diff --git a/src/DataInterpolations.jl b/src/DataInterpolations.jl
index 96f9ebab..1d59e0a1 100644
--- a/src/DataInterpolations.jl
+++ b/src/DataInterpolations.jl
@@ -61,7 +61,18 @@ struct RegularizationSmooth{uType, tType, FT, T, T2} <: AbstractInterpolation{FT
     λ::T2        # regularization parameter
     alg::Symbol  # how to determine λ: `:fixed`, `:gcv_svd`, `:gcv_tr`, `L_curve`
     Aitp::AbstractInterpolation{FT, T}
-    function RegularizationSmooth{FT}(u, û, t, t̂, wls, wr, d, λ, alg, Aitp) where {FT}
+    extrapolate::Bool
+    function RegularizationSmooth{FT}(u,
+            û,
+            t,
+            t̂,
+            wls,
+            wr,
+            d,
+            λ,
+            alg,
+            Aitp,
+            extrapolate) where {FT}
         new{typeof(u), typeof(t), FT, eltype(u), typeof(λ)}(u,
             û,
             t,
@@ -71,12 +82,57 @@ struct RegularizationSmooth{uType, tType, FT, T, T2} <: AbstractInterpolation{FT
             d,
             λ,
             alg,
-            Aitp)
+            Aitp,
+            extrapolate)
     end
 end
 
 export RegularizationSmooth
 
+# CurveFit
+struct CurvefitCache{
+    uType,
+    tType,
+    mType,
+    p0Type,
+    ubType,
+    lbType,
+    algType,
+    pminType,
+    FT,
+    T,
+} <: AbstractInterpolation{FT, T}
+    u::uType
+    t::tType
+    m::mType        # model type
+    p0::p0Type      # intial params
+    ub::ubType      # upper bound of params
+    lb::lbType      # lower bound of params
+    alg::algType    # alg to optimize cost function
+    pmin::pminType  # optimized params
+    extrapolate::Bool
+    function CurvefitCache{FT}(u, t, m, p0, ub, lb, alg, pmin, extrapolate) where {FT}
+        new{typeof(u), typeof(t), typeof(m),
+            typeof(p0), typeof(ub), typeof(lb),
+            typeof(alg), typeof(pmin), FT, eltype(u)}(u,
+            t,
+            m,
+            p0,
+            ub,
+            lb,
+            alg,
+            pmin,
+            extrapolate)
+    end
+end
+
+# Define an empty function, so that it can be extended via `DataInterpolationsOptimExt`
+function Curvefit()
+    error("CurveFit requires loading Optim and ForwardDiff, e.g. `using Optim, ForwardDiff`")
+end
+
+export Curvefit
+
 @static if !isdefined(Base, :get_extension)
     using Requires
 end
@@ -87,7 +143,9 @@ end
             include("../ext/DataInterpolationsChainRulesCoreExt.jl")
         end
         Requires.@require Optim="429524aa-4258-5aef-a3af-852621145aeb" begin
-            include("../ext/DataInterpolationsOptimExt.jl")
+            Requires.@require ForwardDiff="f6369f11-7733-5829-9624-2563aa707210" begin
+                include("../ext/DataInterpolationsOptimExt.jl")
+            end
         end
         Requires.@require RegularizationTools="29dad682-9a27-4bc3-9c72-016788665182" begin
             include("../ext/DataInterpolationsRegularizationToolsExt.jl")
@@ -98,11 +156,6 @@ end
     end
 end
 
-# Define an empty function, so that it can be extended via `DataInterpolationsOptimExt`
-Curvefit() = error("CurveFit requires loading Optim, e.g. `using Optim`")
-
-export Curvefit
-
 # Deprecated April 2020
 export ZeroSpline