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Adjoint based gradient calculation - advantantages and challenges

Adjoint based gradient calculation - advantantages and challenges. Bjarne Foss, Ruben Ringset The Norwegian University of Science & Technology – NTNU IO center. Outline Motivation A simple example to illustrate the potential of adjoints Where are the hurdles? Conclusions. Motivation.

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Adjoint based gradient calculation - advantantages and challenges

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  1. Adjoint based gradient calculation - advantantages and challenges Bjarne Foss, Ruben Ringset The Norwegian University of Science & Technology – NTNU IO center • Outline • Motivation • A simple example to illustrate the potential of adjoints • Where are the hurdles? • Conclusions

  2. Motivation Model Norne field StatoilHydro Eni, Petoro Data

  3. Optimize Parameter estimation Motivation now now time history well schedule model simulator forecast for k=1 to N ...simulate(k) end + Uncertainty

  4. Motivation Inlet separator Pipelines/tankers Market Wells Pipelines Reservoir Process Utilities Reservoir and well models (Eclipse) Network model (GAP, MaxPro, OLGA) Process model (HYSIS) Application Value chain optimization Optimization requires a large number of gradient calculations Efficient gradient computations are important

  5. A simple example

  6. A simple example

  7. A simple example

  8. A simple example

  9. Adjoint gradient computation

  10. Adjoint gradient computation Forward simulation

  11. Adjoint gradient computation One forward simulation One reverse simulation

  12. Forward method N forward simulations (nested loops)

  13. The output constraint challenge – possible remedies Reducing the number of constraints • Enforcing them on parts of a prediction horizon • Lumping output constraints together • One interesting application of this is found in the Standford GPRS reservoir simulator (Sarma et al, 2006)

  14. The output constraint challenge

  15. The output constraint challenge – possible remedies Reducing the number of constraints • Enforcing them on parts of a prediction horizon • Lumping output constraints together • One interesting application of this is found in the Standford GPRS reservoir simulator (Sarma et al, 2006) Taking advantage of barrier or interior point optimization methods • Removing output constraints without introducing slack variables • Model constraints (i.e. equality constraints) can be removed by a single shooting method (in eg. MPC)

  16. Adjoint based gradient calculation - advantantages and challenges • Conclusions • Adjoint based gradient calculation may give huge improvements in run-time • Output constraints is a challenge

  17. Once again - A very simple example Let Lagrangian function and assume that is the independent variable, i.e. Compute the gradient wrt (”reverse simulation”) Choose

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