CN110298375A - The parallel gradient of solving condition nonlinear optimal perturbation defines data processing method - Google Patents
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Abstract
The present invention relates to a kind of parallel gradients of solving condition nonlinear optimal perturbation to define data processing method, belongs to computer and Atmosphere and Ocean subject crossing field, can be used for the predictability research of the Numerical Weather and climatic phenomenon in Atmosphere and Ocean field.It is to define method using gradient to solve gradient information of the objective function about optimized variable instead of adjoint mode that solution CNOP parallel gradient of the invention, which defines method, and then the calculating process parallel optimization of gradient information being used by the constrained optimization method based on gradient information by the MPI concurrent technique of computer field --- SPG2 gradient project algorithms Optimization Solution obtains CNOP.Compared with prior art, the present invention has many advantages, such as that accuracy height, solving speed are fast.
Description
Technical field
It is non-linear most more particularly, to a kind of solving condition the present invention relates to computer and Atmosphere and Ocean subject crossing field
The parallel gradient of excellent disturbance defines data processing method.
Background technique
Condition nonlinear optimal perturbation (CNOP) refers under certain physical constraint condition have at the forecast moment maximum non-
A kind of initial disturbance of development of linear, what this method had been widely used in inquiring into weather and climatic study predictive asks
Topic.
Mathematically, the solution of CNOP belongs to the function optimization problem of belt restraining, and Atmosphere and Ocean field is generally adopted at present
It is solved with the constrained optimization method (such as SPG, SQP, L-BFGS) for providing gradient information based on adjoint mode.It is practical
On, defining direct solution objective function about the gradient of optimized variable using gradient is most basic, simplest method, but
The complexity of numerical model is generally higher in Atmosphere and Ocean science, and dimension is substantially all in 10^3 or more.In view of asking for calculation amount
Topic, Atmosphere and Ocean scientific domain are based on the corresponding adjoint mode of numerical model generally to solve gradient information, this makes CNOP's
Solution is highly dependent on adjoint mode, and the exploitation and verifying of adjoint mode generally require to consume huge workload, this is big
The extensive use of CNOP is limited greatly.In recent years, widely available with computer and the relevant technologies, such as concurrent technique, dimensionality reduction
Technology etc. defines the excessive problem of the direct calculation amount for carrying out gradient solution using gradient, it is already possible to by using computer
The relevant technologies solve.The present invention provides a kind of parallel gradient for Efficient Solution CNOP and defines method, it is intended to promote the side CNOP
Application of the method in Numerical Weather and the research of weather predictability.
Summary of the invention
It is an object of the present invention to overcome the above-mentioned drawbacks of the prior art and provide a kind of solving condition is non-thread
The parallel gradient of property Optimal Disturbance defines data processing method.
The purpose of the present invention can be achieved through the following technical solutions:
A kind of parallel gradient of solving condition nonlinear optimal perturbation defines data processing method, comprising the following steps:
Step 1: initializing related optimized variable；
Step 2: method solution being defined using gradient and obtains condition nonlinear optimal perturbation optimal value result；
Step 3: loop iteration step 2 simultaneously judges whether to meet stopping iterated conditional；
Step 4: the condition nonlinear optimal perturbation optimal value of original solution room is exported when meeting and stopping iterated conditional
As a result.
Further, the step 2 specifically include it is following step by step:
Step 21: gradient of the objective function of solving condition nonlinear optimal perturbation about optimized variable；
Step 22: the mesh of optimal value result can be converted into along the direction that gradient declines search using SPG2 gradient project algorithms
Scalar functions minimum value.
Further, gradient of the objective function in the step 21 about optimized variable, its calculation formula is:
In formula, f ' (X) indicates gradient of the objective function about optimized variable,Indicate optimization
First-order partial derivative of each variable of variable about objective function.
Further, calculation formula of each variable of the optimized variable about the first-order partial derivative of objective function are as follows:
In formula, Δ x indicates Delta, x1,…,xi,…,xnIndicate all optimized variables.
Further, the optimization of the gradient in the step 21, which is calculated, carries out parallel computation using MPI technology, described parallel
The MS master-slave process that uses is calculated, the host process in the MS master-slave process is for being responsible for the distribution of task and the collection of result and will appoint
Business is divided equally, if task can not timesharing by be calculated as subprocess distribute task.
Further, when the dimension of numerical model needs dimensionality reduction, in the data processing method further include: excellent to what is obtained
The sample data for changing variable carries out ladder in feature space using after singular value decomposition algorithm or Principal Component Analysis Algorithm progress dimensionality reduction
The solution and optimizing of degree.
Further, the stopping iterated conditional in the step 3 are as follows: whether be more than greatest iteration step number or optimal value whether
It is remained unchanged more than setting number.
Compared with prior art, the invention has the following advantages that
(1) precision is high, and it is to define method using gradient to replace with mould that the present invention, which solves CNOP parallel gradient and defines method,
Formula solves gradient information of the objective function about optimized variable, and by the MPI concurrent technique of computer field by gradient information
Calculating process parallel optimization, then use the constrained optimization method based on gradient information --- SPG2 gradient project algorithms optimization
Solution obtains CNOP, and the accuracy of solving result is high
(2) solving speed is fast, and it is that method is defined using gradient instead of companion that the present invention, which solves CNOP parallel gradient and defines method,
Gradient information of the objective function about optimized variable is solved with mode, and by the MPI concurrent technique of computer field by gradient
The calculating process parallel optimization of information, then uses the constrained optimization method based on gradient information --- SPG2 gradient project algorithms
Optimization Solution obtains CNOP, and in addition to this, inventive algorithm is provided with parallel MPI master also directed to the calculating process that gradient defines
From process, in addition, also introducing singular value decomposition algorithm SVD or Principal Component Analysis Algorithm in the present invention if data dimension is excessively high
PCA carries out dimensionality reduction to luv space data and is converted back to luv space from feature space when finally solving result to ensure
The quick degree of integrated solution speed.
Detailed description of the invention
Fig. 1 is the flow chart that parallel gradient of the present invention defines method solving condition nonlinear optimal perturbation.
Specific embodiment
Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete
Site preparation description, it is clear that described embodiment is a part of the embodiments of the present invention, rather than whole embodiments.Based on this hair
Embodiment in bright, those of ordinary skill in the art's every other reality obtained without making creative work
Example is applied, all should belong to the scope of protection of the invention.
Embodiment
As shown in Figure 1 it is the idiographic flow schematic diagram of the method for the present invention, now wherein step is specifically described as follows:
A. mathematically, gradient refers to single order local derviation vector of the function of many variables about multivariable.Assuming that objective function hair f
(X) it indicates, optimized variable is the vector of n dimension, is expressed as X (x1,x2,x3,…,xi,…,xn), i=1,2,3 ..., n, then excellent
Change variable per one-dimensional xiFirst-order partial derivative about objective function f (X) is represented byAnd so on, then obtain following formula
Gradient vector f ' (X), it may be assumed that
In formula, f ' (X) indicates gradient of the objective function about optimized variable,Indicate optimization
First-order partial derivative of each variable of variable about objective function.
B. per one-dimensional optimized variable xiSingle order local derviation about objective function f (X) is calculated using the definition of derivative, root
According to definition optimized variable xiSingle order local derviation be equal to when objective function f (X) independent variable xiOn certain point increase increment Delta x
When, the increment f (x of objective function output valve1,…,xi+Δx,…,xn)-f(x1,…,xi,…,xn) with independent variable increment Delta x's
The limit of the ratio when Δ x tends to 0, formula are expressed as follows, and wherein Δ x is a small increment:
In formula, Δ x indicates Delta, x1,…,xi,…,xnIndicate all optimized variables.
C. when carrying out CNOP solution, target function value needs logarithm mode to be integrated, if Δ x value is too small, that
It will lead to numerical model not develop, i.e. f (x1,…,xi+Δx,…,xn)-f(x1,…,xi,…,xn)=0, then finally
The gradient being calculated is 0 vector.And Δ x value is excessive, the definition with derivative is disagreed.In order to obtain most suitable Δ x value,
The value of Δ x is adaptively adjusted by the value of optimized variable, and specific scheme is true by following formula progress adaptability
It is fixed.
D. in Atmosphere and Ocean scientific domain, the optimized variable dimension that CNOP solves the objective function being related to is very high, gradient
The dimension of vector and the dimension of optimized variable are identical, serial to solve the excessive problem of gradient vector calculation amount.But gradient vector
It is mutually independent when the calculating of each dimension there is no dependence.The calculating of gradient vector can be carried out with MPI technology parallel
Change to improve computational efficiency.Information is carried out by mpi_send and mpi_recv function between each process during MPI is parallel
Interaction.
E. gradient vector parallel computation strategy uses the way to manage of MS master-slave process on the whole, and host process is responsible for task
Distribution and result collection.Gradient vector is calculated as a calculating task per one-dimensional, it is assumed that gradient vector is that n is tieed up, always into
Number of passes is PN, and n is indicated divided by the remainder of PN with rd, and n is indicated divided by the commercial qu of PN.If rd=0, then all processes are divided equally
It is fitted on qu task；If rd ≠ 0, preceding rd subprocess distributes qu+1 task, remaining subprocess and host process point
With qu task.
F. if the dimension of numerical model is very high, even calculation amount is also very big after parallel, at this moment can first make
Dimensionality reduction is carried out with singular value decomposition algorithm SVD/ Principal Component Analysis Algorithm PCA method.The sample data of optimized variable is obtained first,
Then dimensionality reduction is carried out using Principal Component Analysis Algorithm PCA/ singular value decomposition algorithm SVD, and selected characteristic value accounting is big and accumulative
Characteristic value accounting is more than 90% preceding PCs feature vector, as feature space.
G. it is defined after objective function is calculated about the gradient information of optimized variable in method using gradient, reuses SPG2 ladder
It spends projection algorithm and obtains CNOP in solution room Optimization Solution.SPG2 gradient project algorithms are a kind of algorithms for solving minimum value,
If optimization problem is not minimum problems.It can carry out the Solve problems that certain processing is converted to minimum value.SPG2 gradient projection
Algorithm needs to provide gradient information of the objective function about optimized variable, solves to obtain target using the definition of gradient in the present invention
Gradient information of the function about optimized variable.
H. parallel gradient defines the process that method is an iteration optimizing, and iteration can all record optimal solution each time, if repeatedly
Generation number is more than greatest iteration step number (being denoted as maxIter) or the optimal value that finds is more than to remain unchanged for limits times, optimizing
Terminate, algorithm exports to obtain optimal value, if having carried out dimensionality reduction, needs to revert to optimal value original solution space and obtains CNOP, also
Former process is carried out using eigenvectors matrix.
The above description is merely a specific embodiment, but scope of protection of the present invention is not limited thereto, any
Those familiar with the art in the technical scope disclosed by the present invention, can readily occur in various equivalent modifications or replace
It changes, these modifications or substitutions should be covered by the protection scope of the present invention.Therefore, protection scope of the present invention should be with right
It is required that protection scope subject to.
Claims (7)
1. a kind of parallel gradient of solving condition nonlinear optimal perturbation defines data processing method, which is characterized in that including with
Lower step:
Step 1: initializing related optimized variable；
Step 2: method solution being defined using gradient and obtains condition nonlinear optimal perturbation optimal value result；
Step 3: loop iteration step 2 simultaneously judges whether to meet stopping iterated conditional；
Step 4: the condition nonlinear optimal perturbation optimal value result of original solution room is exported when meeting and stopping iterated conditional.
2. a kind of parallel gradient of solving condition nonlinear optimal perturbation according to claim 1 defines data processing side
Method, which is characterized in that the step 2 specifically include it is following step by step:
Step 21: gradient of the objective function of solving condition nonlinear optimal perturbation about optimized variable；
Step 22: the target letter of optimal value result can be converted into along the direction that gradient declines search using SPG2 gradient project algorithms
Number minimum value.
3. a kind of parallel gradient of solving condition nonlinear optimal perturbation according to claim 2 defines data processing side
Method, which is characterized in that gradient of the objective function about optimized variable in the step 21, its calculation formula is:
In formula, f ' (X) indicates gradient of the objective function about optimized variable,Indicate optimized variable
First-order partial derivative of each variable about objective function.
4. a kind of parallel gradient of solving condition nonlinear optimal perturbation according to claim 3 defines data processing side
Method, which is characterized in that calculation formula of each variable of the optimized variable about the first-order partial derivative of objective function are as follows:
In formula, Δ x indicates Delta, x1,…,xi,…,xnIndicate all optimized variables.
5. a kind of parallel gradient of solving condition nonlinear optimal perturbation according to claim 2 defines data processing side
Method, which is characterized in that the optimization of the gradient in the step 21, which is calculated, carries out parallel computation, the parallel meter using MPI technology
It calculates and uses MS master-slave process, the host process in the MS master-slave process is for being responsible for the distribution of task and the collection of result and by task
Respectively, if task can not timesharing by be calculated as subprocess distribute task.
6. a kind of parallel gradient of solving condition nonlinear optimal perturbation according to claim 1 defines data processing side
Method, which is characterized in that when the dimension of numerical model needs dimensionality reduction, in the data processing method further include: the optimization to obtaining
The sample data of variable carries out gradient in feature space using after singular value decomposition algorithm or Principal Component Analysis Algorithm progress dimensionality reduction
Solution and optimizing.
7. a kind of parallel gradient of solving condition nonlinear optimal perturbation according to claim 1 defines data processing side
Method, which is characterized in that the stopping iterated conditional in the step 3 are as follows: whether be more than whether greatest iteration step number or optimal value surpass
Setting number is crossed to remain unchanged.
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Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101763087A (en) * | 2009-12-29 | 2010-06-30 | 浙江大学 | Industrial process dynamic optimization system and method based on nonlinear conjugate gradient method |
| CN105631556A (en) * | 2016-02-23 | 2016-06-01 | 徐强强 | Non-constant condition non-linear optimal parameter disturbance calculating method |
| CN106228234A (en) * | 2016-07-20 | 2016-12-14 | 浙江工业大学 | A kind of multi-objective particle swarm optimization method based on gradient descent method |
| CN108334973A (en) * | 2017-12-18 | 2018-07-27 | 浙江大学 | The colony intelligence of mixed integer nonlinear programming problem and linear programming Synergistic method |
-
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Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101763087A (en) * | 2009-12-29 | 2010-06-30 | 浙江大学 | Industrial process dynamic optimization system and method based on nonlinear conjugate gradient method |
| CN105631556A (en) * | 2016-02-23 | 2016-06-01 | 徐强强 | Non-constant condition non-linear optimal parameter disturbance calculating method |
| CN106228234A (en) * | 2016-07-20 | 2016-12-14 | 浙江工业大学 | A kind of multi-objective particle swarm optimization method based on gradient descent method |
| CN108334973A (en) * | 2017-12-18 | 2018-07-27 | 浙江大学 | The colony intelligence of mixed integer nonlinear programming problem and linear programming Synergistic method |
Non-Patent Citations (1)
| Title |
|---|
| BIN MU: ""An Efficient Approach Based on the Gradient Definition for Solving Conditional Nonlinear Optimal Perturbation"", 《MATHEMATICAL PROBLEMS IN ENGINEERING》 * |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113988370A (en) * | 2021-09-26 | 2022-01-28 | 天津大学 | Solving condition nonlinear optimal disturbance method based on analytical four-dimensional set variation |
| CN113988370B (en) * | 2021-09-26 | 2024-05-28 | 天津大学 | Solving condition nonlinear optimal disturbance method based on analysis four-dimensional set variation |
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