Modeling of the radiation belt megnetosphere in decisional timeframes

1. A computerized method of accelerating calculation of L* in accordance with physics-based model of conditions in a magnetosphere comprising:

defining a surrogate model to be a surrogate for a physics-based model of L* for magnetic belts based on formula L*=(2πμ 0 )/(ΦR E )

providing surrogate model computer instructions and surrogate model data;

training the surrogate model to be a surrogate for the physics-based model of L* for magnetic belts based on the formula L*=(2πμ 0 )/(ΦR E ), wherein the physics-based model uses a plurality of physics-based model parameters, further comprising:

providing physics data based on the physics-based model parameters;

providing spatial data representing spatial coordinates for the location where L* is to be calculated;

providing surrogate models including sets of data for the physics-based model for each of a plurality of pitch angles;

selecting from the plurality of surrogate models at least one surrogate model set of data and instructions that calculate a closed drift shell for the physics-based model parameters and the spatial coordinates; and

calculating L* by providing the physics-based model parameters and the spatial coordinates to the selected surrogate models that calculate a closed drift shell; and

processing the trained surrogate model with a computer processor to accelerate the calculation of L* over a physics-based model.

2. The computerized method of claim 1 , wherein the computer instructions and data comprise a feedforward neural network.

3. The computerized method of claim 1 , wherein the physics-based model comprises the TSK03 model, a type of physics-based model for calculating L*.

4. The computerized method of claim 1 wherein the surrogate model instructions are configured to provide:

a first plurality of input-layer units, there being at least one input-layer unit for each physics-based model parameter;

a second plurality of hidden layer units;

at least one output unit for the value of L*;

a third plurality of first communication avenues, each first communication avenue connecting one of first plurality of input-layer units to one of the second plurality of hidden layer units, each communication avenue having a weighting value that represents the weight that the respective individual hidden layer unit gives to the respective input-layer unit; and

a fourth plurality of second communication avenues, each second communication avenue connecting one of second plurality of hidden layer units to the output unit, each second communication avenue having a weighting value that represents the weight that the output unit gives to the respective hidden layer unit.

5. The computerized method of claim 4 , wherein calculating L* comprises:

providing data values to each of the first plurality of input-layer units;

generating values for each of second plurality of hidden layer units, the values associated with each of the hidden-layer units being determined by the weights that the respective hidden layer unit gives to each of the input-layer units that it is connected to by a communication avenue; and

generating a value of L* from the values generated for the second plurality of hidden layer units, the value of L* being determined by the weights that the output layer unit gives to each of the hidden-layer units that it is connected to by a communication line.

6. The computerized method of claim 1 , adapted to predict an environment in the magnetosphere for a location at a second time later than a first time comprising:

calculating L* for the location at the first time using the surrogate model;

providing charge flux information for the location at the first time;

calculating a phase space density at the location at the first time from the value of L* at the location at the first time and the charge flux information for the location at the first time;

providing a radiation belt model;

forecasting the phase space density at the location at the second time using the radiation belt model and data assimilation methods;

calculating L* for the location at the second time using the surrogate model; and

converting the phase space density at the location at the second time into a value of charge flux using the value of L* for the location at the second time.

7. The computerized method of claim 6 adapted to operate a satellite, wherein the calculated phase space density at the second time is compared to a predetermined value of phase space density to decide about operating the satellite's protections against space weather.

8. A computerized method of accelerating calculation of L* in accordance with physics-based model of conditions in a magnetosphere comprising:

defining a surrogate model to be a surrogate for a physics-based model of L* for magnetic belts based on formula L*=(2πμ 0 )/(ΦR E );

providing surrogate model computer instructions and surrogate model data;

training the surrogate model to be a surrogate for the physics-based model of L* for magnetic belts based on the formula L*=(2πμ 0 )/(ΦR E );

processing the trained surrogate model with a computer processor to accelerate the calculation of L* over a physics-based model; and

predicting an environment in the magnetosphere for a location at a second time later than a first time comprising:

calculating L* for the location at the first time using the surrogate model;

providing charge flux information for the location at the first time;

calculating the phase space density at the location at the first time from the value of L* at the location at the first time and the charge flux information for the location at the first time;

providing a radiation belt model;

forecasting the phase space density at the location at the second time using the radiation belt model and data assimilation methods;

calculating L* for the location at the second time using the surrogate model; and

convert the phase space density at the location at the second time into a value of charge flux using the value of L* for the location at the second time,

wherein the calculated phase space density at the second time is compared to a predetermined value of phase space density to decide about operating a satellite's protections against space weather.

9. The computerized method of claim 8 , wherein the computer instructions and data comprise a feedforward neural network.

10. The computerized method of claim 8 , wherein the physics-based model comprises the TSK03 model, a type of physics-based model for calculating L*.

11. The computerized method of claim 8 wherein the physics-based model uses a plurality of physics-based model parameters, further comprising:

providing physics data based on the physics-based model parameters;

providing spatial data representing spatial coordinates for the location where L* is to be calculated;

providing surrogate models including sets of data for the physics-based model for each of a plurality of pitch angles;

selecting from the plurality of surrogate models at least one surrogate model set of data and instructions that calculate a closed drift shell for the physics-based model parameters and the spatial coordinates;

calculating L* by providing the physics-based model parameters and the spatial coordinates to the selected surrogate models that calculate a closed drift shell.

12. The computerized method of claim 8 wherein the surrogate model instructions are configured to provide:

a first plurality of input-layer units, there being at least one input-layer unit for each physics-based model parameter;

a second plurality of hidden layer units;

at least one output unit for the value of L*;

a third plurality of first communication avenues, each first communication avenue connecting one of first plurality of input-layer units to one of the second plurality of hidden layer units, each communication avenue having a weighting value that represents the weight that the respective individual hidden layer unit gives to the respective input-layer unit; and

a fourth plurality of second communication avenues, each second communication avenue connecting one of second plurality of hidden layer units to the output unit, each second communication avenue having a weighting value that represents the weight that the output unit gives to the respective hidden layer unit.

13. The computerized method of claim 12 , wherein calculating L* comprises:

providing data values to each of the first plurality of input-layer units;

generating values for each of second plurality of hidden layer units, the values associated with each of the hidden-layer units being determined by the weights that the respective hidden layer unit gives to each of the input-layer units that it is connected to by a communication avenue; and

generating a value of L* from the values generated for the second plurality of hidden layer units, the value of L* being determined by the weights that the output layer unit gives to each of the hidden-layer units that it is connected to by a communication line.