Repository: fitbenchmarking/fitbenchmarking

Issue:
Add a data assimilation problem
Add some data assimilation problems (Culham? Reading?)



Discussion:
AndrewLister-STFC: @tyronerees Do you know why numdifftools seems to convert the params to a complex space?
AndrewLister-STFC: > 
> 
> This looks great -- there's tons of potential here for people to working in data assimilation to use this!
> 
> One thing I do think is missing is some more docs -- there's not much to explain what's going on. Could you add something to the page [here](https://fitbenchmarking--779.org.readthedocs.build/en/779/users/BenchmarkProblems.html) describing what's actually happening.
> 
> Some ideas, but probably for other pull requests:
> 
>     * it would be good to include analytic Jacobians
> 
>     * we should add plots
> 
>     * (related to the plots) data assimilation is all about forecasting, so it would be good to add a parameter to plot the forecast window (basically, you expect the learned parameters to fit the data you have well, but that may, or may not, predict the future well)
> 
> 
> We can discuss and create issues for these together.

I forgot this page was even there! I guess I also need to package up the examples?
AndrewLister-STFC: My understanding is that the issues to split off are:
- Add time series data
- Add a way of plotting the time series data with the prediction. Possibly splitting the data so that there's something to compare the prediction to.
- Add analytic jacobians

Patch:
diff --git a/docs/source/users/BenchmarkProblems.rst b/docs/source/users/BenchmarkProblems.rst
index ea098140..417d4521 100644
--- a/docs/source/users/BenchmarkProblems.rst
+++ b/docs/source/users/BenchmarkProblems.rst
@@ -199,6 +199,23 @@ that are added, and also that any new parsers reimplement these
 data sets and models (if possible).
 
 
+Data Assimilation
+=================
+
+**Download** :download:`.zip <http://numerical.rl.ac.uk/fitbenchmarking/data_assimilation.zip>`
+or :download:`.tar.gz <http://numerical.rl.ac.uk/fitbenchmarking/data_assimilation.tar.gz>`
+
+This folder (also found in `examples/benchmark_problems/data_assimilation`) contains
+two examples using the data assimilation problem definition in fitbenchmarking.
+These examples follow the method set out in 
+`this paper <https://www.researchgate.net/publication/324956488_Data_assimilation_approach_to_analysing_systems_of_ordinary_differential_equations>`_.
+
+These data files are synthetic and have been generated as an initial test of
+the minimizers. We plan to extend this with time series data which is more
+representative of the expectations for data assimilation in future updates.
+
+
+
 .. |CUTEstWarning| replace::
 		   The external packages CUTEst and pycutest must be installed to run
 		   this data set.   See :ref:`external-instructions` for details.
diff --git a/docs/source/users/problem_definition_files/native.rst b/docs/source/users/problem_definition_files/native.rst
index 35e32b8e..b74077d4 100644
--- a/docs/source/users/problem_definition_files/native.rst
+++ b/docs/source/users/problem_definition_files/native.rst
@@ -4,7 +4,7 @@
 Native File Format
 ******************
 
-In FitBenchmarking, the native file format is used to read Mantid and
+In FitBenchmarking, the native file format is used to read IVP, Mantid, and
 SASView problems.
 
 In this format, data is separated from the function. This allows running the
@@ -13,6 +13,8 @@ appropriate.
 
 Examples of native problems are:
 
+.. literalinclude:: ../../../../examples/benchmark_problems/Data_Assimilation/lorentz.txt
+
 .. literalinclude:: ../../../../examples/benchmark_problems/Muon/Muon_HIFI_113856.txt
 
 .. literalinclude:: ../../../../examples/benchmark_problems/SAS_modelling/1D/prob_def_1.txt
@@ -22,9 +24,9 @@ indicating it is a FitBenchmark problem followed by key-value pairs. Available
 keys are described below:
 
 software
-  Either 'Mantid' or 'SasView' (case insensitive).
+  Either 'IVP', 'Mantid', or 'SasView' (case insensitive).
   
-  This defines whether to use Mantid or SasView to generate the model.
+  This defines whether to use an IVP format, Mantid, or SasView to generate the model.
   The 'Mantid' software also supports Mantid's MultiFit functionality, which
   requires the parameters listed here to be defined slightly differently.
   More information can be found in :ref:`multifit`.
@@ -45,24 +47,52 @@ description
 input_file
   The name of a file containing the data to fit.
 
-  The file must be in a subdirectory named `data_files`, and should have the form::
+  The file must be in a subdirectory named ``data_files``, and should have the form::
 
      header
 
-     x1 y1 [e1]
-     x2 y2 [e2]
+     x11 [x12 [x13 ...]] y11 [y12 [y13 ...]] [e11 [e12 ...]]
+     x21 [x22 [x23 ...]] y21 [y22 [y23 ...]] [e21 [e22 ...]]
      ...
 
   Mantid uses the convention of ``# X Y E`` as the header and SASView uses
   the convention ``<X>   <Y>   <E>``, although neither of these are enforced.
   The error column is optional in this format.
 
+  If the data contains multiple inputs or outputs, the header must be written
+  in one of the above conventions with the labels as "x", "y", or "e" followed by
+  a number. An example of this can be seen in
+  ``examples/benchmark_problems/Data_Assimilation/data_files/lorentz.txt``
+
 function
   This defines the function that will be used as a model for the fitting.
 
   Inside FitBenchmarking, this is passed on to the specified software and, as
   such, the format is specific to the package we wish to use, as described below.
 
+  **IVP**
+
+  The IVP parser allows a user to define ``f`` in the following equation:
+
+  .. math:: x' = f(t, x, *args)
+
+  To do this we use a python module to define the function. As in the above
+  formula, the function can take the following arguments:
+
+  - *t* (float): The time to evaluate at
+  - *x* (np.array): A value for x to evaluate at
+  - *\*args* (floats): The parameters to fit
+
+  To link to this function we use a function string with the following
+  parameters:
+
+  - *module*: The path to the module
+  - *func*: The name of the function within the module
+  - *step*: The time step that the input data uses
+    (currently only fixed steps are supported - if you need
+    varying time steps please raise an issue on our GitHub)
+  - *\*args*: Starting values for the parameters
+
   **Mantid**
 
   A Mantid function consists of one or more base functions separated by a semicolon.
@@ -91,7 +121,7 @@ parameter_ranges
   An optional setting which specifies upper and lower bounds for 
   parameters in the problem.
 
-  Similarly to `fit_ranges`, it takes the form where the first number
+  Similarly to ``fit_ranges``, it takes the form where the first number
   is the minimum in the range and the second is the maximum.
 
   Currently in Fitbenchmarking, problems with `parameter_ranges` can
diff --git a/examples/benchmark_problems/Data_Assimilation/META.txt b/examples/benchmark_problems/Data_Assimilation/META.txt
new file mode 100644
index 00000000..e3010c63
--- /dev/null
+++ b/examples/benchmark_problems/Data_Assimilation/META.txt
@@ -0,0 +1,5 @@
+Data_Assimilation
+
+These data files are synthetic and have been generated as an initial test of
+the minimizers. We plan to extend this with time series data which is more
+representative of the expectations for data assimilation in future updates.
diff --git a/examples/benchmark_problems/Data_Assimilation/data_files/lorentz3d.txt b/examples/benchmark_problems/Data_Assimilation/data_files/lorentz3d.txt
new file mode 100644
index 00000000..64f02dd9
--- /dev/null
+++ b/examples/benchmark_problems/Data_Assimilation/data_files/lorentz3d.txt
@@ -0,0 +1,1001 @@
+# x0 x1 x2 y0 y1 y2
+0.0 0.0 0.0 0.0 0.0 0.0
+0.0 0.0 0.1 0.0 0.0 0.07659283582144003
+0.0 0.0 0.2 0.0 0.0 0.15318567161814128
+0.0 0.0 0.3 0.0 0.0 0.22977850741485423
+0.0 0.0 0.4 0.0 0.0 0.30637134321157017
+0.0 0.0 0.5 0.0 0.0 0.3829641790082872
+0.0 0.0 0.6 0.0 0.0 0.4595570148050049
+0.0 0.0 0.7 0.0 0.0 0.5361498506017229
+0.0 0.0 0.8 0.0 0.0 0.6127426863984412
+0.0 0.0 0.9 0.0 0.0 0.6893355221951594
+0.0 0.1 0.0 0.09104784522080188 0.20857248227422026 0.0006228786500006853
+0.0 0.1 0.1 0.0910495987975315 0.20857013744550942 0.07721568490090139
+0.0 0.1 0.2 0.09104963281676476 0.20857009081324177 0.15380851858869116
+0.0 0.1 0.3 0.09104964417724334 0.20857007523749016 0.23040135245128981
+0.0 0.1 0.4 0.09104964986131772 0.2085700674437433 0.3069941863574509
+0.0 0.1 0.5 0.09104965327298274 0.20857006276562504 0.3835870202810139
+0.0 0.1 0.6 0.09104965554793296 0.2085700596461023 0.46017985421327173
+0.0 0.1 0.7 0.09104965717314527 0.20857005741749185 0.5367726881504953
+0.0 0.1 0.8 0.09104965839218977 0.2085700557458262 0.6133655220908217
+0.0 0.1 0.9 0.09104965934041562 0.20857005444551904 0.689958356033216
+0.0 0.2 0.0 0.1817665794391492 0.415625014875972 0.0024834524589209175
+0.0 0.2 0.1 0.18176366723722073 0.41562899907931883 0.0790763502928858
+0.0 0.2 0.2 0.18176364770594025 0.4156290260045543 0.15566918451370004
+0.0 0.2 0.3 0.18176364116080862 0.41562903502833815 0.23226201855142053
+0.0 0.2 0.4 0.18176363788172817 0.41562903954937563 0.30885485254341316
+0.0 0.2 0.5 0.18176363591219433 0.41562904226492636 0.38544768651712263
+0.0 0.2 0.6 0.1817636345983023 0.4156290440765142 0.46204052048169314
+0.0 0.2 0.7 0.18176363365938242 0.4156290453711033 0.538633354441042
+0.0 0.2 0.8 0.1817636329549595 0.4156290463423722 0.615226188397128
+0.0 0.2 0.9 0.18176363240693716 0.4156290470979974 0.6918190223510386
+0.0 0.3 0.0 0.2721521408340588 0.6211792022693268 0.005569781359064263
+0.0 0.3 0.1 0.2721479318755926 0.6211847718584949 0.08216283562233362
+0.0 0.3 0.2 0.27214791319602427 0.6211847971366394 0.15875567014021746
+0.0 0.3 0.3 0.27214790701478614 0.6211848055057775 0.23534850425868117
+0.0 0.3 0.4 0.27214790393293725 0.621184809679311 0.3119413382796758
+0.0 0.3 0.5 0.27214790208667206 0.6211848121798504 0.38853417226207293
+0.0 0.3 0.6 0.2721479008570212 0.6211848138453748 0.4651270062252808
+0.0 0.3 0.7 0.2721478999792872 0.6211848150342947 0.541719840177564
+0.0 0.3 0.8 0.27214789932130656 0.6211848159255816 0.6183126741230369
+0.0 0.3 0.9 0.2721478988097375 0.6211848166185608 0.6949055080639784
+0.0 0.4 0.0 0.362206836720031 0.8252477884744633 0.009870017754167383
+0.0 0.4 0.1 0.36220033799348555 0.8252558495749909 0.08646347056720494
+0.0 0.4 0.2 0.36220031854168266 0.8252558752707484 0.16305630546857441
+0.0 0.4 0.3 0.3622003123032701 0.8252558835287342 0.23964913968746002
+0.0 0.4 0.4 0.3622003092311151 0.8252558875988192 0.3162419737496959
+0.0 0.4 0.5 0.3622003074030094 0.8252558900218531 0.39283480775155194
+0.0 0.4 0.6 0.3622003061906302 0.8252558916292468 0.4694276417238568
+0.0 0.4 0.7 0.3622003053277684 0.8252558927734731 0.5460204756795107
+0.0 0.4 0.8 0.362200304682336 0.8252558936294968 0.6226133096248614
+0.0 0.4 0.9 0.3622003041813472 0.8252558942940227 0.6992061435633945
+0.0 0.5 0.0 0.4519271318498014 1.027850855017639 0.015372760449630067
+0.0 0.5 0.1 0.45192371436628975 1.0278538877229049 0.09196660888752436
+0.0 0.5 0.2 0.45192366361053027 1.027853951828231 0.16855944636160733
+0.0 0.5 0.3 0.45192364709299704 1.0278539727112388 0.24515228139415096
+0.0 0.5 0.4 0.4519236389123352 1.0278539830579327 0.3217451158517193
+0.0 0.5 0.5 0.45192363402930835 1.0278539892351182 0.39833795008510214
+0.0 0.5 0.6 0.4519236307846153 1.0278539933402817 0.47493078420802065
+0.0 0.5 0.7 0.4519236284722256 1.027853996266157 0.5515236182684186
+0.0 0.5 0.8 0.451923626740814 1.0278539984570583 0.6281164522900051
+0.0 0.5 0.9 0.4519236253958723 1.0278540001590095 0.7047092862858484
+0.0 0.6 0.0 0.5413102547022217 1.2290069177135448 0.02206694532828532
+0.0 0.6 0.1 0.5413196889966262 1.2289917061794249 0.09866084308148483
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+0.0 0.6 0.3 0.5413196644730547 1.228991737792849 0.25184651397572855
+0.0 0.6 0.4 0.5413196617552811 1.2289917414233504 0.3284393481634203
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+0.0 0.6 0.6 0.5413196591180608 1.2289917449787686 0.4816250162292962
+0.0 0.6 0.7 0.5413196583795041 1.2289917459806539 0.5582178502014651
+0.0 0.6 0.8 0.5413196578299696 1.2289917467279685 0.6348106841546007
+0.0 0.6 0.9 0.5413196574051582 1.228991747306777 0.7114035180954115
+0.0 0.7 0.0 0.6303706377786022 1.428710924483806 0.02994125678579312
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+0.0 0.7 0.4 0.6303870759806719 1.428685878586505 0.33631341614557014
+0.0 0.7 0.5 0.6303870792718556 1.428685874001391 0.41290625020409993
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+0.0 0.8 0.0 0.7191203899809314 1.6269624800050342 0.038983422003752766
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diff --git a/examples/benchmark_problems/Data_Assimilation/data_files/noisy_lorentz3d.txt b/examples/benchmark_problems/Data_Assimilation/data_files/noisy_lorentz3d.txt
new file mode 100644
index 00000000..eb39fe74
--- /dev/null
+++ b/examples/benchmark_problems/Data_Assimilation/data_files/noisy_lorentz3d.txt
@@ -0,0 +1,1001 @@
+# x0 x1 x2 y0 y1 y2
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+0.9 0.9 0.9 1.9794335242823315 3.831528301081434 0.8825895670521522
diff --git a/examples/benchmark_problems/Data_Assimilation/data_files/noisy_simplified_anac.txt b/examples/benchmark_problems/Data_Assimilation/data_files/noisy_simplified_anac.txt
new file mode 100644
index 00000000..5f16162e
--- /dev/null
+++ b/examples/benchmark_problems/Data_Assimilation/data_files/noisy_simplified_anac.txt
@@ -0,0 +1,101 @@
+# x0 x1, y0, y1
+0.0 0.0 0.1181555484141891 0.06986998821191734
+0.1 0.0 0.12624777093939638 0.016339579466552845
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+0.3 0.0 0.3284525883537706 0.23624251375896987
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+0.5 0.0 0.4057148744129107 0.604881813906248
+0.6 0.0 0.5779602329184671 0.5955320147159967
+0.7 0.0 0.8216497527778293 0.5815345539987031
+0.8 0.0 0.9226581337763985 0.5934719330801819
+0.9 0.0 0.9428973357156536 0.9742251390466896
+0.0 0.1 0.09559651176554815 0.12422987838431668
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+0.2 0.1 0.37778442964098213 0.21114615459064143
+0.3 0.1 0.22290049439093312 0.38221137420528783
+0.4 0.1 0.3915594611157795 0.3643175720196358
+0.5 0.1 0.4698588098283541 0.5003691219920156
+0.6 0.1 0.6411466434035371 0.7571064690401914
+0.7 0.1 0.8198147497247441 0.8333226959156473
+0.8 0.1 0.6070490718359451 1.0220933843900293
+0.9 0.1 0.9087978301923544 1.022120803686605
+0.0 0.2 -0.061618213032879926 0.09591253865080826
+0.1 0.2 0.30926257216136455 0.3964719734360218
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+0.3 0.2 0.4013378887807302 0.5169798381109107
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+0.3 0.4 0.33897998741531277 0.6858235903057637
+0.4 0.4 0.40124448850221495 0.6770193428777442
+0.5 0.4 0.5448880709671884 1.0518394171679155
+0.6 0.4 0.7073579510165408 1.1451663975673934
+0.7 0.4 0.7408600470470316 1.0953842614522413
+0.8 0.4 0.8616966881907164 1.1162028901991166
+0.9 0.4 1.1575142154004605 1.287814334817948
+0.0 0.5 0.15412744819901825 0.650634034368999
+0.1 0.5 0.13849307486766593 0.6743662904339663
+0.2 0.5 0.2811711740467601 0.8693153959038609
+0.3 0.5 0.198687484324005 0.867033352865686
+0.4 0.5 0.5773962550461395 0.8401520058007378
+0.5 0.5 0.462572171652644 1.0617775405849135
+0.6 0.5 0.753116652862858 1.0788964564662222
+0.7 0.5 0.8721695570600173 1.3339747785425113
+0.8 0.5 0.6953047121381043 1.1463484383535871
+0.9 0.5 1.1425692116933464 1.3794822447697814
+0.0 0.6 0.04982092799861449 0.5706169027471586
+0.1 0.6 0.18286638369042943 0.7354668970118556
+0.2 0.6 0.17520124294994 0.9987561287103337
+0.3 0.6 0.37420559800688624 0.9212122345212532
+0.4 0.6 0.49950668749698407 0.9728257306025653
+0.5 0.6 0.48404214963443204 1.0145684625435152
+0.6 0.6 0.759570767920935 1.2500390353825515
+0.7 0.6 0.9136245649741578 1.2936710465958676
+0.8 0.6 1.0561932061992874 1.3829044380705198
+0.9 0.6 0.829110915911238 1.3517545780989804
+0.0 0.7 0.07444686510510781 0.763683845681119
+0.1 0.7 0.125013099566676 0.6201080759092997
+0.2 0.7 0.342914527371367 0.6946559085150987
+0.3 0.7 0.4338279631913827 1.1310972901880234
+0.4 0.7 0.630779607849637 1.0972073056874954
+0.5 0.7 0.7084840039315126 1.5005262078380408
+0.6 0.7 0.6964606911739429 1.439259284197221
+0.7 0.7 0.8614024865382137 1.541995763742046
+0.8 0.7 0.9172616972049392 1.6226745037705796
+0.9 0.7 0.9446514909817897 1.5916266772101473
+0.0 0.8 0.07312616007053338 0.8827786989270263
+0.1 0.8 0.12746530704250073 1.0538920830397438
+0.2 0.8 0.24831997978176443 1.0784103485604113
+0.3 0.8 0.5356750179120429 1.1335745692491617
+0.4 0.8 0.5280049062998993 1.2281543366255852
+0.5 0.8 0.7051554938603233 1.1940073456823244
+0.6 0.8 0.7748964849430645 1.6573183425988804
+0.7 0.8 0.871483296298676 1.641039063059016
+0.8 0.8 0.631928254818725 1.5700259489690152
+0.9 0.8 1.0741544428075163 1.755619703407831
+0.0 0.9 0.06099859838344748 1.0355836274239856
+0.1 0.9 0.38486484934775805 1.084320391722057
+0.2 0.9 0.37106977820809245 1.1332119930434665
+0.3 0.9 0.36417373036208817 1.3030647391187213
+0.4 0.9 0.6144508643999324 1.3376959080081803
+0.5 0.9 0.6016537166082013 1.4507471049792302
+0.6 0.9 0.7323767029989898 1.6209165641311407
+0.7 0.9 0.9777065492117032 1.7191719817361728
+0.8 0.9 0.9078203693282666 1.646171497859926
+0.9 0.9 1.2746735972052636 1.9327943387766593
diff --git a/examples/benchmark_problems/Data_Assimilation/data_files/simplified_anac.txt b/examples/benchmark_problems/Data_Assimilation/data_files/simplified_anac.txt
new file mode 100644
index 00000000..fbc670d5
--- /dev/null
+++ b/examples/benchmark_problems/Data_Assimilation/data_files/simplified_anac.txt
@@ -0,0 +1,101 @@
+# x0 x1 y0 y1
+0.0 0.0 0.0 0.0
+0.1 0.0 0.10504078546698457 0.10165363692657119
+0.2 0.0 0.21007534074698186 0.2031790402448081
+0.3 0.0 0.3150975048739934 0.30444796461856505
+0.4 0.0 0.4201010653690826 0.40533224556560454
+0.5 0.0 0.5250798197898161 0.5057037913564505
+0.6 0.0 0.6300275688036315 0.6054346155095812
+0.7 0.0 0.734938116712285 0.7043968619896837
+0.8 0.0 0.8398052719466603 0.8024628309816272
+0.9 0.0 0.9446228475860821 0.8995050047845863
+0.0 0.1 0.010167501072660692 0.10504181528345628
+0.1 0.1 0.11520816619043839 0.20669202952440668
+0.2 0.1 0.22024241723004512 0.3082075969275837
+0.3 0.1 0.3252640519849578 0.4094602845610277
+0.4 0.1 0.4302668740667119 0.5103219252379961
+0.5 0.1 0.5352446827506092 0.6106644296624175
+0.6 0.1 0.6401912788365867 0.7103598154365122
+0.7 0.1 0.745100466742453 0.8092802325004727
+0.8 0.1 0.8499660549819773 0.9072979884984216
+0.9 0.1 0.9547818567284064 1.0042855744823573
+0.0 0.2 0.020335003175232274 0.21008357142901965
+0.1 0.2 0.12537554780032212 0.31172996132152375
+0.2 0.2 0.23040947207805135 0.4132352785205733
+0.3 0.2 0.3354305722634268 0.5144713064866596
+0.4 0.2 0.4404326452292696 0.6153098809167199
+0.5 0.2 0.545409492462552 0.715622918823024
+0.6 0.2 0.6503549160123503 0.8152824432010832
+0.7 0.2 0.7552627253144161 0.9141606104337654
+0.8 0.2 0.860126728824208 1.0121297345455993
+0.9 0.2 0.9649407398717987 1.1090623145406784
+0.0 0.3 0.030502503144487353 0.3151252828614024
+0.1 0.3 0.135542917809322 0.41676740840473453
+0.2 0.3 0.24057650392140434 0.5182620527485791
+0.3 0.3 0.34559705815599856 0.6194809990172104
+0.4 0.3 0.4505983785115274 0.7202960860814489
+0.5 0.3 0.5555742635648265 0.8205792341387669
+0.6 0.3 0.660518517028101 0.9202024723952426
+0.7 0.3 0.7654249451328946 1.0190379633241207
+0.8 0.3 0.8702873568474966 1.1169580289904693
+0.9 0.3 0.9750995678210959 1.2138351778856356
+0.0 0.4 0.040670000980946926 0.4201669073139179
+0.1 0.4 0.14571027559924832 0.5218043396586571
+0.2 0.4 0.2507435131749953 0.6232878887340036
+0.3 0.4 0.3557635107608575 0.724489330880942
+0.4 0.4 0.46076406641555795 0.8252805080774882
+0.5 0.4 0.5657389801932646 0.9255333452930968
+0.6 0.4 0.670682054078916 1.0251198762263483
+0.7 0.4 0.7755870936943089 1.1239122699602395
+0.8 0.4 0.8804479100429643 1.2217828570363216
+0.9 0.4 0.9852583174911912 1.318604154343392
+0.0 0.5 0.05083749604393753 0.5252084116969771
+0.1 0.5 0.15587762055384163 0.6268407239674826
+0.2 0.5 0.26091049922215354 0.7283127553657667
+0.3 0.5 0.36592992979010747 0.8294962711016765
+0.4 0.5 0.47092971037760645 0.9302631163145931
+0.5 0.5 0.5759036411227708 1.0304852203036463
+0.6 0.5 0.6808455248161276 1.1300346225721998
+0.7 0.5 0.7857491675232996 1.2287834988318327
+0.8 0.5 0.8906083774976706 1.3266041861741757
+0.9 0.5 0.9954169711633349 1.4233692115561154
+0.0 0.6 0.06100498777508606 0.6302497635317875
+0.1 0.6 0.1660449520571678 0.7318765302154931
+0.2 0.6 0.2710774614468502 0.8333366215329318
+0.3 0.6 0.3760963146276678 0.9345017885759648
+0.4 0.6 0.48109530978158277 1.0352438796994912
+0.5 0.6 0.5860682471315515 1.1354348285864375
+0.6 0.6 0.6910089295757329 1.2349466802891995
+0.7 0.6 0.7959111633207678 1.3336516172370938
+0.8 0.6 0.9007687585141851 1.4314219851927588
+0.9 0.6 1.0055755287400452 1.5281303185317778
+0.0 0.7 0.07117247562078514 0.7352909308059323
+0.1 0.7 0.17621226949338747 0.8369117272871431
+0.2 0.7 0.281244399233244 0.9383594561248582
+0.3 0.7 0.3862626646577351 1.0395058522007794
+0.4 0.7 0.49126086401176233 1.1402227671394631
+0.5 0.7 0.5962327976040013 1.2403821390617493
+0.6 0.7 0.7011722684411265 1.3398560186231145
+0.7 0.7 0.8060730828610705 1.4385165950190606
+0.8 0.7 0.9109290511654 1.5362362219392347
+0.9 0.7 1.015733988250671 1.632887443459473
+0.0 0.8 0.08133995901531735 0.8403318818235657
+0.1 0.8 0.18637957224669838 0.9419462840670852
+0.2 0.8 0.29141131196556785 1.0433812280312489
+0.3 0.8 0.396428979264614 1.144508430873576
+0.4 0.8 0.5014263724525627 1.2451997475424186
+0.5 0.8 0.6063972919246897 1.3453271206506343
+0.6 0.8 0.7113355407970693 1.4447626065108299
+0.7 0.8 0.8162349255398094 1.5433784011386522
+0.8 0.8 0.921089256609396 1.6410468662046185
+0.9 0.8 1.0258923490800147 1.7376405549235194
+0.0 0.9 0.09150743738080391 0.94537258508822
+0.1 0.9 0.19654685970131608 1.0469801694401861
+0.2 0.9 0.3015781990280897 1.148401906142172
+0.3 0.9 0.40659525783266126 1.2495094934923188
+0.4 0.9 0.5115918344884692 1.3501747898169227
+0.5 0.9 0.6165617294782703 1.4502697422749546
+0.6 0.9 0.7214987460284217 1.5496664128901894
+0.7 0.9 0.8263966907420895 1.6482370045523802
+0.8 0.9 0.9312493742315624 1.7458538869667701
+0.9 0.9 1.0360506117495354 1.842389622540845
diff --git a/examples/benchmark_problems/Data_Assimilation/functions/lorentz.py b/examples/benchmark_problems/Data_Assimilation/functions/lorentz.py
new file mode 100644
index 00000000..731c79e5
--- /dev/null
+++ b/examples/benchmark_problems/Data_Assimilation/functions/lorentz.py
@@ -0,0 +1,30 @@
+"""
+This file contains the functions required to run lorentz system examples.
+"""
+import numpy as np
+
+
+# pylint: disable=unused-argument
+def lorentz3d(t, x, sigma, r, b):
+    """
+    Calculates the rhs of a Lorentz system defined by:
+
+    x'[0] = sigma*(x[1]-x[0])
+    x'[1] = r*x[0]-x[1]-x[0]*x[2]
+    x'[2] = x[0]*x[1]-b*x[2]
+
+    Args:
+        t (float): The time to evaluate at
+        x (np.ndarray): The x vector (current location)
+        sigma (float): The value in the above equations
+        r (float): The value in the above equations
+        b (float): The value in the above equations
+    """
+    if len(x.shape) == 1:
+        return np.array([
+            sigma * (x[1] - x[0]),
+            r * x[0] - x[1] - x[0] * x[1],
+            x[0] * x[1] - b * x[2]
+        ])
+
+    raise ValueError('x is the wrong shape in lorentz3d call.')
diff --git a/examples/benchmark_problems/Data_Assimilation/functions/simplified_anac.py b/examples/benchmark_problems/Data_Assimilation/functions/simplified_anac.py
new file mode 100644
index 00000000..51968db8
--- /dev/null
+++ b/examples/benchmark_problems/Data_Assimilation/functions/simplified_anac.py
@@ -0,0 +1,28 @@
+"""
+This file contains the functions required to run the simplified anac system
+examples.
+"""
+import numpy as np
+
+
+# pylint: disable=unused-argument
+def simplified_anac(t, x, gamma, mu):
+    """
+    Calculates the rhs of the system defined by:
+
+    x'[0] = x[1]
+    x'[1] = gamma*x[0]+2*mu*x[0]^3
+
+    Args:
+        t (float): The time to evaluate at
+        x (np.ndarray): The x vector (current location)
+        gamma (float): The value in the above equations
+        mu (float): The value in the above equations
+    """
+    if len(x.shape) == 1:
+        return np.array([
+            x[1],
+            gamma * x[0] + 2 * mu * x[0]**3
+        ])
+
+    raise ValueError('x is the wrong shape in simplified_anac call.')
diff --git a/examples/benchmark_problems/Data_Assimilation/lorentz.txt b/examples/benchmark_problems/Data_Assimilation/lorentz.txt
new file mode 100644
index 00000000..27b16bea
--- /dev/null
+++ b/examples/benchmark_problems/Data_Assimilation/lorentz.txt
@@ -0,0 +1,6 @@
+# Fitbenchmark Problem
+software = 'ivp'
+name = 'Lorentz'
+description = 'A simple lorentz system for testing the ivp parser. Exact results should be 10, 28, 8/3.'
+input_file = 'lorentz3d.txt'
+function = 'module=functions/lorentz,func=lorentz3d,step=0.1,sigma=11,r=30,b=3'
diff --git a/examples/benchmark_problems/Data_Assimilation/noisy_lorentz.txt b/examples/benchmark_problems/Data_Assimilation/noisy_lorentz.txt
new file mode 100644
index 00000000..76040fdf
--- /dev/null
+++ b/examples/benchmark_problems/Data_Assimilation/noisy_lorentz.txt
@@ -0,0 +1,6 @@
+# Fitbenchmark Problem
+software = 'ivp'
+name = 'Noisy Lorentz'
+description = 'A synthetic lorentz system with gaussian noise for testing the ivp parser. Exact results should be 10, 28, 8/3.'
+input_file = 'noisy_lorentz3d.txt'
+function = 'module=functions/lorentz,func=lorentz3d,step=0.1,sigma=11,r=30,b=3'
diff --git a/examples/benchmark_problems/Data_Assimilation/noisy_simplified_anac.txt b/examples/benchmark_problems/Data_Assimilation/noisy_simplified_anac.txt
new file mode 100644
index 00000000..a5862349
--- /dev/null
+++ b/examples/benchmark_problems/Data_Assimilation/noisy_simplified_anac.txt
@@ -0,0 +1,6 @@
+# Fitbenchmark Problem
+software = 'ivp'
+name = 'Noisy Nonlinear Oscillator'
+description = 'A synthetic noisy dataset for a simplified version of the axisymetric non-axisymmetric coupled system generated to test the ivp parser. Exact results should be 10, -0.1.'
+input_file = 'noisy_simplified_anac.txt'
+function = 'module=functions/simplified_anac,func=simplified_anac,step=0.1,gamma=15,mu=-0.5'
diff --git a/examples/benchmark_problems/Data_Assimilation/simplified_anac.txt b/examples/benchmark_problems/Data_Assimilation/simplified_anac.txt
new file mode 100644
index 00000000..ff0647a3
--- /dev/null
+++ b/examples/benchmark_problems/Data_Assimilation/simplified_anac.txt
@@ -0,0 +1,6 @@
+# Fitbenchmark Problem
+software = 'ivp'
+name = 'Simplified ANAC'
+description = 'A simplified version of the axisymetric non-axisymmetric coupled system generated to test the ivp parser. Exact results should be 10, -0.1.'
+input_file = 'simplified_anac.txt'
+function = 'module=functions/simplified_anac,func=simplified_anac,step=0.1,gamma=15,mu=-0.5'
diff --git a/examples/benchmark_problems/scripts/generate_data_assim.py b/examples/benchmark_problems/scripts/generate_data_assim.py
new file mode 100644
index 00000000..f0c6561a
--- /dev/null
+++ b/examples/benchmark_problems/scripts/generate_data_assim.py
@@ -0,0 +1,59 @@
+"""
+This function was used to generate data for the data assimilation directory.
+"""
+
+import numpy as np
+from scipy.integrate import solve_ivp
+
+
+def write_data(fun, args, fname='data.txt', step=0.1, sd=0.1):
+    """
+    Generate a dataset consisting of 10^n points arranged in a grid,
+    where n in the dimension of the function input.
+    These points are then propagated through time using scipy.solve_ivp
+    and gaussian noise is added.
+
+    This format of data can be thought of as random samples from a time
+    series rather than the time series itself.
+
+    Args:
+        fun (callable): The function f in the problem definition: x' = f(x, p)
+        args (list): The parameters p in the problem definition: x' = f(x, p)
+        fname (str, optional): The name of the generated file.
+                               Defaults to 'data.txt'.
+        step (float, optional): The amount of time that passes between the x
+                                and y values. Defaults to 0.1.
+        sd (float, optional): The standard deviation of the gaussian noise.
+                              Defaults to 0.1.
+    """
+    out = fun(0, np.zeros((10)), *args)
+    dim = len(out)
+    tmp_x = [[i/10] for i in range(10)]
+    for _ in range(dim-1):
+        tmp_x = [a + [i/10]
+                 for a in tmp_x
+                 for i in range(10)]
+    x = np.array(tmp_x)
+
+    exact_y = np.zeros_like(x)
+    for i, y0 in enumerate(x):
+        soln = solve_ivp(fun=fun,
+                         t_span=(0, step),
+                         y0=y0,
+                         t_eval=[step],
+                         args=args)
+
+        exact_y[i] = soln.y[:, -1]
+
+    noisy_y = exact_y + np.random.normal(loc=0, scale=sd, size=exact_y.shape)
+
+    x_header = ' '.join(["x" + str(i) for i in range(dim)])
+    y_header = ' '.join(["y" + str(i) for i in range(dim)])
+    header = f'# {x_header} {y_header}\n'
+    for name, y in zip([fname, 'noisy_' + fname], [exact_y, noisy_y]):
+        with open(name, 'w') as f:
+            f.write(header)
+            for xs, ys in zip(x, y):
+                x_str = ' '.join(str(i) for i in xs)
+                y_str = ' '.join(str(i) for i in ys)
+                f.write(f'{x_str} {y_str}\n')
diff --git a/fitbenchmarking/core/results_output.py b/fitbenchmarking/core/results_output.py
index 3aeb4957..115301dd 100644
--- a/fitbenchmarking/core/results_output.py
+++ b/fitbenchmarking/core/results_output.py
@@ -12,6 +12,7 @@ import fitbenchmarking
 from fitbenchmarking.results_processing import (performance_profiler, plots,
                                                 support_page, tables)
 from fitbenchmarking.utils import create_dirs
+from fitbenchmarking.utils.exceptions import PlottingError
 from fitbenchmarking.utils.misc import get_css, get_js
 
 
@@ -145,9 +146,14 @@ def create_plots(options, results, best_results, figures_dir):
     """
     for best, prob_result in zip(best_results, results):
 
-        plot = plots.Plot(best_result=best,
-                          options=options,
-                          figures_dir=figures_dir)
+        try:
+            plot = plots.Plot(best_result=best,
+                              options=options,
+                              figures_dir=figures_dir)
+        except PlottingError as e:
+            for result in prob_result:
+                result.figure_error = str(e)
+            continue
 
         # Create a plot showing the initial guess and get filename
         initial_guess_path = plot.plot_initial_guess()
diff --git a/fitbenchmarking/cost_func/hellinger_nlls_cost_func.py b/fitbenchmarking/cost_func/hellinger_nlls_cost_func.py
index 71af19d6..a42aef23 100644
--- a/fitbenchmarking/cost_func/hellinger_nlls_cost_func.py
+++ b/fitbenchmarking/cost_func/hellinger_nlls_cost_func.py
@@ -1,7 +1,7 @@
 """
 Implements the root non-linear least squares cost function
 """
-from numpy import sqrt
+from numpy import sqrt, ravel
 
 from fitbenchmarking.cost_func.nlls_base_cost_func import BaseNLLSCostFunc
 from fitbenchmarking.utils.exceptions import CostFuncError
@@ -58,6 +58,10 @@ class HellingerNLLSCostFunc(BaseNLLSCostFunc):
                                 'len(x)={} and len(y)= {}.'.format(len(x),
                                                                    len(y)))
         result = sqrt(y) - sqrt(self.problem.eval_model(params=params, x=x))
+
+        # Flatten in case of a vector function
+        result = ravel(result)
+
         self.cache_rx['params'] = params
         self.cache_rx['value'] = result
         return result
diff --git a/fitbenchmarking/cost_func/nlls_cost_func.py b/fitbenchmarking/cost_func/nlls_cost_func.py
index bf09ee5c..d00e69ba 100644
--- a/fitbenchmarking/cost_func/nlls_cost_func.py
+++ b/fitbenchmarking/cost_func/nlls_cost_func.py
@@ -1,6 +1,8 @@
 """
 Implements the non-weighted non-linear least squares cost function
 """
+from numpy import ravel
+
 from fitbenchmarking.cost_func.nlls_base_cost_func import BaseNLLSCostFunc
 from fitbenchmarking.utils.exceptions import CostFuncError
 
@@ -50,9 +52,13 @@ class NLLSCostFunc(BaseNLLSCostFunc):
         y = kwargs.get("y", self.problem.data_y)
         if len(x) != len(y):
             raise CostFuncError('The length of the x and y are not the same, '
-                                'len(x)={} and len(y)= {}.'.format(len(x),
-                                                                   len(y)))
+                                'len(x)={} and len(y)={}.'.format(len(x),
+                                                                  len(y)))
         result = y - self.problem.eval_model(params=params, x=x)
+
+        # Flatten in case of a vector function
+        result = ravel(result)
+
         self.cache_rx['params'] = params
         self.cache_rx['value'] = result
         return result
diff --git a/fitbenchmarking/cost_func/poisson_cost_func.py b/fitbenchmarking/cost_func/poisson_cost_func.py
index 9506ac2e..8976c37f 100644
--- a/fitbenchmarking/cost_func/poisson_cost_func.py
+++ b/fitbenchmarking/cost_func/poisson_cost_func.py
@@ -2,7 +2,7 @@
 Implements a Poisson deviance cost function based on Mantid's:
 https://docs.mantidproject.org/nightly/fitting/fitcostfunctions/Poisson.html
 """
-from numpy import log, finfo, float64
+from numpy import log, finfo, float64, ravel
 
 from fitbenchmarking.cost_func.base_cost_func import CostFunc
 from fitbenchmarking.utils.exceptions import CostFuncError
@@ -59,7 +59,11 @@ class PoissonCostFunc(CostFunc):
         # Penalise nagative f(x, p)
         f_xp[f_xp <= 0.0] = finfo(float).max
 
-        result = sum(_safe_a_log_b(y, y) - _safe_a_log_b(y, f_xp) - (y - f_xp))
+        residuals = _safe_a_log_b(y, y) - _safe_a_log_b(y, f_xp) - (y - f_xp)
+
+        # Flatten in case of a vector function
+        result = sum(ravel(residuals))
+
         self.cache_cost_x['params'] = params
         self.cache_cost_x['value'] = result
         return result
diff --git a/fitbenchmarking/cost_func/weighted_nlls_cost_func.py b/fitbenchmarking/cost_func/weighted_nlls_cost_func.py
index 1bcd5c1d..dc529437 100644
--- a/fitbenchmarking/cost_func/weighted_nlls_cost_func.py
+++ b/fitbenchmarking/cost_func/weighted_nlls_cost_func.py
@@ -1,6 +1,8 @@
 """
 Implements the weighted non-linear least squares cost function
 """
+from numpy import ravel
+
 from fitbenchmarking.cost_func.nlls_base_cost_func import BaseNLLSCostFunc
 from fitbenchmarking.utils.exceptions import CostFuncError
 
@@ -53,6 +55,9 @@ class WeightedNLLSCostFunc(BaseNLLSCostFunc):
                                 'the same, len(x)={}, len(y)={} and '
                                 'len(e)={}'.format(len(x), len(y), len(e)))
         result = (y - self.problem.eval_model(params=params, x=x)) / e
+
+        # Flatten in case of a vector function
+        result = ravel(result)
         self.cache_rx['params'] = params
         self.cache_rx['value'] = result
         return result
diff --git a/fitbenchmarking/parsing/fitbenchmark_parser.py b/fitbenchmarking/parsing/fitbenchmark_parser.py
index 3bd706d5..15a90496 100644
--- a/fitbenchmarking/parsing/fitbenchmark_parser.py
+++ b/fitbenchmarking/parsing/fitbenchmark_parser.py
@@ -4,11 +4,13 @@ This file implements a parser for the Fitbenchmark data format.
 
 from __future__ import absolute_import, division, print_function
 
+import importlib
+import inspect
 import os
+import sys
 from collections import OrderedDict
 
 import numpy as np
-
 from fitbenchmarking.parsing.base_parser import Parser
 from fitbenchmarking.parsing.fitting_problem import FittingProblem
 from fitbenchmarking.utils.exceptions import MissingSoftwareError, ParsingError
@@ -17,6 +19,13 @@ from fitbenchmarking.utils.log import get_logger
 LOGGER = get_logger()
 
 import_success = {}
+try:
+    from scipy.integrate import solve_ivp
+    import_success['ivp'] = (True, None)
+except ImportError as ex:
+    import_success['ivp'] = (False, ex)
+
+
 try:
     import mantid.simpleapi as msapi
     import_success['mantid'] = (True, None)
@@ -25,9 +34,9 @@ except ImportError as ex:
 
 
 try:
-    from sasmodels.data import empty_data1D
-    from sasmodels.core import load_model
     from sasmodels.bumps_model import Experiment, Model
+    from sasmodels.core import load_model
+    from sasmodels.data import empty_data1D
     import_success['sasview'] = (True, None)
 except ImportError as ex:
     import_success['sasview'] = (False, ex)
@@ -59,10 +68,15 @@ class FitbenchmarkParser(Parser):
 
         self._entries = self._get_data_problem_entries()
         software = self._entries['software'].lower()
-        if not (software in import_success and import_success[software][0]):
+        if software not in import_success:
+            raise MissingSoftwareError(
+                f'Did not recognise software: {software}'
+            )
+        if not import_success[software][0]:
             error = import_success[software][1]
-            raise MissingSoftwareError('Requirements are missing for {} parser'
-                                       ': {}'.format(software, error))
+            raise MissingSoftwareError(
+                f'Requirements are missing for {software} parser: {error}'
+            )
 
         self._parsed_func = self._parse_function()
 
@@ -82,16 +96,48 @@ class FitbenchmarkParser(Parser):
         elif software == 'sasview':
             fitting_problem.function = self._create_sasview_function()
             fitting_problem.format = 'sasview'
+        elif software == 'ivp':
+            fitting_problem.function = self._create_ivp_function()
+            fitting_problem.format = 'ivp'
+
+        # If using a multivariate function wrap the call to take a single
+        # argument
+        if len(data_points[0]['x'].shape) > 1:
+            old_function = fitting_problem.function
+            all_data = []
+            count = 0
+            for dp in data_points:
+                all_data.append(dp['x'])
+                dp['x'] = np.arange(count, count + dp['x'].shape[0])
+                count = count + dp['x'].shape[0]
+            all_data = np.concatenate(all_data)
+
+            def new_function(x, *p):
+                inp = all_data[x]
+                return old_function(inp, *p)
+
+            fitting_problem.function = new_function
+            fitting_problem.multivariate = True
+
+        # Set this flag if the output is non-scalar either
+        if len(data_points[0]['y'].shape) > 2:
+            fitting_problem.multivariate = True
 
         # EQUATION
-        equation_count = len(self._parsed_func)
-        if equation_count == 1:
-            fitting_problem.equation = self._parsed_func[0]['name']
+        if software == 'ivp':
+            fitting_problem.equation = self._ivp_equation_name
         else:
-            fitting_problem.equation = '{} Functions'.format(equation_count)
+            equation_count = len(self._parsed_func)
+            if equation_count == 1:
+                fitting_problem.equation = self._parsed_func[0]['name']
+            else:
+                fitting_problem.equation = '{} Functions'.format(
+                    equation_count)
 
         # STARTING VALUES
-        if software == 'mantid':
+        if software == 'ivp':
+            fitting_problem.starting_values = self._ivp_starting_values
+        elif software == 'mantid':
             fitting_problem.starting_values = self._mantid_starting_values
         else:
             fitting_problem.starting_values = self._get_starting_values()
@@ -111,9 +157,9 @@ class FitbenchmarkParser(Parser):
 
         if fitting_problem.multifit:
             num_files = len(data_points)
-            fitting_problem.data_x = [d[:, 0] for d in data_points]
-            fitting_problem.data_y = [d[:, 1] for d in data_points]
-            fitting_problem.data_e = [d[:, 2] if d.shape[1] > 2 else None
+            fitting_problem.data_x = [d['x'] for d in data_points]
+            fitting_problem.data_y = [d['y'] for d in data_points]
+            fitting_problem.data_e = [d['e'] if 'e' in d else None
                                       for d in data_points]
 
             if not fit_ranges:
@@ -125,10 +171,10 @@ class FitbenchmarkParser(Parser):
                                      for f in fit_ranges]
 
         else:
-            fitting_problem.data_x = data_points[0][:, 0]
-            fitting_problem.data_y = data_points[0][:, 1]
-            if data_points[0].shape[1] > 2:
-                fitting_problem.data_e = data_points[0][:, 2]
+            fitting_problem.data_x = data_points[0]['x']
+            fitting_problem.data_y = data_points[0]['y']
+            if 'e' in data_points[0]:
+                fitting_problem.data_e = data_points[0]['e']
 
             if fit_ranges and 'x' in fit_ranges[0]:
                 fitting_problem.start_x = fit_ranges[0]['x'][0]
@@ -148,12 +194,12 @@ class FitbenchmarkParser(Parser):
 
     def _get_data_file(self):
         """
-        Find/create the (full) path to a data_file specified in a FitBenchmark
-        definition file, where the data_file is searched for in the directory
-        of the definition file and subfolders of this file.
+        Find/create the (full) path to a data_file(s) specified in a
+        FitBenchmark definition file, where the data_file is searched for in
+        the directory of the definition file and subfolders of this file.
 
         :return: (full) path to a data file. Return None if not found
-        :rtype: str or None
+        :rtype: list<str>
         """
         data_file_name = self._entries['input_file']
         if data_file_name.startswith('['):
@@ -380,6 +426,54 @@ class FitbenchmarkParser(Parser):
 
         return fitFunction
 
+    def _create_ivp_function(self):
+        """
+        Process the IVP formatted function into a callable.
+
+        Expected function format:
+        function='module=my_python_file,func=my_function_name,
+                  step=0.5,p0=0.1,p1...'
+
+        :return: the model
+        :rtype: callable
+        """
+        if len(self._parsed_func) > 1:
+            raise ParsingError('Could not parse IVP problem. Please ensure '
+                               'only 1 function definition is present')
+
+        pf = self._parsed_func[0]
+        path = os.path.join(os.path.dirname(self._filename), pf['module'])
+        sys.path.append(os.path.dirname(path))
+        module = importlib.import_module(os.path.basename(path))
+        fun = getattr(module, pf['func'])
+        time_step = pf['step']
+        sig = inspect.signature(fun)
+        # params[0] should be t
+        # parmas[1] should be x so start after.
+        p_names = list(sig.parameters.keys())[2:]
+
+        # pylint: disable=attribute-defined-outside-init
+        self._ivp_equation_name = fun.__name__
+        self._ivp_starting_values = [
+            OrderedDict([(n, pf[n])
+                         for n in p_names])
+        ]
+
+        def fitFunction(x, *p):
+            if len(x.shape) == 1:
+                x = np.array([x])
+            y = np.zeros_like(x)
+            for i, inp in enumerate(x):
+                soln = solve_ivp(fun=fun,
+                                 t_span=[0, time_step],
+                                 y0=inp,
+                                 args=p,
+                                 vectorized=False)
+                y[i, :] = soln.y[:, -1]
+            return y
+
+        return fitFunction
+
     def _parse_ties(self):
         try:
             ties = []
@@ -458,8 +552,8 @@ def _get_data_points(data_file_path):
     :param data_file_path: The path to the file to load the points from
     :type data_file_path: str
 
-    :return: data points
-    :rtype: np.ndarray
+    :return: data
+    :rtype: dict<str, np.ndarray>
     """
 
     with open(data_file_path, 'r') as f:
@@ -468,24 +562,59 @@ def _get_data_points(data_file_path):
     # Find the line where data starts
     # i.e. the first line with a float on it
     first_row = 0
-
-    # Loop until break statement
-    while True:
+    for i, line in enumerate(data_text):
+        line = line.strip()
+        if not line:
+            continue
         try:
-            line = data_text[first_row].strip()
-        except IndexError as e:
-            raise ParsingError('Could not find data points') from e
-        if line != '':
-            x_val = line.split()[0]
-            try:
-                _ = float(x_val)
-            except ValueError:
-                pass
-            else:
-                break
-        first_row += 1
+            float(line.split()[0])
+        except ValueError:
+            continue
+        first_row = i
+        break
+    else:
+        raise ParsingError('Could not find data points')
 
     dim = len(data_text[first_row].split())
+    cols = {'x': [],
+            'y': [],
+            'e': []}
+    num_cols = 0
+    if first_row != 0:
+        header = data_text[0].split()
+        for heading in header:
+            if heading == '#':
+                continue
+            if heading[0] == '<' and heading[-1] == '>':
+                heading = heading[1:-1]
+            col_type = heading[0].lower()
+            if col_type in ['x', 'y', 'e']:
+                cols[col_type].append(num_cols)
+                num_cols += 1
+            else:
+                raise ParsingError(
+                    'Unrecognised header line, header names must start with '
+                    '"x", "y", or "e".'
+                    'Examples are: '
+                    '"# X Y E", "#   x0 x1 y e", "# X0 X1 Y0 Y1 E0 E1", '
+                    '"<X> <Y> <E>", "<X0> <X1> <Y> <E>"...')
+        if dim != num_cols:
+            raise ParsingError('Could not match header to columns.')
+    else:
+        cols['x'] = [0]
+        cols['y'] = [1]
+        if dim == 3:
+            cols['e'] = [2]
+        elif dim != 2:
+            raise ParsingError(
+                'Cannot infer size of inputs and outputs in datafile. '
+                'Headers are required when not using 1D inputs and outputs.')
+
+    if not cols['x'] or not cols['y']:
+        raise ParsingError('Input files need both X and Y values.')
+    if cols['e'] and len(cols['y']) != len(cols['e']):
+        raise ParsingError('Error must be of the same dimension as Y.')
+
     data_points = np.zeros((len(data_text) - first_row, dim))
 
     for idx, line in enumerate(data_text[first_row:]):
@@ -494,10 +623,21 @@ def _get_data_points(data_file_path):
         try:
             point = [float(val) for val in point_text]
         except ValueError:
-            point = [np.nan for val in point_text]
+            point = [np.nan for _ in point_text]
         data_points[idx, :] = point
 
     # Strip all np.nan entries
     data_points = data_points[~np.isnan(data_points[:, 0]), :]
 
-    return data_points
+    # Split into x, y, and e
+    data = {key: data_points[:, cols[key]]
+            for key in ['x', 'y']}
+    if cols['e']:
+        data['e'] = data_points[:, cols['e']]
+
+    # Flatten if the columns are 1D
+    for key, col in cols.items():
+        if len(col) == 1:
+            data[key] = data[key].flatten()
+
+    return data
diff --git a/fitbenchmarking/parsing/fitting_problem.py b/fitbenchmarking/parsing/fitting_problem.py
index 05020b93..febdf421 100644
--- a/fitbenchmarking/parsing/fitting_problem.py
+++ b/fitbenchmarking/parsing/fitting_problem.py
@@ -96,6 +96,11 @@ class FittingProblem:
         #: Callable function for the Jacobian
         self.jacobian = None
 
+        #: *bool*
+        #: Whether the function has been wrapped to reduce the dimension of x
+        #: on function calls
+        self.multivariate = False
+
     def eval_model(self, params, **kwargs):
         """
         Function evaluation method
diff --git a/fitbenchmarking/results_processing/plots.py b/fitbenchmarking/results_processing/plots.py
index 26fca7f4..9dffdd83 100644
--- a/fitbenchmarking/results_processing/plots.py
+++ b/fitbenchmarking/results_processing/plots.py
@@ -4,8 +4,11 @@ guess plot.
 """
 import os
 import matplotlib
+
+from fitbenchmarking.utils.exceptions import PlottingError
+
 matplotlib.use('Agg')
-# pylint: disable=wrong-import-position
+# pylint: disable=ungrouped-imports,wrong-import-position,wrong-import-order
 import matplotlib.pyplot as plt  # noqa: E402
 
 
@@ -17,6 +20,9 @@ class Plot:
     def __init__(self, best_result, options, figures_dir):
         self.cost_func = best_result.cost_func
         self.problem = self.cost_func.problem
+        if self.problem.multivariate:
+            raise PlottingError(
+                'Plots cannot be generated for multivariate problems')
         self.options = options
 
         self.result = best_result
@@ -73,7 +79,8 @@ class Plot:
         """
         Close the matplotlib figure
         """
-        plt.close(self.fig)
+        if not self.problem.multivariate:
+            plt.close(self.fig)
 
     def format_plot(self):
         """
diff --git a/fitbenchmarking/utils/exceptions.py b/fitbenchmarking/utils/exceptions.py
index 6a2d7794..c71c6a52 100644
--- a/fitbenchmarking/utils/exceptions.py
+++ b/fitbenchmarking/utils/exceptions.py
@@ -189,3 +189,11 @@ class MissingBoundsError(FitBenchmarkException):
                     'are required to use this ' \
                     'software.'
     error_code = 20
+
+
+class PlottingError(FitBenchmarkException):
+    """
+    Indicates an error during plotting results
+    """
+    class_message = 'An error occurred during plotting.'
+    error_code = 21


Test patch:
diff --git a/fitbenchmarking/core/tests/test_results_output.py b/fitbenchmarking/core/tests/test_results_output.py
index b24de5d2..3e044ea4 100644
--- a/fitbenchmarking/core/tests/test_results_output.py
+++ b/fitbenchmarking/core/tests/test_results_output.py
@@ -2,18 +2,26 @@
 Results output tests
 """
 
-from __future__ import (absolute_import, division, print_function)
-import unittest
+from __future__ import absolute_import, division, print_function
+
 import os
 import shutil
+import unittest
+from tempfile import TemporaryDirectory
+from unittest import mock
+
 import numpy as np
 
+from fitbenchmarking.core.results_output import (create_directories,
+                                                 create_plots,
+                                                 create_problem_level_index,
+                                                 preproccess_data,
+                                                 save_results)
 from fitbenchmarking.cost_func.nlls_cost_func import NLLSCostFunc
 from fitbenchmarking.jacobian.scipy_jacobian import Scipy
 from fitbenchmarking.parsing.fitting_problem import FittingProblem
+from fitbenchmarking.utils.exceptions import PlottingError
 from fitbenchmarking.utils.fitbm_result import FittingResult
-from fitbenchmarking.core.results_output import create_directories, \
-    save_results, preproccess_data, create_plots, create_problem_level_index
 from fitbenchmarking.utils.options import Options
 
 
@@ -240,11 +248,13 @@ class CreatePlotsTests(unittest.TestCase):
         """
         Setting up paths and results folders
         """
+        self.tempdir = TemporaryDirectory()
+        self.dirname = os.path.join(self.tempdir.name, 'figures_dir')
         self.results, self.options, self.min_chi_sq, self.min_runtime = \
             generate_mock_results()
         self.best_results = preproccess_data(self.results)
 
-    @unittest.mock.patch('fitbenchmarking.results_processing.plots.Plot')
+    @mock.patch('fitbenchmarking.results_processing.plots.Plot')
     def test_create_plots_with_params(self, plot_mock):
         """
         Tests for create_plots where the results object params are not None
@@ -252,7 +262,7 @@ class CreatePlotsTests(unittest.TestCase):
         expected_plot_initial_guess = "initial_guess"
         expected_plot_best = "plot_best"
         expected_plot_fit = "plot_fit"
-        plot_instance = unittest.mock.MagicMock()
+        plot_instance = mock.MagicMock()
         plot_instance.plot_initial_guess.return_value = \
             expected_plot_initial_guess
         plot_instance.plot_best.return_value = expected_plot_best
@@ -261,7 +271,7 @@ class CreatePlotsTests(unittest.TestCase):
         # Return the above created `plot_instance`
         plot_mock.return_value = plot_instance
         create_plots(self.options, self.results,
-                     self.best_results, "figures_dir")
+                     self.best_results, self.dirname)
         for result, best_result in zip(self.results, self.best_results):
             # Check initial guess is correctly set in results
             assert best_result.start_figure_link == expected_plot_initial_guess
@@ -273,7 +283,7 @@ class CreatePlotsTests(unittest.TestCase):
             assert all(r.figure_link == expected_plot_fit
                        if not r.is_best_fit else True for r in result)
 
-    @unittest.mock.patch('fitbenchmarking.results_processing.plots.Plot')
+    @mock.patch('fitbenchmarking.results_processing.plots.Plot')
     def test_create_plots_without_params(self, plot_mock):
         """
         Tests for create_plots where the results object params are None
@@ -283,14 +293,14 @@ class CreatePlotsTests(unittest.TestCase):
             for r in result:
                 r.params = None
         expected_plot_initial_guess = "initial_guess"
-        plot_instance = unittest.mock.MagicMock()
+        plot_instance = mock.MagicMock()
         plot_instance.plot_initial_guess.return_value = \
             expected_plot_initial_guess
 
         # Return the above created `plot_instance`
         plot_mock.return_value = plot_instance
         create_plots(self.options, self.results,
-                     self.best_results, "figures_dir")
+                     self.best_results, self.dirname)
         for result, best_result in zip(self.results, self.best_results):
             # Check initial guess is correctly set in results
             assert best_result.start_figure_link == expected_plot_initial_guess
@@ -309,6 +319,23 @@ class CreatePlotsTests(unittest.TestCase):
             assert all(r.figure_error == expected_message
                        if not r.is_best_fit else True for r in result)
 
+    def test_plot_error(self):
+        """
+        Test that errors are passed correctly when the plotting fails.
+        """
+        with mock.patch(
+                'fitbenchmarking.results_processing.plots.Plot',
+                side_effect=PlottingError('Faked plot')):
+
+            create_plots(self.options, self.results,
+                         self.best_results, self.dirname)
+
+        expected = 'An error occurred during plotting.\nDetails: Faked plot'
+        for result, best_result in zip(self.results, self.best_results):
+            self.assertEqual(best_result.figure_error, expected)
+            for r in result:
+                self.assertEqual(r.figure_error, expected)
+
 
 class CreateProblemLevelIndex(unittest.TestCase):
     """
diff --git a/fitbenchmarking/parsing/tests/fitbenchmark/data_files/simplified_anac.txt b/fitbenchmarking/parsing/tests/fitbenchmark/data_files/simplified_anac.txt
new file mode 100644
index 00000000..fbc670d5
--- /dev/null
+++ b/fitbenchmarking/parsing/tests/fitbenchmark/data_files/simplified_anac.txt
@@ -0,0 +1,101 @@
+# x0 x1 y0 y1
+0.0 0.0 0.0 0.0
+0.1 0.0 0.10504078546698457 0.10165363692657119
+0.2 0.0 0.21007534074698186 0.2031790402448081
+0.3 0.0 0.3150975048739934 0.30444796461856505
+0.4 0.0 0.4201010653690826 0.40533224556560454
+0.5 0.0 0.5250798197898161 0.5057037913564505
+0.6 0.0 0.6300275688036315 0.6054346155095812
+0.7 0.0 0.734938116712285 0.7043968619896837
+0.8 0.0 0.8398052719466603 0.8024628309816272
+0.9 0.0 0.9446228475860821 0.8995050047845863
+0.0 0.1 0.010167501072660692 0.10504181528345628
+0.1 0.1 0.11520816619043839 0.20669202952440668
+0.2 0.1 0.22024241723004512 0.3082075969275837
+0.3 0.1 0.3252640519849578 0.4094602845610277
+0.4 0.1 0.4302668740667119 0.5103219252379961
+0.5 0.1 0.5352446827506092 0.6106644296624175
+0.6 0.1 0.6401912788365867 0.7103598154365122
+0.7 0.1 0.745100466742453 0.8092802325004727
+0.8 0.1 0.8499660549819773 0.9072979884984216
+0.9 0.1 0.9547818567284064 1.0042855744823573
+0.0 0.2 0.020335003175232274 0.21008357142901965
+0.1 0.2 0.12537554780032212 0.31172996132152375
+0.2 0.2 0.23040947207805135 0.4132352785205733
+0.3 0.2 0.3354305722634268 0.5144713064866596
+0.4 0.2 0.4404326452292696 0.6153098809167199
+0.5 0.2 0.545409492462552 0.715622918823024
+0.6 0.2 0.6503549160123503 0.8152824432010832
+0.7 0.2 0.7552627253144161 0.9141606104337654
+0.8 0.2 0.860126728824208 1.0121297345455993
+0.9 0.2 0.9649407398717987 1.1090623145406784
+0.0 0.3 0.030502503144487353 0.3151252828614024
+0.1 0.3 0.135542917809322 0.41676740840473453
+0.2 0.3 0.24057650392140434 0.5182620527485791
+0.3 0.3 0.34559705815599856 0.6194809990172104
+0.4 0.3 0.4505983785115274 0.7202960860814489
+0.5 0.3 0.5555742635648265 0.8205792341387669
+0.6 0.3 0.660518517028101 0.9202024723952426
+0.7 0.3 0.7654249451328946 1.0190379633241207
+0.8 0.3 0.8702873568474966 1.1169580289904693
+0.9 0.3 0.9750995678210959 1.2138351778856356
+0.0 0.4 0.040670000980946926 0.4201669073139179
+0.1 0.4 0.14571027559924832 0.5218043396586571
+0.2 0.4 0.2507435131749953 0.6232878887340036
+0.3 0.4 0.3557635107608575 0.724489330880942
+0.4 0.4 0.46076406641555795 0.8252805080774882
+0.5 0.4 0.5657389801932646 0.9255333452930968
+0.6 0.4 0.670682054078916 1.0251198762263483
+0.7 0.4 0.7755870936943089 1.1239122699602395
+0.8 0.4 0.8804479100429643 1.2217828570363216
+0.9 0.4 0.9852583174911912 1.318604154343392
+0.0 0.5 0.05083749604393753 0.5252084116969771
+0.1 0.5 0.15587762055384163 0.6268407239674826
+0.2 0.5 0.26091049922215354 0.7283127553657667
+0.3 0.5 0.36592992979010747 0.8294962711016765
+0.4 0.5 0.47092971037760645 0.9302631163145931
+0.5 0.5 0.5759036411227708 1.0304852203036463
+0.6 0.5 0.6808455248161276 1.1300346225721998
+0.7 0.5 0.7857491675232996 1.2287834988318327
+0.8 0.5 0.8906083774976706 1.3266041861741757
+0.9 0.5 0.9954169711633349 1.4233692115561154
+0.0 0.6 0.06100498777508606 0.6302497635317875
+0.1 0.6 0.1660449520571678 0.7318765302154931
+0.2 0.6 0.2710774614468502 0.8333366215329318
+0.3 0.6 0.3760963146276678 0.9345017885759648
+0.4 0.6 0.48109530978158277 1.0352438796994912
+0.5 0.6 0.5860682471315515 1.1354348285864375
+0.6 0.6 0.6910089295757329 1.2349466802891995
+0.7 0.6 0.7959111633207678 1.3336516172370938
+0.8 0.6 0.9007687585141851 1.4314219851927588
+0.9 0.6 1.0055755287400452 1.5281303185317778
+0.0 0.7 0.07117247562078514 0.7352909308059323
+0.1 0.7 0.17621226949338747 0.8369117272871431
+0.2 0.7 0.281244399233244 0.9383594561248582
+0.3 0.7 0.3862626646577351 1.0395058522007794
+0.4 0.7 0.49126086401176233 1.1402227671394631
+0.5 0.7 0.5962327976040013 1.2403821390617493
+0.6 0.7 0.7011722684411265 1.3398560186231145
+0.7 0.7 0.8060730828610705 1.4385165950190606
+0.8 0.7 0.9109290511654 1.5362362219392347
+0.9 0.7 1.015733988250671 1.632887443459473
+0.0 0.8 0.08133995901531735 0.8403318818235657
+0.1 0.8 0.18637957224669838 0.9419462840670852
+0.2 0.8 0.29141131196556785 1.0433812280312489
+0.3 0.8 0.396428979264614 1.144508430873576
+0.4 0.8 0.5014263724525627 1.2451997475424186
+0.5 0.8 0.6063972919246897 1.3453271206506343
+0.6 0.8 0.7113355407970693 1.4447626065108299
+0.7 0.8 0.8162349255398094 1.5433784011386522
+0.8 0.8 0.921089256609396 1.6410468662046185
+0.9 0.8 1.0258923490800147 1.7376405549235194
+0.0 0.9 0.09150743738080391 0.94537258508822
+0.1 0.9 0.19654685970131608 1.0469801694401861
+0.2 0.9 0.3015781990280897 1.148401906142172
+0.3 0.9 0.40659525783266126 1.2495094934923188
+0.4 0.9 0.5115918344884692 1.3501747898169227
+0.5 0.9 0.6165617294782703 1.4502697422749546
+0.6 0.9 0.7214987460284217 1.5496664128901894
+0.7 0.9 0.8263966907420895 1.6482370045523802
+0.8 0.9 0.9312493742315624 1.7458538869667701
+0.9 0.9 1.0360506117495354 1.842389622540845
diff --git a/fitbenchmarking/parsing/tests/fitbenchmark/function_evaluations.json b/fitbenchmarking/parsing/tests/fitbenchmark/function_evaluations.json
index 64dc0d0b..b83668c3 100644
--- a/fitbenchmarking/parsing/tests/fitbenchmark/function_evaluations.json
+++ b/fitbenchmarking/parsing/tests/fitbenchmark/function_evaluations.json
@@ -21,4 +21,8 @@
                   [2.1, [1.0, 2.0, 3.0, 4.0, 5.0, 6.0], 5.2],
                   [2.1, [1.1, 1.2, 1.3, 1.4, 1.5, 1.6], 3.61981077919],
                   [2.1, [-1.0, 1.0, -1.0, 1.0, -1.0, 1.0], 1.08867480177],
-                  [2.1, [4.3, 2.1, -0.1, 80.0, 20.1, 15.6], 8.71]]}
\ No newline at end of file
+                  [2.1, [4.3, 2.1, -0.1, 80.0, 20.1, 15.6], 8.71]],
+"simplified_anac.txt": [[0, [0.0, 0.0], [0.0, 0.0]],
+                        [55, [1.0, 1.0], [0.55397341, 0.58186415]],
+                        [38, [1.0, 1.0], [0.83940457, 0.49138703]],
+                        [38, [0.1, 3.0], [0.84651695, 0.63981776]]]}
\ No newline at end of file
diff --git a/fitbenchmarking/parsing/tests/fitbenchmark/functions/simplified_anac.py b/fitbenchmarking/parsing/tests/fitbenchmark/functions/simplified_anac.py
new file mode 100644
index 00000000..d64ed982
--- /dev/null
+++ b/fitbenchmarking/parsing/tests/fitbenchmark/functions/simplified_anac.py
@@ -0,0 +1,28 @@
+import numpy as np
+
+
+def simplified_anac(t, x, gamma, mu):
+    """
+    Calculates the rhs of the system defined by:
+
+    x'[0] = x[1]
+    x'[1] = gamma*x[0]+2*mu*x[0]^3
+
+    Args:
+        t (float): The time to evaluate at
+        x (np.ndarray): The x vector (current location)
+        gamma (float): The value in the above equations
+        mu (float): The value in the above equations
+    """
+    if len(x.shape) == 1:
+        return np.array([
+            x[1],
+            gamma * x[0] + 2 * mu * x[0]**3
+        ])
+    elif len(x.shape) == 2:
+        return np.array([
+            x[:, 1],
+            gamma * x[:, 0] + 2 * mu * x[:, 0]**3
+        ])
+    else:
+        raise ValueError('x is the wrong shape in simplified_anac call.')
diff --git a/fitbenchmarking/parsing/tests/fitbenchmark/simplified_anac.txt b/fitbenchmarking/parsing/tests/fitbenchmark/simplified_anac.txt
new file mode 100644
index 00000000..ff0647a3
--- /dev/null
+++ b/fitbenchmarking/parsing/tests/fitbenchmark/simplified_anac.txt
@@ -0,0 +1,6 @@
+# Fitbenchmark Problem
+software = 'ivp'
+name = 'Simplified ANAC'
+description = 'A simplified version of the axisymetric non-axisymmetric coupled system generated to test the ivp parser. Exact results should be 10, -0.1.'
+input_file = 'simplified_anac.txt'
+function = 'module=functions/simplified_anac,func=simplified_anac,step=0.1,gamma=15,mu=-0.5'
diff --git a/fitbenchmarking/results_processing/tests/test_plots.py b/fitbenchmarking/results_processing/tests/test_plots.py
index f0f76eb9..53c3b400 100644
--- a/fitbenchmarking/results_processing/tests/test_plots.py
+++ b/fitbenchmarking/results_processing/tests/test_plots.py
@@ -12,11 +12,12 @@ except ImportError:
     from backports.tempfile import TemporaryDirectory
 
 from fitbenchmarking.cost_func.nlls_cost_func import NLLSCostFunc
-from fitbenchmarking.parsing.fitting_problem import FittingProblem
 from fitbenchmarking.jacobian.scipy_jacobian import Scipy
+from fitbenchmarking.parsing.fitting_problem import FittingProblem
+from fitbenchmarking.results_processing import plots
+from fitbenchmarking.utils.exceptions import PlottingError
 from fitbenchmarking.utils.fitbm_result import FittingResult
 from fitbenchmarking.utils.options import Options
-from fitbenchmarking.results_processing import plots
 
 
 class PlotTests(unittest.TestCase):
@@ -119,6 +120,17 @@ class PlotTests(unittest.TestCase):
         path = os.path.join(self.dir.name, file_name)
         self.assertTrue(os.path.exists(path))
 
+    def test_multivariate_plot(self):
+        """
+        Test that the plotting fails gracefully for multivariate problems.
+        """
+        self.fr.cost_func.problem.multivariate = True
+
+        with self.assertRaises(PlottingError):
+            self.plot = plots.Plot(best_result=self.fr,
+                                   options=self.opts,
+                                   figures_dir=self.dir.name)
+
 
 if __name__ == "__main__":
     unittest.main()