Add DataIntegralProblem

src/SciMLBase.jl

@@ -760,9 +760,7 @@ export solve, solve!, init, discretize, symbolic_discretize
 
 export LinearProblem,
     NonlinearProblem, IntervalNonlinearProblem,
-    IntegralProblem, OptimizationProblem
-
-export IntegralProblem
+    IntegralProblem, SampledIntegralProblem, OptimizationProblem
 
 export DiscreteProblem, ImplicitDiscreteProblem
 export SteadyStateProblem, SteadyStateSolution

src/problems/basic_problems.jl

@@ -334,10 +334,12 @@ which are `Number`s or `AbstractVector`s with the same geometry as `u`.
 
 ### Constructors
 
+```
 IntegralProblem{iip}(f,lb,ub,p=NullParameters();
                   nout=1, batch = 0, kwargs...)
+```
 
-- f: the integrand, `y = f(u,p)` for out-of-place or `f(y,u,p)` for in-place.
+- f: the integrand, callable function `y = f(u,p)` for out-of-place or `f(y,u,p)` for in-place.
 - lb: Either a number or vector of lower bounds.
 - ub: Either a number or vector of upper bounds.
 - p: The parameters associated with the problem.
@@ -375,14 +377,16 @@ struct IntegralProblem{isinplace, P, F, B, K} <: AbstractIntegralProblem{isinpla
         batch = 0, kwargs...) where {iip}
         @assert typeof(lb)==typeof(ub) "Type of lower and upper bound must match"
         warn_paramtype(p)
-        new{iip, typeof(p), typeof(f), typeof(lb), typeof(kwargs)}(f, lb, ub, nout, p,
+        new{iip, typeof(p), typeof(f), typeof(lb), typeof(kwargs)}(f,
+            lb, ub, nout, p,
             batch, kwargs)
     end
 end
 
 TruncatedStacktraces.@truncate_stacktrace IntegralProblem 1 4
 
-function IntegralProblem(f, lb, ub, args...; kwargs...)
+function IntegralProblem(f, lb, ub, args...;
+    kwargs...)
     IntegralProblem{isinplace(f, 3)}(f, lb, ub, args...; kwargs...)
 end
 
@@ -391,6 +395,56 @@ struct QuadratureProblem end
 
 @doc doc"""
 
+Defines a integral problem over pre-sampled data.
+Documentation Page: https://docs.sciml.ai/Integrals/stable/
+
+## Mathematical Specification of a data Integral Problem
+
+Sampled integral problems are defined as:
+
+```math
+\sum_i w_i y_i
+```
+where `y_i` are sampled values of the integrand, and `w_i` are weights 
+assigned by a quadrature rule, which depend on sampling points `x`. 
+
+## Problem Type
+
+### Constructors
+
+```
+SampledIntegralProblem(x::AbstractVector, y::AbstractArray; dim=1, kwargs...)
+```
+- y: The sampled integrand, must be a subtype of `AbstractArray`. 
+  It is assumed that the values of `y` along dimension `dim` 
+  correspond to the integrand evaluated at sampling points `x`
+- x: Sampling points, must be a subtype of `AbstractVector`.   
+- dim: Dimension along which to integrate.
+- kwargs: Keyword arguments copied to the solvers.
+
+### Fields
+
+The fields match the names of the constructor arguments.
+"""
+struct SampledIntegralProblem{Y, X, D, K} <: AbstractIntegralProblem{false}
+    y::Y
+    x::X
+    dim::D
+    kwargs::K
+    @add_kwonly function SampledIntegralProblem(y::AbstractArray, x::AbstractVector;
+        dim = 1,
+        kwargs...)
+        @assert dim <= ndims(y) "The integration dimension `dim` is larger than the number of dimensions of the integrand `y`"
+        @assert length(x)==size(y, dim) "The integrand `y` must have the same length as the sampling points `x` along the integrated dimension."
+        @assert axes(x, 1)==axes(y, dim) "The integrand `y` must obey the same indexing as the sampling points `x` along the integrated dimension."
+        new{typeof(y), typeof(x), Val{dim}, typeof(kwargs)}(y, x, Val(dim), kwargs)
+    end
+end
+
+TruncatedStacktraces.@truncate_stacktrace SampledIntegralProblem 1 4
+
+@doc doc"""
+
 Defines an optimization problem.
 Documentation Page: https://docs.sciml.ai/Optimization/stable/API/optimization_problem/
 

test/function_building_error_messages.jl

@@ -453,7 +453,17 @@ NonlinearFunction(nfoop, vjp = nvjp)
 intf(u) = 1.0
 @test_throws SciMLBase.TooFewArgumentsError IntegralProblem(intf, 0.0, 1.0)
 intf(u, p) = 1.0
+p = 2.0
+
 IntegralProblem(intf, 0.0, 1.0)
+IntegralProblem(intf, 0.0, 1.0, p)
+IntegralProblem(intf, [0.0], [1.0])
+IntegralProblem(intf, [0.0], [1.0], p)
+
+x = [1.0, 2.0]
+y = rand(2, 2)
+SampledIntegralProblem(y, x)
+SampledIntegralProblem(y, x; dim=2)
 
 # Optimization