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22 Author: Jean-Philippe Argaud, jean-philippe.argaud@edf.fr, EDF R&D
24 .. _section_methodology:
26 ================================================================================
27 **[DocT]** Methodology to elaborate a Data Assimilation or Optimization study
28 ================================================================================
30 This section presents a generic methodology to build a Data Assimilation or
31 Optimization study. It describes the conceptual steps to build autonomously this
32 study. It is not dependent of any tool, but the ADAO module allows to set up
33 efficiently such a study, following :ref:`section_using`. Notations are the same
34 than the ones used in :ref:`section_theory`.
36 Logical procedure for a study
37 -----------------------------
39 For a generic Data Assimilation or Optimization study, the main methodological
40 steps can be the following:
42 - :ref:`section_m_step1`
43 - :ref:`section_m_step2`
44 - :ref:`section_m_step3`
45 - :ref:`section_m_step4`
46 - :ref:`section_m_step5`
47 - :ref:`section_m_step6`
48 - :ref:`section_m_step7`
50 Each step will be detailed in the next sections.
52 Detailed procedure for a study
53 ------------------------------
57 STEP 1: Specifying the resolution of the physical problem and the parameters to adjust
58 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
60 An essential knowledge about the studied physical system is the numerical
61 simulation. It is often available through calculation case(s), and symbolized as
62 a **simulation operator** (previously included in :math:`H`). A standard
63 calculation case gathers model hypothesis, numerical implementation, computing
64 capacities, etc. in order to represent the behavior of the physical system.
65 Moreover, a calculation case is characterized for example by its computing time
66 and memory requirements, its data and results sizes, etc. The knowledge of all
67 these elements is of primary importance in the setup of the data assimilation or
70 To state correctly the study, one have also to choose the optimization unknowns
71 in the simulation. Frequently, this can be through physical models of which the
72 parameters can be adjusted. Moreover, it is always useful to add some knowledge
73 of sensitivity, for example of the numerical simulation to the parameters that
74 can be adjusted. More general elements, like stability or regularity of the
75 simulation with respect to the unknown inputs, are also of great interest.
77 Technically, optimization methods can require gradient information of the
78 simulation with respect to unknowns. In this case, explicit gradient code has to
79 be given, or numerical gradient has to be tuned. Its quality is in relation with
80 the simulation code stability or regularity, and it has to be checked carefully
81 before establishing optimization calculations. Specific conditions has to be
82 used for these checkings.
84 An **observation operator** is always required, in complement of the simulation
85 operator. This observation operator, denoted as :math:`H` or included in, has to
86 convert the numerical simulation outputs into something that is directly
87 comparable to observations. It is an essential operator, as it is the practical
88 way to compare simulations and observations. It is usually done by sampling,
89 projection or integration, of the simulation outputs, but it can be more
90 complicated. Often, because the observation operator directly follows the
91 simulation one in simple data assimilation schemes, this observation operator
92 heavily use the postprocessing and extraction capacities of the simulation code.
96 STEP 2: Specifying the criteria for physical results qualification
97 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
99 Because the studied system are real physical ones, it is of great importance to
100 express the **physical information that can help to qualify a simulated system
101 state**. There are two main types of such information that leads to criteria
102 allowing qualification and quantification of optimization results.
104 First, coming from mathematical or numerical knowledge, a lot of standard
105 criteria allow to qualify, relatively or in absolute, the interest of an
106 optimized state. For example, balance equations or equation closing conditions
107 are good complementary measures of system state quality. Well chosen criteria
108 like RMS, RMSE, field extrema, integrals, etc. are also of great interest to
109 assess optimized state quality.
111 Second, coming from physical or experimental knowledge, valuable information can
112 be obtained from the meaning of optimized results. In particular, physical
113 validity or technical interest can assess of the numerical results of the
116 In order to get helpful information from these two main types of knowledge, it
117 is recommended, if possible, to build numerical criteria to ease the assessment
118 of global quality of numerical results.
122 STEP 3: Identifying and describe the available observations
123 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
125 As the second main source of knowledge of the physical system to be studied, the
126 **observations, or measures,** denoted as :math:`\mathbf{y}^o`, has to be
127 properly described. The quality of the measures, their intrinsic errors, their
128 special features, are worth to know, in order to introduce these information in
129 the data assimilation or optimization calculations.
131 The observations have not only to be available, but also to be efficiently
132 introduced in the numerical framework of calculation or optimization. So the
133 computing environment giving access to the observations is of great importance
134 to smooth the effective use of various measures and sources of measures, and to
135 promote extensive tests using measures. Computing environment covers
136 availability in database or not, data formats, application interfaces, etc.
140 STEP 4: Specifying the DA/Optimization modeling elements (covariances, background...)
141 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
143 Additional Data Assimilation or Optimization modeling elements allows to
144 improve information about the fine physical representation of the studied
147 The *a-priori* knowledge of the system state can be modelized using the
148 **background**, denoted as :math:`\mathbf{x}^b`, and the **background error
149 covariance matrix**, denoted as :math:`\mathbf{B}`. These information are
150 extremely important to complete, in particular in order to obtain meaningful
151 results from Data Assimilation.
153 On the other hand, information on observation errors can be used to fill the
154 **observation error covariance matrix** denoted as :math:`\mathbf{R}`. As for
155 :math:`\mathbf{B}`, it is recommended to use carefully checked data to fill
156 these covariance matrices.
158 In case of dynamic simulation, one has to define also an **evolution operator**
159 and the associated **evolution error covariance matrix**.
163 STEP 5: Choosing the optimization algorithm and its parameters
164 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
166 Data Assimilation or Optimization requires to solve an optimization problem,
167 more often modelized as a minimization problem. Depending on the availability of
168 the gradient of the cost function with respect to the optimization parameters,
169 recommended class of methods are different. Variational or locally linearized
170 minimization methods requires this gradient. On the opposite, derivative free
171 optimization methods doesn't requires this gradient, but present usually a
172 really higher computational price.
174 Inside a class of optimization methods, for each method, there is usually a
175 trade-off between the *"generic capacity of the method"* and its *"particular
176 performance on a specific problem"*. Most generic methods, as for example
177 variational minimization using the :ref:`section_ref_algorithm_3DVAR`, present
178 remarkable numerical properties of efficiency, robustness and reliability, that
179 leads to recommend it independently of the problem to solve. Moreover, it is
180 generally difficult to tune the parameters of an optimization method, so the
181 most robust one is often the one with the less parameters. Finally, at least for
182 the beginning, it is recommended to use the most generic methods and to change
183 the less possible the known default parameters.
187 STEP 6: Conducting the optimization calculations and get the results
188 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
190 After setting up the Data Assimilation or Optimization study, the calculation
191 has to be done in an efficient way.
193 Because optimizing usually involves a lot of elementary physical simulation of
194 the system, the calculations are often done in Hight Performance Computing (HPC)
195 environment to reduce the overall user time. Even if the optimization problem is
196 small, the physical system simulation time can be long, requiring efficient
197 computing resources. These requirements have to be taken into account early
198 enough in the study procedure to be satisfied without needing too much effort.
200 For the same reason of hight computing requirements, it is important to
201 carefully prepare the outputs of the optimization procedure. The optimal state
202 is the main required information, but a lot of other special information can be
203 obtained during or at the end of the optimization process: error evaluations,
204 intermediary states, quality indicators, etc. All these information, sometimes
205 requiring additional processing, have to be known and asked at the beginning of
206 the optimization process.
210 STEP 7: Exploiting the results and qualify their physical properties
211 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
213 Once getting the results, they have to be interpreted in terms of physical and
214 numerical meaning. Even if the optimization calculation always give a new
215 optimal state at least as good as the *a priori* one, and most hopefully better,
216 this optimal state has for example to be checked with respect to the quality
217 criteria identified when :ref:`section_m_step2`. This can lead to physical,
218 statistical or numerical studies in order to assess the interest of the optimal
219 state to represent the physical system.
221 Besides this analysis that has to be done for each Data Assimilation or
222 Optimization study, it can be worth to exploit the optimization results as part
223 of a more complete study of the physical system of interest.
