# Automated adjoints: how much do we really know about the source of the Indian Ocean Tsunami?

Lead Research Organisation:
Imperial College London

Department Name: Earth Science and Engineering

### Abstract

Tsunamis are one of the most rapid and destructive of the geohazards which humanity faces and the Indian Ocean Tsunami of 26 December 2004 was the most powerful and destructive in recent history. In the intervening five years, much scientific effort has been expended attempting to understand the source and propagation of the tsunami. In many cases, hypotheses about the source region of the tsunami, which have been derived from geological, seismic and GPS data, have been tested by running a numerical ocean model starting from that source and comparing the results to tide gauge data and satellite altimetry taken during the actual tsunami event. These studies are an important contribution to our understanding of this devastating event, but they miss one important question: to what extent do the observations constrain the source region or could there be important differences in the source region which are not detectable in the relatively small number of observations we have to compare with? One reason that the existing studies have generally not addressed this problem is that studying the sensitivity of the model outputs to the model inputs, which is the essence of the question here, requires the use of an adjoint, or inverse, model. Producing forward ocean models is already a significant research task and producing a correct and matching adjoint model is very difficult and the resulting model system is typically very expensive in processor time to run. This project will employ exciting new software and hardware technology to vastly simplify the process of producing an adjoint model and deliver the performance increases needed to make adjoint problems tractable. The software technology in question is automatic code generation. In this approach the mathematical formulation of the finite element problem is automatically converted into highly efficient computer code. This dramatically reduces both developer effort and the incidence of code bugs. The novel aspect here will be to use this high level mathematical formulation to automatically generate the adjoint formulation, thereby avoiding the difficulty of building two models and ensuring consistency between forward and adjoint models. The novel hardware technology is graphical processing units (GPUs). Initial studies at Imperial College have indicated that automatically generated model code for GPUs can run more than twenty times faster than the equivalent code for ordinary processors. This combination of hardware and software will result in a step-change in the ease of development and the cost of running adjoint tsunami models. The resulting model will be used to conduct the missing sensitivity analysis of a number of the published tsunami source scenarios and will thereby enable us to answer the question: 'how much do we really know about the source of the Indian Ocean Tsunami?'.

## People |
## ORCID iD |

David Ham (Principal Investigator) |

### Publications

*Automated Derivation of the Adjoint of High-Level Transient Finite Element Programs*in SIAM Journal on Scientific Computing

Description | This grant resulted in a major breakthrough in inverse simulation technology. By successfully capturing the mathematical form of a numerical simulation, we were able to form the inverse problem automatically and execute it with very high performance. The software which resulted from this grant was recognised with the 2015 Wilkinson Prize for Numerical Software, the world's leading numerical software prize. |

Exploitation Route | Inverse simulation problems are pervasive in science and engineering: from data assimilate in weather forecasting to optimal design, science and engineering are not just about asking "what happens if..."; asking "what causes this?" is more prevalent. In simulation science, this requires the solution of inverse problems. Dolfin-adjoint is released, professionally engineered software. It is in use at universities around the UK and overseas for the solution of inverse problems in fluid and solid mechanics. Plans are underway to extend its capabilities to include shape optimisation, which is critical for optimal engineering design problems. |

Sectors | Aerospace, Defence and Marine,Chemicals,Energy,Environment,Manufacturing, including Industrial Biotechology |

URL | http://www.dolfin-adjoint.org/ |

Description | NERC Independent Research Fellowship |

Amount | £492,313 (GBP) |

Funding ID | NE/K008951/1 |

Organisation | Natural Environment Research Council |

Sector | Public |

Country | United Kingdom |

Start | 09/2013 |

End | 08/2018 |

Description | Automating the adjoints of finite element models in the FEniCS framework |

Organisation | Simula Research Laboratory |

Country | Norway |

Sector | Academic/University |

PI Contribution | In the context of this grant I established a collaboration with the Simula Research Laboratory in Norway to automate the calculation of the adjoints to a much broader class of models. This involves manipulating the mathematical formulation of those models at a far higher level than is possible in conventional models. The result is that forming the adjoint of a model is almost automatic, and the adjoint execution is almost optimally efficient. By conventional mechanisms, the development of an adjoint model is massively labour-intensive and error-prone, and the resulting code is frequently very inefficient. On the basis of this collaboration, we engaged with Simula as a partner on a Marie Curie Innovative Doctoral Programme proposal which is currently at the shortlisting stage. |

Start Year | 2011 |

Title | dolfin-adjoint |

Description | The dolfin-adjoint project automatically derives the discrete adjoint and tangent linear models from a forward model written in the Python interface to DOLFIN. These adjoint and tangent linear models are key ingredients in many important algorithms, such as data assimilation, optimal control, sensitivity analysis, design optimisation, and error estimation. Such models have made an enormous impact in fields such as meteorology and oceanography, but their use in other scientific fields has been hampered by the great practical difficulty of their derivation and implementation. |

Type Of Technology | Software |

Year Produced | 2012 |

Open Source License? | Yes |

Impact | dolfin-adjoint is the core technolgy enabling the opentidalfarm tidal energy optimisation simulator. It also underlies the adjoint-beat inverse electrocardiosimulator. |

URL | http://dolfin-adjoint.org/ |