Abstract:
An approximation is determined for the future system behavior by a similarity analysis using a previously known behavior of the dynamic system, whereupon the future system behavior is determined by using the approximation for the future behavior of the dynamic system as well as a neuronal network structure, especially a causal retro-causal network (causality analysis).

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
   This application is based on and hereby claims priority to PCT Application No. PCT/EP2004/050468 filed on Apr. 7, 2004 and German Application No. 10324045.4 filed on May 27, 2003, the contents of which are hereby incorporated by reference. 
   BACKGROUND OF THE INVENTION 
   The invention relates to a method and a computer program with program code for determining a future system response of a dynamic system. 
   It is known from S. Haykin, “Neural Networks: A Comprehensive Foundation,” Prentice Hall, Second Edition, ISBN 0-13-273350-1, pages 732-789, 1999 (“the Haykin reference”) that a neural structure, for example a neural network, can be used to describe and model a dynamic system or dynamic process and its process response. 
   Generally a dynamic system or dynamic process is described by a status transition description that is not visible to an observer of the dynamic process and an output equation that describes observable quantities of the technical dynamic process. 
   Such a process response of a dynamic process is shown in  FIG. 2 . 
   The dynamic process  200  or dynamic system  200 , in which the dynamic process operates, is subject to the influence of an external input quantity u of predefinable dimension, with an input quantity u t  at a point in time t being referred to as:
 
u t ∉             1 ,
 
where 1 refers to a natural number.

   The input quantity at a point in time t causes a change in the dynamic process. 
   An internal status s t  (s t ε             m ) of predefinable dimension m at a point in time t cannot be observed by an observer of the dynamic system  200 .
   A status transition of the internal status s t  of the dynamic process is caused as a function of the internal status s t  and the input quantity u t  and the status of the dynamic process switches to a successor status s t+1  at a subsequent point in time t+1. 
   The following is thereby valid:
 
 S   t+1   =f ( s   t   ,u   t ).  (1)
 
where f(.) refers to a general mapping rule.
 
   An output quantity y t  that can be observed by an observer of the dynamic system  200  at a point in time t is a function of the input quantity u t  and the internal status s t . 
   The output quantity y t  (y t ε             n ) is a predefinable dimension n.
   The dependency of the output quantity y t  on the input quantity u t  and the internal status s t  of the dynamic process is defined by the following general rule:
 
 y   t   =g ( s   t ),  (2)
 
where g. refers to a general mapping rule.
 
   To describe the dynamic system  200  in the Haykin reference a neural structure is used comprising computer elements connected to one another in the form of a neural network of neurons connected to one another. The connections between the neurons of the neural network are weighted. The weightings of the neural network are combined in a parameter vector v. 
   An internal status of a dynamic system that underlies a dynamic process is thus a function, according to the following rule, of the input quantity u t  and the internal status of the preceding point in time s t  and the parameter vector v:
 
 s   t+1   =NN ( v,s   t   ,u   t )  (3)
 
where NN(.) refers to a mapping rule predefined by the neural network.
 
   This description of the dynamic system  200  according to equation (3) is also referred to as the forecast approach. 
   Alternatively the dynamic system can also be described by:
 
 s   t   =f ( s   t−1   ,u   t )  (1′)
 
with
 
 s   t   =NN ( v,s   t−1   ,u   t )  (3′)
 
which is referred to as the consistency approach. The forecast approach and consistency approach result in minor structural differences in the respective network structures but are equivalent, alternative forms of description for dynamic systems.
 
   A further neural structure to describe the dynamic system  200 , a neural network referred to as a time delay recurrent neural network (TDRNN), is known from David E. Rumelhart et al., “Parallel Distributed Processing, Explorations in the Microstructure of Cognition”, vol. 1: Foundations, A Bradford Book, The MIT Press, Cambridge, Mass., London, England, 1987 (“David E. Rumelhart et al.”). 
   The known TDRNN is shown in  FIG. 5  as a neural network  500  developed over a finite number of points in time (5 points in time shown: t−4, t−3, t−2, t−1, t). 
   The neural network  500  shown in  FIG. 5  has an input layer  501  having five sub-input layers  521 ,  522 ,  523 ,  524  and  525  that respectively contain a predefinable number of input computer elements, to which input quantities u t−4 , u t−3 , u t−2 , u t−1 , u t  can be applied at predefinable points in time t−4, t−3, t−2, t−1, t, i.e. time row values with predefined time steps described below. 
   Input computer elements, i.e. input neurons, are connected via variable connections to neurons of a predefinable number of hidden layers  505  (5 hidden layers shown). 
   Neurons of a first  531 , a second  532 , a third  533 , a fourth  534  and a fifth  535  hidden layer are thereby connected respectively to neurons of the first  521 , second  522 , third  523 , fourth  524  and fifth  525  sub-input layer. 
   The connections between the first  531 , second  532 , third  533 , fourth  534  and fifth  535  hidden layer and the first  521 , second  522 , third  523 , fourth  524  and fifth  525  sub-input layer respectively are the same in each instance. The weightings of all connections are respectively contained in a first connection matrix B 1 . 
   The outputs of neurons of the first hidden layer  531  are also connected to inputs of neurons of the second hidden layer  532  according to a structure defined by a second connection matrix A 1 . The outputs of neurons of the second hidden layer  532  are connected to inputs of neurons of the third hidden layer  533  according to a structure defined by the second connection matrix A 1 . The outputs of neurons of the third hidden layer  533  are connected to inputs of neurons of the fourth hidden layer  534  according to a structure defined by the second connection matrix A 1 . The outputs of neurons of the fourth hidden layer  534  are connected to inputs of neurons of the fifth hidden layer  535  according to a structure defined by the second connection matrix A 1 . 
   In the hidden layers, the first hidden layer  531 , the second hidden layer  532 , the third hidden layer  533 , the fourth hidden layer  534  and the fifth hidden layer  535 , “internal” statuses or “internal” system statuses s t−4 , s t−3 , s t−2 , s t−1 , and s t  of a dynamic process described by the TDRNN are represented respectively at five successive points in time t−4, t−3, t−2, t−1 and t. 
   The particulars in the indices in the respective layers respectively indicate the point in time t−4, t−3, t−2, t−1 and t, to which the signals that can be taken or supplied respectively at the outputs of the respective layer refer (u t−4 , u t−3 , u t−2 , u t−1 , u t ). 
   An output layer  520  comprises five sub-output layers, a first sub-output layer  541 , a second sub-output layer  542 , a third sub-output layer  543 , a fourth sub-output layer  544  and a fifth sub-output layer  545 . Neurons of the first sub-output layer  541  are connected to neurons of the first hidden layer  531  according to a structure defined by an output connection matrix C 1 . Neurons of the second sub-output layer  542  are connected to neurons of the second hidden layer  532  also according to the structure defined by the output connection matrix C 1 . Neurons of the third sub-output layer  543  are connected to neurons of the third hidden layer  533  according to the output connection matrix C 1 . Neurons of the fourth sub-output layer  544  are connected to neurons of the fourth hidden layer  534  according to the output connection matrix C 1 . Neurons of the fifth sub-output layer  545  are connected to neurons of the fifth hidden layer  535  according to the output connection matrix C 1 . The output quantities for a respective point in time t−4, t−3, t−2, t−1, t can be taken at the neurons of the sub-output layers  541 ,  542 ,  543 ,  544  and  545  (y t−4 , y t−3 , y t−2 , y t−1 , y t ) 
   The principle that equivalent connection matrices in a neural network exhibit the same values at a respective point in time is referred to as the so-called shared weights principle. 
   The system known from David E. Rumelhart et al. and referred to as a time delay recurrent neural network (TDRNN) is trained in a training phase such that a respective target quantity y t   d  at a real dynamic system is determined for an input quantity u t . The tupel (input quantity, determined target quantity) is referred to as training datum. A plurality of such training data forms a training data set. 
   Temporally successive tupels (u t−4 , y t−4   d ), (u t−3 , y t−3   d ), (u t−2 , y t−2   d ) of the points in time (t−4, t−3, t−3, . . . ) of the training data set each exhibit a predefined time step. 
   The TDRNN is trained with the training data set. An overview of various training methods can likewise be found in the Haykin reference and WO00/08599. 
   It should be emphasized at this point that only the output quantities y t−4 , y t−3 , . . . , y t  at points in time t−4, t−3, . . . , t of the dynamic system  200  can be identified. The “internal” system statuses s t−4 , s t−3 , . . . , s t  cannot be observed. 
   The following cost function E is usually minimized in the training phase: 
                   E   =         1   T     ⁢       ∑     t   =   1     T     ⁢       (       y   t     -     y   t   d       )     2         -&gt;     min     f   ,   g           ,           (   4   )               
where T refers to a plurality of points in time taken into consideration.
 
   Developments of the neural structure known from David E. Rumelhart et al. and referred to as a time delay recurrent neural network (TDRNN) are known from WO00/55809 and Zimmermann H. G., Neunier R., Grothmann R., “Modelling of Dynamic Systems by Error-Correction-Neural-Networks”, in Soofe and Cao (eds.), Forecasting Financial Data, Kluwer Verlag, ISBN 0792376803, 2002 (“Zimmermann H. G. et al.”). 
   The developments from WO00/55809 are particularly suitable for determining future statuses of a dynamic process, which is referred to as “overshooting”. 
     FIG. 1   a  from WO00/55809 shows a basic structure, on which the developments known from WO00/55809 are based. 
   The basic structure is a neural network developed over three points in time t, t+1, t+2. 
   It has an input layer, having a predefinable plurality of input neurons, to which input quantities u t  can be applied at predefinable points in time t, i.e. time row values with predefined time steps as described below. 
   The input neurons are connected via variable connections to neurons of a predfinable plurality of hidden layers (3 hidden layers shown). 
   Neurons of a first hidden layer are thereby connected to neurons of the first input layer. 
   The connection between the first hidden layer and the first input layer has weightings, which are contained in a first connection matrix B. 
   The outputs of neurons of the first hidden layer are also connected to inputs of neurons of a second hidden layer according to a structure defined by a second connection matrix A. The outputs of neurons of the second hidden layer are connected to inputs of neurons of a third hidden layer according to a structure defined by the second connection matrix A. 
   In the hidden layers, the first hidden layer, the second hidden layer and the third hidden layer, “internal” statuses or “internal” system statuses s t , s t+1 , s t+2  of the described dynamic process are represented respectively at three successive points in time t, t+1, t+2. 
   The particulars in the indices in the respective layers respectively indicate the point in time t, t+1, t+2, to which the signals (ut) that can be taken or supplied respectively at the outputs of the respective layer refer. 
   An output layer  120  has two sub-output layers, a first sub-output layer and a second sub-output layer. Neurons of the first sub-output layer are connected to neurons of the first hidden layer according to a structure defined by an output connection matrix C. Neurons of the second sub-output layer are connected to neurons of the second hidden layer also according to the structure defined by the output connection matrix C. 
   The output quantities for a respective point in time t+1, t+2 can be taken at the neurons of the sub-output layers (y t+1 , y t+2 ). 
   A development of this basic structure from WO00/55809 is shown in  FIG. 6 . 
   Developments of the TDRNN structure from Zimmermann H. G. et al., so-called error correction recurrent neural networks (ECRNN), relate to a structurally necessary error correction mechanism, which is integrated as a structural component in a neural structure.  FIG. 7  shows a basic structure with corresponding functional equations for an ECRNN. 
   A further neural structure to describe the dynamic system  200 , a neural network referred to as a causal-retro-causal time delay recurrent neural network or causal-retro-causal neural network (CRCNN) is known from WO02/27654. 
     FIG. 3  shows a basic structure  300  with corresponding functional equations for a CRCNN. 
   Two neural sub-structures  310 ,  320  are linked together with this CRCNN. A first internal sub-status s t  ( 311 - 314 ) of the first neural sub-structure  310  and a second internal sub-status r t  ( 321 - 324 ) of the second neural sub-structure  320  are thereby a function according to the following rules of the input quantity u t  ( 301 - 304 ), the first internal sub-status s t−1  ( 311 - 314 ), the second internal sub-status r t+1  ( 321 - 324 ) and parameter vectors v s , v t , v y :
 
 s   t   =NN ( v   s   ,s   t−1   , u   t ),  (8)
 
 r   t   =NN ( v   r   ,r   t+1   ,u   t )  (9)
 
 y   t   =NN ( v   y   ,s   t   ,r   t )  (10)
 
where NN(.) refers to a mapping rule predefined by the neural network.
 
   Connections between the neurons of the CRCNN are weighted. The weightings are combined in parameter vectors vs, vt, vy. 
   The CRCNN  300  according to  FIG. 3  is a neural network developed over four points in time, t−1, t, t+1, t+2) (see TDRNN,  FIG. 5 ). 
   Essential features of a neural network developed over a finite number of points in time are described in David E. Rumelhart et al. and above in relation to the known TDRNN (see  FIG. 5 ). 
   An overview of the basic principles of neural networks and the possible applications of neural networks in the economic field can also be found in H. Rehkugler and H. G. Zimmermann,“Neuronale Netze in der Ökonomie, Grundlagen und finanzwirtschaftliche Anwendungen (Neural networks in economics, Basic principles and financial applications)”, Verlag Franz Vahlen Munich, ISBN 3-8006-1871-0, pages 3-90, 1994. 
   The known systems and methods in particular have the disadvantage that they only describe a dynamic system to be described with inadequate accuracy and they are therefore only able to forecast future developments of the system with inadequate accuracy. 
   This is particularly true of dynamic systems, which are subject to a planning influence, i.e. dynamic systems that are not just purely market-driven. 
   SUMMARY OF THE INVENTION 
   One possible object of the invention is therefore to specify a method for determining a future system response of a dynamic system, said method not being subject to the disadvantages of the known systems and methods, in particular their inaccuracies. 
   This object maybe achieved by the method and by the computer program for determining a future system response of a dynamic system. 
   With the method for determining a future system response of a dynamic system, a known system response of the dynamic system is used to determine an approximation of the future system response by a similarity comparison or similarity analysis. 
   The future system response is then determined using the approximation of the future system response of the dynamic system and a neural network structure (causality analysis), with the approximation of the future system response of the dynamic system being fed to the neural network structure as an input quantity and an output quantity of the neural network structure representing the future system response. 
   Graphically speaking, the method represents a combination of a similarity analysis and a causality analysis using a neural network structure. 
   The similarity analysis is thereby used to determine an approximation of a future (anticipated) system response from a historic system response. Based on this approximation the future system response is then defined or forecast in the manner of a subsequent correction using the neural network structure. 
   This two-step or combined procedure, namely the determination of an approximation by a similarity analysis followed by subsequent correction using a neural network structure, is particularly suitable for forecasting the system response of so-called human controlled systems (HCS). 
   Such HCS are systems that are subject to a controlling influence and/or an influence based on planning intervention. 
   Examples of such HCS are energy consumption, power consumption or gas consumption or a corresponding energy consumption response. 
   Energy or power/gas consumption is thereby a function of energy supply and demand. The interaction of supply and demand underlies (economic) legalities or mechanisms in the form of market mechanisms. However it is possible to intervene in the interaction or the market dynamic, in other words the system, by planning and providing supply quantities correspondingly. 
   Neural network structures that are particularly suitable for an effect-cause (causality) analysis should in particular be used with the method (in the context of the causality analysis). 
   Dynamic systems are usually formulated as cause-effect relationships (see information re  FIG. 2 , equations (1) to (3)), which can be mapped by the neural structures known from the Haykin reference, David E. Rumelhart et al. or WO00/55809. These cause-effect relationships are expressed in these neural structures in that an information flow generated in these neural structures is directed temporally forward, in other words from the past into the future. This is referred to as a forward response. Causes in input quantities u t  at predefined points in time (t−2), (t−1), . . . result in (perceptible) effects in output quantities y t  at the point in time (t or t+1). The input quantities u t  are thereby mapped by the neural cause-effect structure onto the output quantities y t . 
   This “forward directed” information flow is particularly suitable for taking into consideration the influence of market mechanisms. 
   These one-dimensional (forward directed) structures for the cause-effect relationships can be extended to include a neural sub-structure that carries out an effect-cause analysis and therefore provides a causal synthesis. 
   With this (effect-cause) extension structure or effect-cause structure an information flow is generated that is directed temporally backward, i.e. an information flow directed from the future into the past. This is referred to as a backward response. Effects in output quantities y t  at the point in time (t) “result” or have their causes in input quantities u t  at the point in time (t−1), (t−2), . . . . In the opposite fashion to the cause-effect structure, output quantities y t  (as input quantities of the extension structure) are thereby mapped onto the input quantities u t  (as output quantities of the extension structure). 
   This “backward directed” information flow is particularly suitable for taking into consideration the planning and/or controlling influence. 
   The method is particularly suitable for forecasting the future system response of the dynamic system. This forecast can be derived from the future system response determined. 
   The computer program with program code is set up to carry out all steps according to the method when the program is executed on a computer. 
   The computer program product with program code stored on a machine-readable medium is set up to carry out all steps according to the method when the program is executed on a computer. 
   The arrangement and the computer program with program code, set up to carry out all steps according to the method, when the program is executed on a computer, and the computer program product with program code stored on a machine-readable medium, set up to carry out all steps according to the method, when the program is executed on a computer, are particularly suitable for carrying out the method or one of its developments described below. 
   The described software solutions can thereby also be implemented in a decentralized or distributed fashion, i.e. parts of the computer program or parts of the computer program product can operate on or be executed by different (distributed) computers or be stored on different storage media—even as standalone partial solutions. 
   The developments described below relate to the method and to the computer program with program code as well as the computer program product. 
   The Method described below can be implemented in both software and hardware, for example using a specific electrical circuit. 
   The method described below can also be implemented by a computer-readable storage medium, on which the computer program with program code that executes the method is stored. 
   The method described below can also be implemented by a computer program product, having a storage medium, on which the computer program with program code means that executes the method is stored. 
   In a development the neural network structure has two sub-structures that are linked to each other. 
   A first neural substructure is tailored such that its first mapping response describes a forward response of the dynamic system. 
   The first “forward directed” neural network structure, which can be mapped by the neural structures known from the Haykin reference, David E. Rumelhart et al. or WO00/55809, is particularly suitable for simulating or identifying cause-effect relationships (see information relating to  FIG. 2 , equations (1) to (3)). 
   This cause-effect relationship is expressed in this first neural sub-structure in that an information flow generated in said first neural sub-structure is directed temporally forward, i.e. from the past into the future. This is referred to as a forward response. Causes in input quantities u t  at past points in time (t−2), (t−1), . . . result in (perceptible) effects in output quantities y t  at the point in time (t or t+1). The input quantities u t  are thereby mapped by the neural cause-effect structure onto the output quantities y t . 
   The second neural sub-structure is tailored such that its second mapping response describes a backward response of the dynamic system. 
   This second “backward directed” neural network structure, which can be mapped by corresponding neural structures known from the Haykin reference, David E. Rumelhart et al. or WO00/55809, is particularly suitable for simulating or identifying effect-cause relationships. 
   This second “backward directed” neural sub-structure is therefore particularly suitable for carrying out an effect-cause analysis, to provide a causal synthesis. 
   With this (effect-cause) sub-structure, an information flow is generated that is directed temporally backward, i.e. an information flow directed from the future into the past. This is referred to as a backward response. Effects in output quantities y t  at the point in time (t) “result” or have their causes in input quantities u t  at the point in time (t−1), (t−2), . . . . In the opposite fashion to the cause-effect structure, output quantities y t  (as input quantities of the second neural sub-structure) are thereby mapped onto the input quantities u t  (as output quantities of the second neural sub-structure). 
   The first “forward directed” neural sub-structure is also particularly suitable for taking an influence of market mechanisms on the dynamic system into consideration. 
   The second “backward directed” neural sub-structure is particularly suitable for taking a planning influence on the dynamic system into consideration. 
   Based on this “forward directed” cause-effect relationship (causality) and the “backward directed” effect-cause relationship (retro-causality), the neural structure comprising a first and second neural sub-structure can be referred to as a causal-retro-causal neural network. 
   In a development the first and/or the second neural sub-structure is/are a neural network developed over a plurality of points in time, for example a TDRNN, or neural networks developed over a plurality of points in time, in which a temporal dimension of the dynamic system described is developed as a spatial dimension. 
   It can also be expedient for the first and/or second neural sub-structure to be configured as an error correction recurrent neural network (ECRNN). The basic principles of such ECRNNs are described in Zimmermann H. G. et al. and can be incorporated correspondingly in the neural sub-structures. 
   In one embodiment there is provision for determining the known system response of the dynamic system using historic system data. 
   The approximation of the future system response of the dynamic system can be determined such that the known system response is subdivided into segments of predefinable durations, such as a day or an hour. Associated segment system responses are then determined for the segments. 
   Defined segments with the respective associated segment system responses can be selected from the segments. The approximation can be determined using these selected segments and the selected associated segment system responses taking into consideration a calendar effect. 
   In one embodiment segments are selected, the associated segment system response of which exhibits a significant response. 
   When determining the approximation of the future system response of the dynamic system using the selected segment system response, it is possible to interpolate a system response between the selected segment system responses and/or determine the mean and/or insert historic segment system response(s). 
   In embodiments of method is used to forecast energy consumption, in particular the consumption of a quantity of gas. The method can also be used correspondingly to forecast power consumption. 
   Other use scenarios are possible, for example in economic systems (financial services, banks, insurance) or industrial systems (production systems, industrial units, logistics systems). 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     These and other objects and advantages of the present invention will become more apparent and more readily appreciated from the following description of the preferred embodiments, taken in conjunction with the accompanying drawings of which: 
       FIGS. 1   a  and  1   b  show outlines of a two-step procedure for energy forecasting ( 1   a : first step: similarity analysis;  1   b : second step: causality analysis) according to one exemplary embodiment; 
       FIG. 2  shows an outline of a general description of a dynamic system; 
       FIG. 3  shows an outline of a CRCNN with underlying functional equations; 
       FIG. 4  shows an outline of a historic pattern of energy/gas consumption (weekly data for 01/92-10/99); 
       FIG. 5  shows an outline of an arrangement of a TDRNN, developed with a finite number of statuses over time; 
       FIG. 6  shows an outline of a development of a TDRNN suitable for “overshooting”; 
       FIG. 7  shows an outline of an ECRNN with underlying functional equations. 
   

   DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
   Reference will now be made in detail to the preferred embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like reference numerals refer to like elements throughout. 
   Exemplary Embodiment 
   Energy/Gas Consumption Forecast 
   Task definition ( FIG. 4 ) 
     FIG. 4  shows a question  410  from an economic environment, which is resolved by the procedure described in the context of the following exemplary embodiment of the invention. 
   A forecast is required for energy consumption or gas consumption for a future year 2001, based on a predefined scenario of temperature trends for the forecast period. 
     FIG. 4  shows a historic pattern  400  of energy/gas consumption based on weekly consumption data for a period 01/92-10/99 by way of an example of an energy consumption pattern. 
   Gas consumption is thereby generally a function of customer demand (market mechanism) and planning strategy (cost minimization) for gas storage by supply companies (planning influence)  420 . 
   Procedure ( FIGS. 1   a  and  1   b ) 
     FIGS. 1   a  and  1   b  show a procedure used for the energy consumption forecast 2001. 
     FIG. 1   a  shows a first step in the procedure, a similarity analysis (approximation step).  FIG. 1   b  shows a second step in the procedure, a causality analysis (subsequent correction). A result of the first step is both an output and input quantity for the second step. 
   Step 1: Similarity Analysis ( FIG. 1   a ,  110 ) 
   In the course of the similarity analysis  110  a historic, known energy consumption pattern, in this instance the energy consumption for the year 2000  111 , is subdivided into time segments of a day in each instance, referred to as daily slices. 
   Significant energy consumption trends  120 ,  121 , which can comprise one or a plurality of associated daily slices, are also selected from the historic energy consumption pattern  200 . 
   Significant energy consumption trends  120 ,  121  can thereby be trends which show an extraordinary pattern, such as energy consumption peaks. Also of significance are energy consumption trends on significant dates such as holiday dates (Christmas, Easter) or the start of a holiday. 
   Such energy consumption trends thus selected are transferred or projected  130 ,  131  into the year to be forecast 2001 or the period to be forecast 2001 based on the corresponding daily slices taking into consideration a calendar effect. 
   The calendar effect refers to the fact that a “daily slice” or the energy consumption pattern at Easter 2000 (historic) for example can be used as a forecast, approximated “daily slice” or energy consumption pattern for Easter 2001 (forecast approximation) (despite the date difference between Easter 2000 and Easter 2001). 
   The transfer to 2001 proceeds correspondingly  130 ,  131  with all the selected significant energy consumption patterns  120 ,  121  from 2000. 
   (Pattern) gaps  140  occurring in the approximated, forecast energy consumption pattern for 2001 can then be closed. 
   This can be done by interpolation between the significant energy consumption patterns  120 ,  121  from 2000 projected into the year 2001 and/or by determining a mean and/or by using plausible historic consumption patterns. 
   The result of this first step, the similarity analysis  110 , is an approximation of the forecast energy consumption pattern for 2001  112 . 
   Step 2: Causality Analysis ( FIG. 1   b ,  150 ) 
   This approximated, forecast energy consumption pattern  112 ,  152  now serves as an output quantity for the second step, the causality analysis  150 . The result of the causality analysis  150  is the required energy consumption forecast 2001  153 . 
   The causality analysis  150  is carried out using a neural network structure, a so-called causal-retro-causal neural network (CRC NN)  151  or  130  ( FIG. 3 ). 
   Neural Network Structure—CRC NN ( FIG. 3 ) 
     FIG. 3  shows an underlying structure  300  with corresponding functional equations for a CRCNN. 
   With this CRCNN two neural sub-structures  310 ,  320  are linked together. A first internal sub-status s t  ( 311 - 314 ) of the first neural sub-structure  310  and a second internal sub-status r t  ( 321 - 324 ) of the second neural sub-structure  320  are thereby a function according to the following rules of the input quantity u t  ( 301 - 304 ), the first internal sub-status s t−1  ( 311 - 314 ), the second internal sub-status r t+1  ( 321 - 324 ) and parameter vectors v s , v t , v y :
 
 s   t   =NN ( v   s   ,s   t−1   ,u   t ),  (8)
 
 r   t   =NN ( v   r   ,r   t+1   ,u   t )  (9)
 
 y   t   =NN ( v   y   ,s   t   ,r   t )  (10)
 
where NN(.) refers to a mapping rule predefined by the neural network.
 
   Connections between the neurons of the CRCNN are weighted. The weightings are combined in parameter vectors v s , v t , v y . 
   The CRCNN  300  according to  FIG. 3  is a neural network developed over four points in time, t−1, t, t+1, t+2) (see TDRNN,  FIG. 5 ). 
   Essential features of a neural network developed over a finite number of points in time are described in David E. Rumelhart et al. and above in relation to the known TDRNN (see  FIG. 5 ). 
   The input quantity u t  ( 301 - 304 ) is thereby the result of the similarity analysis from the first step ( 110 ), i.e. the approximated pattern of forecast energy consumption  112 ,  152 , as determined in the first step. 
   The output quantity y t  ( 341 - 344 ) is thereby the required result of the causality analysis of the second step ( 150 ), i.e. the subsequently corrected pattern of the forecast energy consumption  153  determined in the second step. 
   Possible implementations of the exemplary embodiments described above can be carried out with the program SENN, version 2.3. 
   The invention has been described in detail with particular reference to preferred embodiments thereof and examples, but it will be understood that variations and modifications can be effected within the spirit and scope of the invention covered by the claims which may include the phrase “at least one of A, B and C” as an alternative expression that means one or more of A, B and C may be used, contrary to the holding in  Superguide v. DIRECTV,  69 USPQ2d 1865 (Fed. Cir. 2004).