Please find attached a patch with an upstream patch to fix this.

Related: https://gcc.gnu.org/gcc-13/porting_to.html#header-dep-changes

>From b07acda4afb3056040bd2b07d209b76bec90a988 Mon Sep 17 00:00:00 2001
From: Amin Bandali <band...@canonical.com>
Date: Fri, 1 Sep 2023 21:11:04 -0400
Subject: [PATCH] Add upstream patch to fix FTBFS with gcc-13 (Closes:
 #1042038)

---
 debian/changelog                      |  7 ++++
 debian/patches/fix-ftbfs-gcc-13.patch | 53 +++++++++++++++++++++++++++
 debian/patches/series                 |  1 +
 3 files changed, 61 insertions(+)
 create mode 100644 debian/patches/fix-ftbfs-gcc-13.patch

diff --git a/debian/changelog b/debian/changelog
index 7d95e4c1e..e30df4c4d 100644
--- a/debian/changelog
+++ b/debian/changelog
@@ -1,3 +1,10 @@
+mfem (4.5.2+ds-2) UNRELEASED; urgency=medium
+
+  * Add upstream patch to fix FTBFS with gcc-13 (Closes: #1042038)
+    - debian/patches/fix-ftbfs-gcc-13.patch
+
+ -- Amin Bandali <band...@ubuntu.com>  Fri, 01 Sep 2023 21:10:21 -0400
+
 mfem (4.5.2+ds-1) unstable; urgency=medium
 
   * Initial release. (Closes: #1023223)
diff --git a/debian/patches/fix-ftbfs-gcc-13.patch b/debian/patches/fix-ftbfs-gcc-13.patch
new file mode 100644
index 000000000..5d202ab25
--- /dev/null
+++ b/debian/patches/fix-ftbfs-gcc-13.patch
@@ -0,0 +1,53 @@
+From 314a32af2ee80af8c9af7d8ad71babd51851154c Mon Sep 17 00:00:00 2001
+From: David Dement <ddeme...@gmail.com>
+Origin: https://github.com/mfem/mfem/commit/314a32af2ee80af8c9af7d8ad71babd51851154c
+Date: Thu, 27 Apr 2023 10:33:51 -0400
+Subject: [PATCH] Fixes comilation errors when compiling with gcc-13 on Fedora
+ 38
+
+When compiling with gcc-13, types such as uint64_t are not defined.
+It is likely that <cstdint> is included implicitly with older compiler
+versions.
+---
+ general/hash.hpp        | 1 +
+ general/mem_manager.cpp | 1 +
+ mesh/vtk.hpp            | 2 ++
+ 3 files changed, 4 insertions(+)
+
+diff --git a/general/hash.hpp b/general/hash.hpp
+index 86d987d8029..288d51288df 100644
+--- a/general/hash.hpp
++++ b/general/hash.hpp
+@@ -16,6 +16,7 @@
+ #include "array.hpp"
+ #include "globals.hpp"
+ #include <type_traits>
++#include <cstdint>
+ 
+ namespace mfem
+ {
+diff --git a/general/mem_manager.cpp b/general/mem_manager.cpp
+index 416a6ac6203..37b80c878ad 100644
+--- a/general/mem_manager.cpp
++++ b/general/mem_manager.cpp
+@@ -16,6 +16,7 @@
+ #include <cstring> // std::memcpy, std::memcmp
+ #include <unordered_map>
+ #include <algorithm> // std::max
++#include <cstdint>
+ 
+ // Uncomment to try _WIN32 platform
+ //#define _WIN32
+diff --git a/mesh/vtk.hpp b/mesh/vtk.hpp
+index a59bed27592..50eeea5bc78 100644
+--- a/mesh/vtk.hpp
++++ b/mesh/vtk.hpp
+@@ -12,6 +12,8 @@
+ #ifndef MFEM_VTK
+ #define MFEM_VTK
+ 
++#include <cstdint>
++
+ #include "../fem/geom.hpp"
+ #include "../general/binaryio.hpp"
+ 
diff --git a/debian/patches/series b/debian/patches/series
index 6f0d8f01a..d42e867b3 100644
--- a/debian/patches/series
+++ b/debian/patches/series
@@ -1,2 +1,3 @@
 static-no-shared-yes
 not-makefile
+fix-ftbfs-gcc-13.patch
-- 
2.39.2

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