris Cedex 05, France
Tel: 33144277370</pre>
</body>
</html>