Tag Archives: simulation

Jigsaw puzzling without a picture

A350 XWB passes Maximum Wing Bending test

A350 XWB passes Maximum Wing Bending test

Research sometimes feels like putting together a jigsaw puzzle without the picture or being sure you have all of the pieces.  The pieces we are trying to fit together at the moment are (i) image decomposition of strain fields [see ‘Recognising strain’ on October 28th 2015] that allows fields containing millions of data values to be represented by a feature vector with only tens of elements which is useful for comparing maps or fields of predictions from a computational model with measurements made in the real-world; (ii) evaluation of the variation in measurement uncertainty over a field of view of measured displacements or strains in a large structure [see ‘Industrial uncertainty’ on December 12th 2018] which provides information about the quality of the measurements; and (iii) a probabilistic validation metric that provides a measure of how well predictions from a computational model represent measurements made in the real world [see ‘Million to one’ on November 21st 2018].  We have found some of the missing pieces of the jigsaw, for example we have established how to represent the distribution of measurement uncertainty in the feature vector domain [see ‘From strain measurements to assessing El Niño events’ on March 17th 2021] so that it can be used to assess the significance of differences between measurements and predictions represented by their feature vectors – this connects (i) and (ii) together.  Very recently we have demonstrated a generic technique for performing image decomposition of irregularly shaped fields of data or data fields with holes [see Christian et al, 2021] which extends the applicability of our method for comparing measurements and predictions to real-world objects rather than idealised shapes.  This allows (i) to be used in industrial applications but we still have to work out how to connect this to the probabilistic metric in (iii) while also incorporating spatially-varying uncertainty.  These techniques can be used in a wide range of applications, as demonstrated in our recent work on El Niño events [see Alexiadis et al, 2021], because, by treating all fields of data as images, the techniques are agnostic about the source and format of the data.  However, at the moment, our main focus is on their application to ground tests on aircraft structures as part of the Smarter Testing project in collaboration with Airbus, Centre for Modelling & Simulation, Dassault Systèmes, GOM UK Ltd, and the National Physical Laboratory with funding from the Aerospace Technology Institute.  Together we are working towards digital continuity across virtual and physical testing of aircraft structures to provide live data fusion and enable condition-led inspections, test control and validation of computational models.  We anticipate these advances will reduce time and costs for physical tests and accelerate the development of new designs of aircraft that will contribute to global sustainability targets (the aerospace industry has committed to reduce CO2 emissions to 50% of 2005 levels by 2050).  The Smarter Testing project has an ambitious goal which reveals that our pieces of the jigsaw puzzle belong to a small section of a much larger one.

For more on the Smarter Testing project see:




Alexiadis A, Ferson S, Patterson EA. Transformation of measurement uncertainties into low-dimensional feature vector space. Royal Society open science. 8(3):201086, 2021.

Christian WJ, Dean AD, Dvurecenska K, Middleton CA, Patterson EA. Comparing full-field data from structural components with complicated geometries. Royal Society open science. 8(9):210916, 2021.

Image: http://www.airbus.com/galleries/photo-gallery

Somethings will always be unknown

Decorative image of a fruit fly nervous system Albert Cardona HHMI Janelia Research Campus Welcome Image Awards 2015The philosophy of science has oscillated between believing that everything is knowable and that somethings will always be unknowable. In 1872, the German physiologist, Emil du Bois-Reymond declared ‘we do not know and will not know’ implying that there would always be limits to our scientific knowledge. Thirty years later, David Hilbert, a German mathematician stated that nothing is unknowable in the natural sciences. He believed that by considering some things to be unknowable we limited our ability to know. However, Kurt Godel, a Viennese mathematician who moved to Princeton in 1940, demonstrated in his incompleteness theorems that for any finite mathematical system there will always be statements which are true but unprovable and that a finite mathematical system cannot demonstrate its own consistency. I think that this implies some things will remain unknowable or at least uncertain. Godel believed that his theorems implied that the power of the human mind is infinitely more powerful than any finite machine and Roger Penrose has deployed these incompleteness theorems to argue that consciousness transcends the formal logic of computers, which perhaps implies that artificial intelligence will never replace human intelligence [see ‘Four requirements for consciousness‘ on January 22nd, 2020].  At a more mundane level, Godel’s theorems imply that engineers will always have to deal with the unknowable when using mathematical models to predict the behaviour of complex systems and, of course, to avoid meta-ignorance, we have to assume that there are always unknown unknowns [see ‘Deep uncertainty and meta-ignorance‘ on July 21st, 2021].

Source: Book review by Nick Stephen, ‘Journey to the Edge of Reason by Stephen Budiansky – ruthless logic‘ FT Weekend, 1st June 2021.

Deep uncertainty and meta-ignorance

Decorative imageThe term ‘unknown unknowns’ was made famous by Donald Rumsfeld almost 20 years ago when, as US Secretary of State for Defense, he used it in describing the lack of evidence about terrorist groups being supplied with weapons of mass destruction by the Iraqi government. However, the term was probably coined by almost 50 years earlier by Joseph Luft and Harrington Ingham when they developed the Johari window as a heuristic tool to help people to better understand their relationships.  In engineering, and other fields in which predictive models are important tools, it is used to describe situations about which there is deep uncertainty.  Deep uncertainty refers situations where experts do not know or cannot agree about what models to use, how to describe the uncertainties present, or how to interpret the outcomes from predictive models.  Rumsfeld talked about known knowns, known unknowns, and unknown unknowns; and an alternative simpler but perhaps less catchy classification is ‘The knowns, the unknown, and the unknowable‘ which was used by Diebold, Doherty and Herring as part of the title of their book on financial risk management.  David Spiegelhalter suggests ‘risk, uncertainty and ignorance’ before providing a more sophisticated classification: aleatory uncertainty, epistemic uncertainty and ontological uncertainty.  Aleatory uncertainty is the inevitable unpredictability of the future that can be fully described using probability.  Epistemic uncertainty is a lack of knowledge about the structure and parameters of models used to predict the future.  While ontological uncertainty is a complete lack of knowledge and understanding about the entire modelling process, i.e. deep uncertainty.  When it is not recognised that ontological uncertainty is present then we have meta-ignorance which means failing to even consider the possibility of being wrong.  For a number of years, part of my research effort has been focussed on predictive models that are unprincipled and untestable; in other words, they are not built on widely-accepted principles or scientific laws and it is not feasible to conduct physical tests to acquire data to demonstrate their validity [see editorial ‘On the credibility of engineering models and meta-models‘, JSA 50(4):2015].  Some people would say untestability implies a model is not scientific based on Popper’s statement about scientific method requiring a theory to be refutable.  However, in reality unprincipled and untestable models are encountered in a range of fields, including space engineering, fusion energy and toxicology.  We have developed a set of credibility factors that are designed as a heuristic tool to allow the relevance of such models and their predictions to be evaluated systematically [see ‘Credible predictions for regulatory decision-making‘ on December 9th, 2020].  One outcome is to allow experts to agree on their disagreements and ignorance, i.e., to define the extent of our ontological uncertainty, which is an important step towards making rational decisions about the future when there is deep uncertainty.


Diebold FX, Doherty NA, Herring RJ, eds. The Known, the Unknown, and the Unknowable in Financial Risk Management: Measurement and Theory Advancing Practice. Princeton, NJ: Princeton University Press, 2010.

Spiegelhalter D,  Risk and uncertainty communication. Annual Review of Statistics and Its Application, 4, pp.31-60, 2017.

Patterson EA, Whelan MP. On the validation of variable fidelity multi-physics simulations. J. Sound and Vibration. 448:247-58, 2019.

Patterson EA, Whelan MP, Worth AP. The role of validation in establishing the scientific credibility of predictive toxicology approaches intended for regulatory application. Computational Toxicology. 100144, 2020.

Negative capability and optimal ambiguity

Decorative photograph of sculpture on Liverpool waterfront at nightHow is your negative capability?  The very term ‘negative capability’ conveys confusion and ambiguity.  It means our ability to accept uncertainty, a lack of knowledge or control.  It was coined by John Keats to describe the skill of appreciating something without fully understanding it.  It implies suspending judgment about something in order to learn more about it.  This is difficult because we have to move out of a low entropy mindset and consider how it fits in a range of possible mindsets or neuronal assemblies, which raises our psychological entropy and with it our anxiety and mental stress [see ’Psychological entropy increased by effectual leaders‘ on February 10th, 2021].  If we are able to tolerate an optimal level of ambiguity and uncertainty then we might be able to develop an appreciation of a complex system and even an ability to anticipate its behaviour without a full knowledge or understanding of it.  Our sub-conscious brain has excellent negative capabilities; for example, most of us can catch a ball without understanding, or even knowing, anything about the mechanics of its flight towards us, or we accept a ride home from a friend with no knowledge of their driving skills and no control over the vehicle.  Although, if our conscious brain knows that they crashed their car last week then it might override the sub-conscious and cause us to think again before declining the offer of a ride home.  Perhaps this is because our conscious brain tends to have less negative capability and likes to be in control.  Engineers like to talk about their intuition which is probably synonymous with their negative capability because it is their ability to appreciate and anticipate the behaviour of an engineering system without a full knowledge and understanding of it.  This intuition is usually based on experience and perhaps resides in the subconscious mind because if you ask an engineer to explain a decision or prediction based on their intuition then they will probably struggle to provide a complete and rational explanation.  They are comfortable with an optimal level of ambiguity although of course you might not be so comfortable.


Richard Gunderman, ‘John Keats’ concept of ‘negative capability’ – or sitting in uncertainty –  is needed now more than ever’.  The Conversation, February 21st, 2021.

David Jeffery, Letter: Keats was uneasy about the pursuit of perfection.  FT Weekend, April 2nd, 2021.

Caputo JD. Truth: philosophy in transit. London: Penguin, 2013.