CN110096738A - Modeling method and device based on sensitivity analysis - Google Patents
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Abstract
The invention discloses a kind of modeling method and device based on sensitivity analysis, wherein this method comprises: obtaining the state vector of circuit system according to the circuit system for meeting default equation form；Presetting method is determined to handle state vector according to the Parameter Conditions of default equation, obtains the sensitivity of state vector；Circuit model is established according to sensitivity.This method can use sensitivity building circuit behavior model or performance model, effectively reduce simulation times, improve model construction rate.
Description
Technical Field
The invention relates to the technical field of electronic design automation, in particular to a modeling method and a modeling device based on sensitivity analysis.
Background
Electronic Design Automation (EDA) is a method for analyzing and predicting the performance of an integrated circuit at the Design stage using software as a carrier, and common circuit simulation tools include HSPICE of Synopsys corporation and spectrum of Cadence corporation. The circuit simulation aims at the circuit described by adopting a circuit network list or other forms, and the electrical characteristics of the circuit are obtained by adopting certain device model calculation.
The circuit simulation establishes an equation through kirchhoff voltage and current laws and solves the equation, and the implementation step is generally composed of two parts. The first part is the establishment of a circuit equation, and in the establishment stage of the circuit equation, circuit simulation establishes an equation according to a circuit structure, the voltage of a node in a circuit and the current of a branch circuit. The second part is the solution of circuit equations, and the types of the specifically solved equations are different according to different circuit simulation methods, including differential equations, linear equations and nonlinear equations.
Transient analysis is a circuit simulation method, and mainly calculates the curve (output result) of voltage change of each node in a circuit along with time according to a circuit structure, a driving signal and simulation parameters (input information).
The input to the transient analysis typically contains the following information:
(1) the circuit structure is as follows: the component composition and topology of the circuit.
(2) The driving signal: an external stimulus signal to the circuit.
(3) Simulation parameters: the simulation attribute needed to be done, such as simulation type, total time, step size, accuracy, etc.
The output of the transient analysis is usually the voltage of each node in the circuit, which is also called the waveform of each node voltage, along with the time variation. Further post-processing can be performed using this waveform to obtain other desired information, such as spectral characteristics of the circuit.
In recent years, the dynamic response precision of large-scale dynamic circuits is improved by the great improvement of the computer computing power, the transient sensitivity between the dynamic response and system parameters plays an important role in an integrated circuit automatic design algorithm, a method for fusing new observation Data in the dynamic operation process of a numerical model is adopted by Data Assimilation ((DA) on the basis of considering Data space-time distribution and errors of an observation field and a background field), and a model track is automatically adjusted by continuously fusing direct or indirect observation information of different sources and different resolutions which are discretely distributed in space-time through the Data Assimilation algorithm in a dynamic framework of the process model so as to improve the estimation precision of the state of the dynamic model and improve the model prediction capability), and the parameter estimation, the quantization uncertainty and the stability analysis are widely applied. Engineering gradients, whose sensitivity is indispensable for the algorithm, are also often used for circuit optimization.
The most important criterion for a gate circuit is the operating speed of the circuit, i.e. the clock frequency. In statistical circuit analysis, statistical time-required analysis is also of interest. The use of Statistical Static Timing Analysis (SSTA) enables Statistical delays to be propagated in a sequential circuit diagram as if they were a single value. In this approach, the distribution of delays is represented in a particular format, typically in the form of a low order of the floating device parameters (or their principal components), so that the distribution representation format can be compared to maximum values and summed as a single value. Or a low-order relation can be directly established according to the final attention delay and the sensitivity of the parameters to search the delay distribution, and the method has a wide application prospect due to the characteristic of rapidness although the method is subjected to global low-order approximation. In either method, the transient sensitivity plays an essential role.
The transient sensitivity of the parameters is determined, the traditional Brute-force Method obtains the sensitivity of all final parameters by perturbing each parameter of each device respectively, and the simulation complexity is in a linear relation with the product of the number of the parameters and the number of the devices. To overcome this complexity, one uses empirical clustering of varying groups of devices, rather than treating them as irrelevant. The method reduces the simulation complexity to be linear relation with the number of parameters, but needs to have deep understanding on the circuit behavior and is mainly suitable for sequential digital logic. The violence solving method needs a plurality of times of simulation, so that the violence solving method is very inconvenient today when a single simulation time can reach a plurality of hours.
Disclosure of Invention
The present invention is directed to solving, at least to some extent, one of the technical problems in the related art.
To this end, it is an object of the present invention to provide a sensitivity analysis-based modeling method that can use sensitivity to build a circuit model for circuit optimization and other applications.
Another object of the present invention is to provide a modeling apparatus based on sensitivity analysis.
In order to achieve the above object, an embodiment of an aspect of the present invention provides a modeling method based on sensitivity analysis, including: acquiring a state vector of a circuit system according to the circuit system meeting a preset equation form; determining a preset method according to the parameter conditions of the preset equation to process the state vector to obtain the sensitivity of the state vector; and establishing a circuit model according to the sensitivity.
The modeling method based on sensitivity analysis of the embodiment of the invention understands the method of calculating the transient sensitivity by the adjoint method from the angle of matrix calculation, uses the directed acyclic graph to assist in understanding the back propagation calculation sensitivity, establishes a circuit behavior model or a performance model by using the sensitivity, reduces the simulation times, lightens the complexity of modeling, improves the model construction rate, and can be applied to circuit optimization and other aspects.
In addition, the modeling method based on sensitivity analysis according to the above embodiment of the present invention may also have the following additional technical features:
further, in an embodiment of the present invention, the preset equation is:
wherein f (x) is a preset equation, x is a state vector of the circuit system, p is a sensitivity parameter of the circuit system, t is time, and B (p, t) is an input vector of the system.
Further, in an embodiment of the present invention, the method further includes:
calculating the Jacobian matrix Jac：
Iterating the state vector x according to the Jacobian matrix so that the state vector x meets the precision requirement, wherein the iteration formula is as follows:
Δx＝(Jac)-1·rhs
wherein, Δ x is the accurate state vector after iteration, rhs represents the residual error of the preset equation, (J)ac)-1Is a Jacobian matrix JacThe inverse matrix of (c).
Further, in one embodiment of the present invention, the sensitivity of the state vector is derived by deriving the preset equation:
wherein,to derive a predetermined equation.
Further, in one embodiment of the present invention, the preset method includes a direct method and a concomitant method;
the determining a preset method according to the parameter condition of the preset equation to process the state vector specifically includes:
when the number of the sensitivity parameters p of the circuit system is less than or equal to a first preset threshold value and the number of the preset equations is greater than or equal to a second preset threshold value, processing the state vector by adopting a direct method;
and when the number of the sensitivity parameters p of the circuit system is larger than a first preset threshold value and the number of the preset equations is smaller than a second preset threshold value, processing the state vector by adopting an adjoint method.
In order to achieve the above object, another embodiment of the present invention provides a modeling apparatus based on sensitivity analysis, including: the first acquisition module is used for acquiring a state vector of a circuit system according to the circuit system meeting a preset equation form; the second acquisition module is used for determining a preset method according to the parameter conditions of the preset equation so as to process the state vector and obtain the sensitivity of the state vector; and the modeling module is used for establishing a circuit model according to the sensitivity.
The modeling device based on sensitivity analysis provided by the embodiment of the invention understands the method of calculating the transient sensitivity by the adjoint method from the angle of matrix calculation, uses the directed acyclic graph to assist in understanding the back propagation calculation sensitivity, establishes a circuit behavior model or a performance model by using the sensitivity, reduces the simulation times, reduces the modeling complexity, improves the model construction rate, and can be applied to circuit optimization and other aspects.
In addition, the modeling apparatus based on sensitivity analysis according to the above embodiment of the present invention may further have the following additional technical features:
further, in an embodiment of the present invention, the preset equation is:
wherein f (x) is a preset equation, x is a state vector of the circuit system, p is a sensitivity parameter of the circuit system, t is time, and B (p, t) is an input vector of the system.
Further, in an embodiment of the present invention, the method further includes: a calculation module and an iteration module;
the calculation module is used for calculating a Jacobian matrix Jac：
The iteration module is used for iterating the state vector x according to the Jacobian matrix so that the state vector x meets the precision requirement, and the iteration formula is as follows:
Δx＝(Jac)-1·rhs
wherein, Δ x is the accurate state vector after iteration, rhs represents the residual error of the preset equation, (J)ac)-1Is a Jacobian matrix JacThe inverse matrix of (c).
Further, in one embodiment of the present invention, the sensitivity of the state vector is derived by deriving the preset equation:
wherein,to derive a predetermined equation.
Further, in one embodiment of the present invention, the preset method includes a direct method and a concomitant method;
the determining a preset method according to the parameter condition of the preset equation specifically includes:
the number of the sensitivity parameters p of the circuit system is less than or equal to a first preset threshold, and when the number of the preset equations is greater than or equal to a second preset threshold, a direct method is adopted;
and when the number of the sensitivity parameters p of the circuit system is larger than a first preset threshold value and the number of the preset equations is smaller than a second preset threshold value, adopting an adjoint method.
Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
Drawings
The foregoing and/or additional aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:
FIG. 1 is a flow diagram of a sensitivity analysis based modeling method according to one embodiment of the invention;
FIG. 2 is a diagram of a fit according to one embodiment of the invention;
FIG. 3 is a simplified schematic illustration of matrix method understanding according to one embodiment of the present invention;
FIG. 4 is a directed acyclic graph according to one embodiment of the present invention;
FIG. 5 is a schematic structural diagram of a modeling apparatus based on sensitivity analysis according to an embodiment of the present invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the drawings are illustrative and intended to be illustrative of the invention and are not to be construed as limiting the invention.
A modeling method and apparatus based on sensitivity analysis proposed according to an embodiment of the present invention will be described below with reference to the accompanying drawings.
A proposed modeling method based on sensitivity analysis according to an embodiment of the present invention will be described first with reference to the accompanying drawings.
FIG. 1 is a flow diagram of a sensitivity analysis based modeling method according to one embodiment of the invention.
As shown in fig. 1, the modeling method based on sensitivity analysis includes the following steps:
in step S101, a state vector of the circuit system is obtained according to the circuit system satisfying a preset equation form.
Further, in one embodiment of the present invention, the preset equation is:
where F (x) is a predetermined equation, x is a state vector of the circuitry, p is a sensitivity parameter of the circuitry, t is time, B (p, t) is an input vector of the system, F is a quantity related to the state and time derivative, and F (p, x) is a quantity related to the state and time.
Further, in an embodiment of the present invention, the method further includes:
calculating the Jacobian matrix Jac：
Iterating the state vector x according to the Jacobian matrix so that the state vector x meets the precision requirement, wherein the iteration formula is as follows:
Δx＝(Jac)-1·rhs
wherein, Δ x is the accurate state vector after iteration, rhs represents the residual error of the preset equation, (J)ac)-1Is a Jacobian matrix JacThe inverse matrix of (c).
In particular, for a non-linear circuit, it can be assumed that the system requiring solution satisfies a Differential Algebraic Equation (DAE) of the form:
where x is a state vector of the system, such as a node voltage or a branch current of the circuit; p is the transient sensitivity parameter to be solved, such as threshold voltage Vth, saturation speed Vsat, u of the MOSFET; t is time, q and f are charge/flow and current, respectively. To calculate the dynamic response of the stiff DAE system, given the initial state x (t0), the time step is determined based on the estimation of Local departure Error (LTE), and the continuous trajectory is discretized in time. In transient analysis, the state x is solved using a method such as newton method or upgraded newton plugging.
To calculate the state vector x, the jacobian Jac is first calculated, i.e. derived from equation (1):
then, continuously and iteratively updating x:
Δx＝(Jac)-1·rhs
wherein rhs represents the residual error of the current formula (1). By iterating x once, the accuracy of x is higher and higher, and the accuracy requirement of the x in the required state can be achieved by 3 iterations.
In step S102, a preset method is determined according to the parameter conditions of the preset equation to process the state vector, so as to obtain the sensitivity of the state vector.
Further, in one embodiment of the present invention, the sensitivity of the state vector is derived by deriving a preset equation:
wherein,to derive a predetermined equation.
Further, in one embodiment of the present invention, the preset method includes a direct method and a concomitant method;
determining a preset method according to parameter conditions of a preset equation to process the state vector, specifically comprising:
when the number of the sensitivity parameters p of the circuit system is less than or equal to a first preset threshold value and the number of the preset equations is greater than or equal to a second preset threshold value, processing the state vector by a direct method;
and when the number of the sensitivity parameters p of the circuit system is larger than a first preset threshold value and the number of the preset equations is smaller than a second preset threshold value, processing the state vector by adopting an adjoint method.
Specifically, the sensitivity of the state vector x is dx/dp, and to calculate dx/dp, p of the preset equation (1) may be differentiated:
to solve the problemNumerical problems solve the final result by solving a form of linear multi-step equations. In the linear multi-step method, the calculation result of a certain step is not only related to the current solution, but also related to the solutions of a plurality of previous steps, namely, the information of the previous steps is used for predicting the result of the next step.
In the embodiment of the invention, the solutionThere are two kinds of calculation methods for numerical values, namely a direct method and a concomitant method.
The direct and adjoint methods can be viewed as solving in a direction different from exhaustive. In the following, an example is described in which O is the objective equation, i.e., the preset equation in the above embodiment, and p is the transient sensitivity parameter to be solved.
The direct method comprises the following steps:
the concomitant method:
in a static circuit, when the parameter p is less, df/dp is a matrix with less columns, the inverse matrix of df/dx is multiplied by df/dp to obtain dx/dp, and then the dx/dp is multiplied by the dx/dp to obtain a smaller calculation amount, so that the sensitivity of all intermediate variables to system parameters is calculated by a direct method until a target equation is finally found.
As shown in FIG. 2, when the objective function O to be solved is less, dO/dx is a matrix with less rows, the inverse matrix of df/dx is multiplied by dO/dx to obtain dO/df, and then multiplied by df/dp, so that the calculation amount is less.
In contrast to the direct method, the adjoint method calculates the sensitivity of the target equation to all intermediate variables until finally the system parameters are found. As shown in fig. 2, when the number of parameters p is small and the number of objective functions O is large, the direct method is preferably used for solving. When the parameter p is more and the objective function O is less, the adjoint method is suitable for solving.
In a dynamic circuit, as shown in fig. 3, the derivative of O with respect to p, which is the sum of the products of the path derivatives of all p to O, is derived by the chain rule, and there are many states x (tn) at time points between the parameter p and the target equation O, the difference between the two methods becomes the difference of the enumerated path directions. The direct method starts from the parameter p and calculates sequentially along the time step until the target equation O is obtained. And after the state of all time steps is determined, the adjoint rule is reversely deduced to the parameter p along the time steps from the target equation O.
And (4) carrying out circuit transient sensitivity simulation, and solving the transient sensitivity by an adjoint method under the conditions of large-scale parameters and small-scale target equations. For a large-scale circuit, parameters are complicated, a companion method is preferably used for circuit simulation, and the circuit simulation time is shortened.
In step S103, a circuit model is established based on the sensitivity.
Further, after the sensitivity is obtained by the above steps, a circuit behavior model or a performance model can be constructed by modeling the sensitivity.
The circuit model is that people assume that a certain mapping relation y (f) (x) exists between a design parameter x and a circuit behavior or circuit performance y, and sample data is obtained through sampling, so that the model fits the existing data as much as possible. Obviously, the more known data that is acquired, the more likely the model is to be built to approximate reality (excluding overfitting).
According to the above description, the analytic values and sensitivities of the circuit state and its function can be obtained through simulation, and the analytic values and sensitivities of the event-triggered target equation can also be obtained, that is, the derivatives of the modeling required data f (x) and f (x) are obtained in one simulation. This knowledge of the sample points and their derivatives is relatively rare in the regression problem of conventional machine learning. The existence of the derivative provides additional information for modeling, the requirement on the number of sampling points can be reduced by utilizing the information, the requirement on the number of the sampling points by modeling can be effectively reduced by utilizing the gradient information of the sampling points, namely, fewer simulation times can be utilized to complete the same modeling precision, the simulation time is reduced, and the circuit design speed is accelerated.
The overfitting can be effectively controlled by utilizing the gradient information of the sampling points.
The application of sensitivity in reducing sampling points is described by taking a linear regression model as an example.
To describe the non-linear relationship between X and Y, dimension expansion of X yields (X, X)2,X3,X4,X5)。Y＝w0+w1*X+w2*X2+w3*X3+w4*X4+w5*X5S
Performing a simulation to obtain a set of corresponding relations x0,y0,y0’。
The equation can be found:
y0＝w0*1+w1*x0+w2*x0 2+w3*x0 3+w4*x0 4+w5*x0 5y0？
＝w0*0+w1*1+w2*(2*x0)+w3 *(3*x0 2)+w4 *(4*x0 3)+w5 *(5*x0 4)
in this process, the derivative expression is taken as w0The coefficient is 0, and other coordinate points correspondingly reduce the power and are multiplied by new coordinate data of the original power to be brought into the modeling calculation, so that the requirement on the number of sampling points can be reduced to a certain extent. In addition, the derivative can be modeled uniformly to obtain w1To w5Obtaining w by regression of original data0。
The introduction of the derivative may also reduce the overfitting to some extent without reducing the sampled point data. Fig. 4(a) shows a non-overfit case, and fig. 4(b) shows an overfit case. The introduction of the derivative limits the trend of the curve, and the decrease when the curve is re-input by about 0.78 does not occur, so that overfitting is restrained.
It is understood that the method of the embodiment of the present invention may not only determine the sensitivity in the circuit system for modeling, but also determine the sensitivity of the target parameter in the target equation to construct a circuit performance model (e.g., a circuit delay model), which is described as an example below.
In transient analysis, events that occur only under certain circumstances (such as the delay of an inverter) are defined, and sensitivity analysis for these events is discussed further on the basis of the above non-practical triggers.
Defining a trigger event requires satisfying the equation:
the target equation:
the solution can be found, event-triggered sensitivity:
wherein,
according to the sensitivity analysis-based modeling method provided by the embodiment of the invention, a method for calculating transient sensitivity by a adjoint method is understood from the angle of matrix calculation, a directed acyclic graph is used for assisting in understanding of back propagation calculation sensitivity, a circuit behavior model or a performance model is established by using the sensitivity, the simulation times are reduced, the complexity of modeling is reduced, the model construction rate is improved, and the method can be applied to circuit optimization and other aspects.
Next, a modeling apparatus based on sensitivity analysis proposed according to an embodiment of the present invention is described with reference to the drawings.
FIG. 5 is a schematic structural diagram of a modeling apparatus based on sensitivity analysis according to an embodiment of the present invention.
As shown in fig. 5, the modeling apparatus based on sensitivity analysis includes: a first acquisition module 100, a second acquisition module 200, and a modeling module 300.
The first obtaining module 100 is configured to obtain a state vector of a circuit system according to the circuit system satisfying a preset equation form. The second obtaining module 200 is configured to determine a preset method according to parameter conditions of a preset equation to process the state vector, so as to obtain the sensitivity of the state vector. The modeling module 300 is used to build a circuit model based on the sensitivity.
The modeling device based on sensitivity analysis can establish a circuit model by using sensitivity, and can be used for circuit optimization and other aspects.
Further, in one embodiment of the present invention, the preset equation is:
wherein f (x) is a preset equation, x is a state vector of the circuit system, p is a sensitivity parameter of the circuit system, t is time, and B (p, t) is an input vector of the system.
Further, in an embodiment of the present invention, the method further includes: a calculation module and an iteration module;
a calculation module for calculating the Jacobian matrix Jac：
The iteration module is used for iterating the state vector x according to the Jacobian matrix so that the state vector x meets the precision requirement, and the iteration formula is as follows:
Δx＝(Jac)-1·rhs
wherein, Δ x is the accurate state vector after iteration, rhs represents the residual error of the preset equation, (J)ac)-1Is a Jacobian matrix JacThe inverse matrix of (c).
Further, in one embodiment of the present invention, the sensitivity of the state vector is derived by deriving a preset equation:
wherein,to derive a predetermined equation.
Further, in one embodiment of the present invention, the preset method includes a direct method and a concomitant method;
the method for determining the preset method according to the parameter condition of the preset equation specifically comprises the following steps:
when the number of the sensitivity parameters p of the circuit system is less than or equal to a first preset threshold value and the number of the preset equations is greater than or equal to a second preset threshold value, a direct method is adopted;
and adopting an adjoint method when the number of the sensitivity parameters p of the circuit system is larger than a first preset threshold value and the number of the preset equations is smaller than a second preset threshold value.
It should be noted that the foregoing explanation of the embodiment of the modeling method based on sensitivity analysis is also applicable to the apparatus of this embodiment, and is not repeated here.
According to the modeling device based on sensitivity analysis provided by the embodiment of the invention, a method for calculating transient sensitivity by a adjoint method is understood from the angle of matrix calculation, a directed acyclic graph is used for assisting in understanding of back propagation calculation sensitivity, a circuit behavior model or a performance model is established by using the sensitivity, the simulation times are reduced, the complexity of modeling is reduced, the model construction rate is improved, and the modeling device can be applied to circuit optimization and other aspects.
Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of the present invention, "a plurality" means at least two, e.g., two, three, etc., unless specifically limited otherwise.
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above are not necessarily intended to refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, various embodiments or examples and features of different embodiments or examples described in this specification can be combined and combined by one skilled in the art without contradiction.
Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention, and that variations, modifications, substitutions and alterations can be made to the above embodiments by those of ordinary skill in the art within the scope of the present invention.
Claims (10)
1. A modeling method based on sensitivity analysis is characterized by comprising the following steps:
acquiring a state vector of a circuit system according to the circuit system meeting a preset equation form;
determining a preset method according to the parameter conditions of the preset equation to process the state vector to obtain the sensitivity of the state vector;
and establishing a circuit model according to the sensitivity.
2. The sensitivity analysis-based modeling method of claim 1, wherein said predetermined equation is:
wherein f (x) is a preset equation, x is a state vector of the circuit system, p is a sensitivity parameter of the circuit system, t is time, and B (p, t) is an input vector of the system.
3. The sensitivity analysis-based modeling method of claim 2, further comprising:
calculating the Jacobian matrix Jac：
Iterating the state vector x according to the Jacobian matrix so that the state vector x meets the precision requirement, wherein the iteration formula is as follows:
Δx＝(Jac)-1·rhs
wherein, Δ x is the accurate state vector after iteration, rhs represents the residual error of the preset equation, (J)ac)-1Is a Jacobian matrix JacThe inverse matrix of (c).
4. The sensitivity analysis-based modeling method of claim 2, wherein the sensitivity of the state vector is derived by deriving the preset equation:
wherein,to derive a predetermined equation.
5. The sensitivity analysis-based modeling method according to claim 1, wherein the preset method includes a direct method and a adjoint method;
the determining a preset method according to the parameter condition of the preset equation to process the state vector specifically includes:
when the number of the sensitivity parameters p of the circuit system is less than or equal to a first preset threshold value and the number of the preset equations is greater than or equal to a second preset threshold value, processing the state vector by adopting a direct method;
and when the number of the sensitivity parameters p of the circuit system is larger than a first preset threshold value and the number of the preset equations is smaller than a second preset threshold value, processing the state vector by adopting an adjoint method.
6. A modeling apparatus based on sensitivity analysis, comprising:
the first acquisition module is used for acquiring a state vector of a circuit system according to the circuit system meeting a preset equation form;
the second acquisition module is used for determining a preset method according to the parameter conditions of the preset equation so as to process the state vector and obtain the sensitivity of the state vector;
and the modeling module is used for establishing a circuit model according to the sensitivity.
7. The sensitivity analysis-based modeling apparatus of claim 6, wherein said predetermined equation is:
wherein f (x) is a preset equation, x is a state vector of the circuit system, p is a sensitivity parameter of the circuit system, t is time, and B (p, t) is an input vector of the system.
8. The sensitivity analysis-based modeling apparatus of claim 7, further comprising: a calculation module and an iteration module;
the calculation module is used for calculating a Jacobian matrix Jac：
The iteration module is used for iterating the state vector x according to the Jacobian matrix so that the state vector x meets the precision requirement, and the iteration formula is as follows:
Δx＝(Jac)-1·rhs
wherein, Δ x is the accurate state vector after iteration, rhs represents the residual error of the preset equation, (J)ac)-1Is a Jacobian matrix JacThe inverse matrix of (c).
9. The sensitivity analysis-based modeling apparatus according to claim 7, wherein the sensitivity of said state vector is derived by deriving said preset equation:
wherein,to derive a predetermined equation.
10. The sensitivity analysis-based modeling apparatus according to claim 6, wherein said preset method includes a direct method and a adjoint method;
the determining a preset method according to the parameter condition of the preset equation to process the state vector specifically includes:
when the number of the sensitivity parameters p of the circuit system is less than or equal to a first preset threshold value and the number of the preset equations is greater than or equal to a second preset threshold value, processing the state vector by adopting a direct method;
and when the number of the sensitivity parameters p of the circuit system is larger than a first preset threshold value and the number of the preset equations is smaller than a second preset threshold value, processing the state vector by adopting an adjoint method.
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