Reproducibility and the Concept of Numerical Solution
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In this paper, we show that reproducibility is a severe problem that concerns simulation models. The reproducibility problem challenges the concept of numerical solution and hence the conception of what a simulation actually does. We provide an expanded picture of simulation that makes visible those steps of simulation modeling that are numerically relevant, but often escape notice in accounts of simulation. Examining these steps and analyzing a number of pertinent examples, we argue that numerical solutions are importantly different from usual mathematical solutions. They are do not merely approximate the latter, but introduce new problems, including issues of artificiality, stability, and well-posedness. Consequently, simulation modelling can attain reproducibility only to a certain degree because it is working with numerical solutions (in a sense we specify in the paper).
KeywordsArtificiality Ill-posed problems Mathematical solution Numerical solution Reproducibility Stability Tractability
We like to thank three anonymous reviewers for useful suggestions and Nicholas Danne for his support in approximating our text to English language.
- Böning, C., Beismann, J.-O., Biastoch, A., Czeschel, L., & Dengg, J. (2002). Ozeanische Aufnahme anthropogener Spurengase: Realistische Darstellung des Effektes mesoskaliger Prozesse in Zirkulationsmodellen. Presentation at DKRZ WLA-Workshop, 24(10), 2002.Google Scholar
- Collins, H. (1985). Replication and induction in scientific practice. Chicago: Chicago University Press.Google Scholar
- Duddeck, F. (2007) Survey on robust design and optimization for crashworthiness. In EUROMECH colloquium 482: Efficient methods for robust design and optimization. Queen Mary, University of London, London, UK.Google Scholar
- Fillion, N. (2017). The vindication of computer simulations. In J. Lenhard, M. Carrier (eds.) Mathematics as a tool (pp. 137–55). Boston Studies in History and Philosophy of Science 327. New York: Springer.Google Scholar
- Hasse, H., & Lenhard, J. (2017). Boon and bane. On the role of adjustable parameters in simulation models. In J. Lenhard, & M. Carrier (eds.) Mathematics as a tool. Tracing new roles of mathematics in the sciences. Boston Studies in the Philosophy and History of Science (Vol. 327, pp. 93–115).Google Scholar
- Kaminski, A., Resch, M., and Küster, U.: Mathematische Opazität. Über Rechtfertigung und Reproduzierbarkeit in der Computersimulation. In A. Friedrich, P. Gehring, C. Hubig, A. Kaminski, & A. Nordmann (eds.) Jahrbuch Technikphilosophie (Vol. 4, pp. 253–277). Nomos Verlag, 2018.Google Scholar
- Lenhard, J. (2016). Computer simulation. In P. Humphreys (Ed.), Oxford handbook in the philosophy of science (pp. 717–737). New York: Oxford University Press.Google Scholar
- Ludwig, T. (2017). Reproducibility in science, computer science and climate science. News from Computational Climate Science. Prsentation in: Leogang, 08.03.2017.Google Scholar
- Parker, W. S. (2013). Computer Simulation. In S. Psillos & M. Curd (Eds.), The routledge companion to philosophy of science (2d ed., pp. 135–145). New York: Routledge.Google Scholar
- Richardson, L. F. (1922). Weather prediction by numerical process, 1st edn. 1922, Cambridge UP; cited according to second unaltered and unabridged edition with new introduction by Sydney Chapman, 1965, Dover.Google Scholar
- Schappals, M., Mecklenfeld, A., Kröger, L., Botan, V., Köster, A., Stephan, S., et al. (2017). Round Robin study: Molecular simulation of thermodynamic properties from models with internal degrees of freedom. Journal of Chemical Theory and Computation, 13, 4270–4280. https://doi.org/10.1021/acs.jctc.7b00489.CrossRefGoogle Scholar
- Winsberg, E. (2018). Computer simulations in science. In Edward N. Zalta (ed.) The stanford encyclopedia of philosophy (Summer 2018 Edition), forthcoming. https://plato.stanford.edu/archives/sum2018/entries/simulations-science/.