diff --git a/Cargo.toml b/Cargo.toml
index 455a68d..2eb2352 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -21,6 +21,11 @@ ndarray = ">=0.15.3, <0.17"
 num-traits = "0.2.15"
 serde = { version = "1.0.103", optional = true, features = ["derive"] }
 serde_unit_struct = { version = "0.1.3", optional = true }
+# TODO: modify when https://github.com/RReverser/serde-ndim/pull/2 merged
+# serde-ndim = { version = "2.0.2", optional = true, features = ["ndarray"] }
+serde-ndim = { git = "https://github.com/kylecarow/serde-ndim.git", optional = true, features = [
+    "ndarray",
+] }
 thiserror = "1.0.1"
 
 [dev-dependencies]
@@ -35,4 +40,9 @@ name = "benchmark"
 harness = false
 
 [features]
-serde = ["dep:serde", "ndarray/serde", "dep:serde_unit_struct"]
+serde = [
+    "dep:serde",
+    "ndarray/serde",
+    "dep:serde_unit_struct",
+    "dep:serde-ndim",
+]
diff --git a/src/interpolator/data.rs b/src/interpolator/data.rs
index f22a9d2..f66f8eb 100644
--- a/src/interpolator/data.rs
+++ b/src/interpolator/data.rs
@@ -23,7 +23,8 @@ pub use two::{InterpData2D, InterpData2DOwned, InterpData2DViewed};
         deserialize = "
             D: DataOwned,
             D::Elem: Deserialize<'de>,
-            Dim<[usize; N]>: Deserialize<'de>,
+            Dim<[usize; N]>: Deserialize<'de> + Dimension,
+            [usize; N]: IntoDimension<Dim = Dim<[usize; N]>>,
             [ArrayBase<D, Ix1>; N]: Deserialize<'de>,
         "
     ))
@@ -38,8 +39,11 @@ where
     /// - 1-D: `[x]`
     /// - 2-D: `[x, y]`
     /// - 3-D: `[x, y, z]`
+    #[cfg_attr(feature = "serde", serde(with = "serde_arr_array"))]
     pub grid: [ArrayBase<D, Ix1>; N],
     /// Function values at coordinates: a single `N`-dimensional [`ArrayBase`].
+    #[cfg_attr(feature = "serde", serde(serialize_with = "serde_ndim::serialize"))]
+    #[cfg_attr(feature = "serde", serde(deserialize_with = "deserialize_fixed"))]
     pub values: ArrayBase<D, Dim<[Ix; N]>>,
 }
 /// [`InterpData`] that views data.
diff --git a/src/interpolator/n/mod.rs b/src/interpolator/n/mod.rs
index 3994cc2..438991f 100644
--- a/src/interpolator/n/mod.rs
+++ b/src/interpolator/n/mod.rs
@@ -29,8 +29,11 @@ where
     D::Elem: PartialEq + Debug,
 {
     /// Coordinate grid: a vector of 1-dimensional [`ArrayBase<D, Ix1>`].
+    #[cfg_attr(feature = "serde", serde(with = "serde_vec_array"))]
     pub grid: Vec<ArrayBase<D, Ix1>>,
     /// Function values at coordinates: a single dynamic-dimensional [`ArrayBase`].
+    #[cfg_attr(feature = "serde", serde(serialize_with = "serde_ndim::serialize"))]
+    #[cfg_attr(feature = "serde", serde(deserialize_with = "deserialize_dyn"))]
     pub values: ArrayBase<D, IxDyn>,
 }
 /// [`InterpDataND`] that views data.
@@ -117,7 +120,7 @@ where
         deserialize = "
             D: DataOwned,
             D::Elem: Deserialize<'de>,
-            S: Deserialize<'de>
+            S: Deserialize<'de>,
         "
     ))
 )]
diff --git a/src/interpolator/n/tests.rs b/src/interpolator/n/tests.rs
index 0eee454..5d2fbd0 100644
--- a/src/interpolator/n/tests.rs
+++ b/src/interpolator/n/tests.rs
@@ -397,4 +397,21 @@ fn test_serde() {
     let ser = serde_json::to_string(&interp).unwrap();
     let de: InterpNDOwned<f64, strategy::Nearest> = serde_json::from_str(&ser).unwrap();
     assert_eq!(interp, de);
+
+    // simple format (new serialization output)
+    let ser0 = "{\"grid\":[[0.1,1.1],[0.2,1.2],[0.3,1.3]],\"values\":[[[0.0,1.0],[2.0,3.0]],[[4.0,5.0],[6.0,7.0]]]}";
+    let de0: InterpDataND<_> = serde_json::from_str(&ser0).unwrap();
+    assert_eq!(interp.data, de0);
+    // mixed format (simple grid)
+    let ser1 = "{\"grid\":[[0.1,1.1],[0.2,1.2],[0.3,1.3]],\"values\":{\"v\":1,\"dim\":[2,2,2],\"data\":[0.0,1.0,2.0,3.0,4.0,5.0,6.0,7.0]}}";
+    let de1: InterpDataND<_> = serde_json::from_str(&ser1).unwrap();
+    assert_eq!(interp.data, de1);
+    // mixed format (simple values)
+    let ser2 = "{\"grid\":[{\"v\":1,\"dim\":[2],\"data\":[0.1,1.1]},{\"v\":1,\"dim\":[2],\"data\":[0.2,1.2]},{\"v\":1,\"dim\":[2],\"data\":[0.3,1.3]}],\"values\":[[[0.0,1.0],[2.0,3.0]],[[4.0,5.0],[6.0,7.0]]]}";
+    let de2: InterpDataND<_> = serde_json::from_str(&ser2).unwrap();
+    assert_eq!(interp.data, de2);
+    // complex format (legacy serialization output)
+    let ser3 = "{\"grid\":[{\"v\":1,\"dim\":[2],\"data\":[0.1,1.1]},{\"v\":1,\"dim\":[2],\"data\":[0.2,1.2]},{\"v\":1,\"dim\":[2],\"data\":[0.3,1.3]}],\"values\":{\"v\":1,\"dim\":[2,2,2],\"data\":[0.0,1.0,2.0,3.0,4.0,5.0,6.0,7.0]}}";
+    let de3: InterpDataND<_> = serde_json::from_str(&ser3).unwrap();
+    assert_eq!(interp.data, de3);
 }
diff --git a/src/interpolator/one/tests.rs b/src/interpolator/one/tests.rs
index ca06dbd..6d956e6 100644
--- a/src/interpolator/one/tests.rs
+++ b/src/interpolator/one/tests.rs
@@ -188,4 +188,21 @@ fn test_serde() {
     let ser = serde_json::to_string(&interp).unwrap();
     let de: Interp1DOwned<f64, strategy::LeftNearest> = serde_json::from_str(&ser).unwrap();
     assert_eq!(interp, de);
+
+    // simple format (new serialization output)
+    let ser0 = "{\"grid\":[[0.0,1.0,2.0,3.0,4.0]],\"values\":[0.2,0.4,0.6,0.8,1.0]}";
+    let de0: InterpData1D<_> = serde_json::from_str(&ser0).unwrap();
+    assert_eq!(interp.data, de0);
+    // mixed format (simple grid)
+    let ser1 = "{\"grid\":[[0.0,1.0,2.0,3.0,4.0]],\"values\":{\"v\":1,\"dim\":[5],\"data\":[0.2,0.4,0.6,0.8,1.0]}}";
+    let de1: InterpData1D<_> = serde_json::from_str(&ser1).unwrap();
+    assert_eq!(interp.data, de1);
+    // mixed format (simple values)
+    let ser2 = "{\"grid\":[{\"v\":1,\"dim\":[5],\"data\":[0.0,1.0,2.0,3.0,4.0]}],\"values\":[0.2,0.4,0.6,0.8,1.0]}";
+    let de2: InterpData1D<_> = serde_json::from_str(&ser2).unwrap();
+    assert_eq!(interp.data, de2);
+    // complex format (legacy serialization output)
+    let ser3 = "{\"grid\":[{\"v\":1,\"dim\":[5],\"data\":[0.0,1.0,2.0,3.0,4.0]}],\"values\":{\"v\":1,\"dim\":[5],\"data\":[0.2,0.4,0.6,0.8,1.0]}}";
+    let de3: InterpData1D<_> = serde_json::from_str(&ser3).unwrap();
+    assert_eq!(interp.data, de3);
 }
diff --git a/src/interpolator/three/tests.rs b/src/interpolator/three/tests.rs
index 2e2fe13..88d917c 100644
--- a/src/interpolator/three/tests.rs
+++ b/src/interpolator/three/tests.rs
@@ -217,15 +217,43 @@ fn test_partialeq() {
 fn test_serde() {
     let interp = Interp3D::new(
         array![0., 1.],
-        array![0., 1.],
-        array![0., 1.],
-        array![[[0., 1.], [2., 3.]], [[4., 5.], [6., 7.]],],
-        strategy::Nearest,
+        array![0., 1., 2.],
+        array![0., 1., 2., 3.],
+        array![
+            [
+                [0.6, 0.8, 1.0, 1.2],
+                [0.8, 1.0, 1.2, 1.4],
+                [1.0, 1.2, 1.4, 1.6],
+            ],
+            [
+                [0.8, 1.0, 1.2, 1.4],
+                [1.0, 1.2, 1.4, 1.6],
+                [1.2, 1.4, 1.6, 1.8],
+            ],
+        ],
+        strategy::Linear,
         Extrapolate::Error,
     )
     .unwrap();
 
     let ser = serde_json::to_string(&interp).unwrap();
-    let de: Interp3DOwned<f64, strategy::Nearest> = serde_json::from_str(&ser).unwrap();
+    let de: Interp3D<_, _> = serde_json::from_str(&ser).unwrap();
     assert_eq!(interp, de);
+
+    // simple format (new serialization output)
+    let ser0 = "{\"grid\":[[0.0,1.0],[0.0,1.0,2.0],[0.0,1.0,2.0,3.0]],\"values\":[[[0.6,0.8,1.0,1.2],[0.8,1.0,1.2,1.4],[1.0,1.2,1.4,1.6]],[[0.8,1.0,1.2,1.4],[1.0,1.2,1.4,1.6],[1.2,1.4,1.6,1.8]]]}";
+    let de0: InterpData3D<_> = serde_json::from_str(&ser0).unwrap();
+    assert_eq!(interp.data, de0);
+    // mixed format (simple grid)
+    let ser1 = "{\"grid\":[[0.0,1.0],[0.0,1.0,2.0],[0.0,1.0,2.0,3.0]],\"values\":{\"v\":1,\"dim\":[2,3,4],\"data\":[0.6,0.8,1.0,1.2,0.8,1.0,1.2,1.4,1.0,1.2,1.4,1.6,0.8,1.0,1.2,1.4,1.0,1.2,1.4,1.6,1.2,1.4,1.6,1.8]}}";
+    let de1: InterpData3D<_> = serde_json::from_str(&ser1).unwrap();
+    assert_eq!(interp.data, de1);
+    // mixed format (simple values)
+    let ser2 = "{\"grid\":[{\"v\":1,\"dim\":[2],\"data\":[0.0,1.0]},{\"v\":1,\"dim\":[3],\"data\":[0.0,1.0,2.0]},{\"v\":1,\"dim\":[4],\"data\":[0.0,1.0,2.0,3.0]}],\"values\":[[[0.6,0.8,1.0,1.2],[0.8,1.0,1.2,1.4],[1.0,1.2,1.4,1.6]],[[0.8,1.0,1.2,1.4],[1.0,1.2,1.4,1.6],[1.2,1.4,1.6,1.8]]]}";
+    let de2: InterpData3D<_> = serde_json::from_str(&ser2).unwrap();
+    assert_eq!(interp.data, de2);
+    // complex format (legacy serialization output)
+    let ser3 = "{\"grid\":[{\"v\":1,\"dim\":[2],\"data\":[0.0,1.0]},{\"v\":1,\"dim\":[3],\"data\":[0.0,1.0,2.0]},{\"v\":1,\"dim\":[4],\"data\":[0.0,1.0,2.0,3.0]}],\"values\":{\"v\":1,\"dim\":[2,3,4],\"data\":[0.6,0.8,1.0,1.2,0.8,1.0,1.2,1.4,1.0,1.2,1.4,1.6,0.8,1.0,1.2,1.4,1.0,1.2,1.4,1.6,1.2,1.4,1.6,1.8]}}";
+    let de3: InterpData3D<_> = serde_json::from_str(&ser3).unwrap();
+    assert_eq!(interp.data, de3);
 }
diff --git a/src/interpolator/two/tests.rs b/src/interpolator/two/tests.rs
index 8f65026..4f9767c 100644
--- a/src/interpolator/two/tests.rs
+++ b/src/interpolator/two/tests.rs
@@ -199,4 +199,21 @@ fn test_serde() {
     let ser = serde_json::to_string(&interp).unwrap();
     let de: Interp2DOwned<f64, strategy::Linear> = serde_json::from_str(&ser).unwrap();
     assert_eq!(interp, de);
+
+    // simple format (new serialization output)
+    let ser0 = "{\"grid\":[[0.05,0.1,0.15],[0.1,0.2,0.3]],\"values\":[[0.0,1.0,2.0],[3.0,4.0,5.0],[6.0,7.0,8.0]]}";
+    let de0: InterpData2D<_> = serde_json::from_str(&ser0).unwrap();
+    assert_eq!(interp.data, de0);
+    // mixed format (simple grid)
+    let ser1 = "{\"grid\":[[0.05,0.1,0.15],[0.1,0.2,0.3]],\"values\":{\"v\":1,\"dim\":[3,3],\"data\":[0.0,1.0,2.0,3.0,4.0,5.0,6.0,7.0,8.0]}}";
+    let de1: InterpData2D<_> = serde_json::from_str(&ser1).unwrap();
+    assert_eq!(interp.data, de1);
+    // mixed format (simple values)
+    let ser2 = "{\"grid\":[{\"v\":1,\"dim\":[3],\"data\":[0.05,0.1,0.15]},{\"v\":1,\"dim\":[3],\"data\":[0.1,0.2,0.3]}],\"values\":[[0.0,1.0,2.0],[3.0,4.0,5.0],[6.0,7.0,8.0]]}";
+    let de2: InterpData2D<_> = serde_json::from_str(&ser2).unwrap();
+    assert_eq!(interp.data, de2);
+    // complex format (legacy serialization output)
+    let ser3 = "{\"grid\":[{\"v\":1,\"dim\":[3],\"data\":[0.05,0.1,0.15]},{\"v\":1,\"dim\":[3],\"data\":[0.1,0.2,0.3]}],\"values\":{\"v\":1,\"dim\":[3,3],\"data\":[0.0,1.0,2.0,3.0,4.0,5.0,6.0,7.0,8.0]}}";
+    let de3: InterpData2D<_> = serde_json::from_str(&ser3).unwrap();
+    assert_eq!(interp.data, de3);
 }
diff --git a/src/lib.rs b/src/lib.rs
index b2ed07a..95c3011 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -57,11 +57,10 @@ pub(crate) use num_traits::{clamp, Euclid, Num, One};
 pub(crate) use dyn_clone::*;
 
 #[cfg(feature = "serde")]
-pub(crate) use ndarray::DataOwned;
+#[path = "serde.rs"]
+mod serde_mod;
 #[cfg(feature = "serde")]
-pub(crate) use serde::{Deserialize, Serialize};
-#[cfg(feature = "serde")]
-pub(crate) use serde_unit_struct::{Deserialize_unit_struct, Serialize_unit_struct};
+pub(crate) use serde_mod::*;
 
 #[cfg(test)]
 /// Alias for [`approx::assert_abs_diff_eq`] with `epsilon = 1e-6`
diff --git a/src/serde.rs b/src/serde.rs
new file mode 100644
index 0000000..83b2deb
--- /dev/null
+++ b/src/serde.rs
@@ -0,0 +1,139 @@
+use super::*;
+
+pub(crate) use ndarray::{DataOwned, IntoDimension};
+pub(crate) use serde::{Deserialize, Serialize};
+pub(crate) use serde_unit_struct::{Deserialize_unit_struct, Serialize_unit_struct};
+
+use serde::de::{Deserializer, Error};
+use serde::ser::{SerializeSeq, Serializer};
+use serde_ndim::de::MakeNDim;
+
+#[derive(Serialize)]
+struct ArrayWrapper<'a, D>(
+    #[serde(serialize_with = "serde_ndim::serialize")] &'a ArrayBase<D, Ix1>,
+)
+where
+    D: Data,
+    D::Elem: Serialize;
+
+#[derive(Deserialize)]
+#[serde(untagged)]
+#[serde(bound = "D::Elem: Deserialize<'de>")]
+enum GridType<D: DataOwned> {
+    VecVec(Vec<Vec<D::Elem>>),
+    VecArray(Vec<ArrayBase<D, Ix1>>),
+}
+
+pub(crate) mod serde_arr_array {
+    use super::*;
+
+    pub fn serialize<D, const N: usize, Ser>(
+        grid: &[ArrayBase<D, Ix1>; N],
+        serializer: Ser,
+    ) -> Result<Ser::Ok, Ser::Error>
+    where
+        D: Data,
+        D::Elem: Serialize,
+        Ser: Serializer,
+    {
+        let mut seq = serializer.serialize_seq(Some(N))?;
+        for arr in grid {
+            seq.serialize_element(&ArrayWrapper(arr))?;
+        }
+        seq.end()
+    }
+
+    pub fn deserialize<'de, D, const N: usize, De>(
+        deserializer: De,
+    ) -> Result<[ArrayBase<D, Ix1>; N], De::Error>
+    where
+        D: DataOwned,
+        D::Elem: Deserialize<'de> + Debug,
+        De: Deserializer<'de>,
+    {
+        match GridType::deserialize(deserializer)? {
+            GridType::VecVec(vecs) => vecs.into_iter().map(|v| v.into()).collect(),
+            GridType::VecArray(arrays) => arrays,
+        }
+        .try_into()
+        .map_err(|e| De::Error::custom(format_args!("expected {N} array(s): {e:?}")))
+    }
+}
+
+pub(crate) mod serde_vec_array {
+    use super::*;
+
+    pub fn serialize<D, Ser>(
+        grid: &[ArrayBase<D, Ix1>],
+        serializer: Ser,
+    ) -> Result<Ser::Ok, Ser::Error>
+    where
+        D: Data,
+        D::Elem: Serialize,
+        Ser: Serializer,
+    {
+        let mut seq = serializer.serialize_seq(Some(grid.len()))?;
+        for arr in grid {
+            seq.serialize_element(&ArrayWrapper(arr))?;
+        }
+        seq.end()
+    }
+
+    pub fn deserialize<'de, D, De>(deserializer: De) -> Result<Vec<ArrayBase<D, Ix1>>, De::Error>
+    where
+        D: DataOwned,
+        D::Elem: Deserialize<'de>,
+        De: Deserializer<'de>,
+    {
+        Ok(match GridType::deserialize(deserializer)? {
+            GridType::VecVec(vecs) => vecs.into_iter().map(|v| v.into()).collect(),
+            GridType::VecArray(arrays) => arrays,
+        })
+    }
+}
+
+#[derive(Deserialize)]
+#[serde(untagged)]
+#[serde(bound = "
+    D::Elem: Deserialize<'de>,
+    ArrayBase<D, Dim>: Deserialize<'de>,
+")]
+enum ValuesType<D, Dim>
+where
+    D: DataOwned,
+    Dim: Dimension,
+    ArrayBase<D, Dim>: MakeNDim<Item = D::Elem>,
+{
+    #[serde(deserialize_with = "serde_ndim::deserialize")]
+    NDimArray(ArrayBase<D, Dim>),
+    Array(ArrayBase<D, Dim>),
+}
+
+pub fn deserialize_fixed<'de, D, const N: usize, De>(
+    deserializer: De,
+) -> Result<ArrayBase<D, Dim<[Ix; N]>>, De::Error>
+where
+    D: DataOwned,
+    D::Elem: Deserialize<'de>,
+    Dim<[Ix; N]>: Dimension + Deserialize<'de>,
+    ArrayBase<D, Dim<[Ix; N]>>: MakeNDim<Item = D::Elem>,
+    De: Deserializer<'de>,
+{
+    Ok(match ValuesType::deserialize(deserializer)? {
+        ValuesType::NDimArray(values) => values,
+        ValuesType::Array(values) => values,
+    })
+}
+
+pub fn deserialize_dyn<'de, D, De>(deserializer: De) -> Result<ArrayBase<D, IxDyn>, De::Error>
+where
+    D: DataOwned,
+    D::Elem: Deserialize<'de>,
+    ArrayBase<D, IxDyn>: MakeNDim<Item = D::Elem>,
+    De: Deserializer<'de>,
+{
+    Ok(match ValuesType::deserialize(deserializer)? {
+        ValuesType::NDimArray(values) => values,
+        ValuesType::Array(values) => values,
+    })
+}