Simulation

Neil D. Lawrence

Game of Life

Loneliness
loneliness

Crowding
overcrowding

Birth
birth

Glider

Glider (1969)

Loafer

Loafer (2013)

Packing Problems

Packing Problems

Packing Problems

\(=f\Bigg(\)\(\Bigg)\)

If we do discover a theory of everything … it would be the ultimate triumph of human reason-for then we would truly know the mind of God

Stephen Hawking in A Brief History of Time 1988

We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, …

… if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes.

— Pierre Simon Laplace (Laplace, 1814)

\[ \text{data} + \text{model} \stackrel{\text{compute}}{\rightarrow} \text{prediction} \]

Laplace’s Gremlin

Philosophical Essay on Probabilities Laplace (1814) pg 5

Precise Physical Laws

  • Newton’s laws
  • Huygens and conservation of energy
  • Daniel Bernoulli and the kinetic theory of gases
  • Modern climate simulation and Navier-Stokes equations

Abstraction and Emergent Properties

Abstraction

  • We often abstract smaller scales away e.g. in statistical mechanics.
  • When we’re abstracting finer length scales we can introduce uncertainties.
    • E.g. Maxwell-Boltzmann distribution for ideal Gas.

Emergence

  • But fine scale local-laws also lead to emergent properties.
  • Some of these properties exist at large scale.
  • In particular, when there are complex interactions between molecules.

Molecular Dynamics Simulations

Quantum Mechanics

Accelerate Programme

  • Computer Lab hosts Accelerate Programme for Scientific Discovery
  • Use ML techniques to deliver scientific advances
  • Four DECAF fellows: MPhil Projects Available!

Bingqing Cheng quoting Paul Dirac

The fundamental laws necessary for the mathematical treatment of a large part of physics and the whole of chemistry are thus completely known, and the difficulty lies only in the fact that application of these laws leads to equations that are too complex to be solved.

..approximate practical methods of applying quantum mechanics should be developed, which can lead to an explanation of the main features of complex atomic systems without too much computation.

— Paul Dirac (6 April 1929)

Accelerate Fellows

Vincent Dutordoir Sarah Morgan Soumya Banerjee Sam Nallaperuma

Probabilistic Programming

  • Dates back to BUGS
  • Modern descendent (same spirit) is Stan
  • Also languages like pyro (based on PyTorch)

Approximate Bayesian Computation

Causality

Conclusion

  • Introduced simulator: body of computer code.
  • Emergent properties
  • Abstractions
  • Levels of fidelity

Thanks!

References

Laplace, P.S., 1814. Essai philosophique sur les probabilités, 2nd ed. Courcier, Paris.
Roh, S.-H., Shekhar, M., Pintilie, G., Chipot, C., Wilkens, S., Singharoy, A., Chiu, W., 2020. Cryo-EM and MD infer water-mediated proton transport and autoinhibition mechanisms of Vo complex. Science Advances 6. https://doi.org/10.1126/sciadv.abb9605
Stromquist, W.R., 1984. Packing unit squares inside squares, III. Daniel H. Wagner Associates.