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    Louis group research interests: Soft and Biological Systems

Research in our group is interdisciplinary, on the border between theoretical physics and chemistry, applied mathematics and biology. We study how complex behaviour emerges from the interactions between many individual objects. We primarily use the tools of statistical mechanics -- especially analytic theories and computer simulations -- to better understand the behaviour of these fascinating systems. "Coarse-graining", where a subset of the (microscopic) degrees of freedom are integrated out to yield a simpler and more tractable problem, is a common theme in these descriptions. Here at Oxford, we work closely with members of the Theory of Soft and Biological Matter group, with whom we share many research interests.

Research Projects in the Louis group

Here are some research projects that give a flavour of the work in our group. In practice, these projects always evolve, in part because research advances rapidly, and in part because we adapt the projects to the particular strengths and interests of the DPhil candidates or postdocs.

  • Fundamental properties of deep neural networks for deep learning

    The current revolution in artificial intelligence (AI) is driven by the amazing computational capacities neural networks, which are simplified models of how our brains works. When linked together into multiple layer architectures, this machine learning approach is called deep learning. In spite of so much practical success, there is little fundamental understanding of why deep learning works so well. For example, deep neural networks (DNNs) perform best in the overparameterised regime, with many more parameters than data points. Physicists are taught from an early age to limit never to have too many parameters. In Freeman Dyson's charming account of his meeting with Enrico Fermi , the latter quotes John von Neumann's aphorism "with four parameters I can fit an elephant, and with five I can make him wiggle his trunk". So given that DNNs have so many millions (or billions) of parameters, why do they work so well?

    We have recently used concepts derived from AIT to argue that

    1. Deep learning generalizes because the parameter-function map is biased towards simple functions. In other words, because in practice deep learning is typically learning relatively simple functions, this intrinsic exponential bias means that it naturally avoids overfitting and can make good predictions (generalise well) on new data that it hasn't seen yet. Without this strong intrinsic bias towards simplicity, deep neural networks would not really work. We are quite excited about this result. There are many further implications of this work that we are currently exploring.
    2. Of course DNNs are normally trained by stochastic gradient descent. However, we have shown that SGD acts almost as a Bayesian sampler , which means that it outputs functions with probabilities close to those predicted from random sampling of the parameter-function map. Thus bias in the map explains bias in SGD trained DNNs, which in turn explains why DNNs generalise well, even though they are overparameterised and highly expressive.
    3. We formalise some of these ideas in our overview paper on Generalization bounds for deep learning , where we also present a new marginal-likelihood bound that, we think, is the best performing bound currently on the market. For physicists who are not familiar with them, such bounds are a staple of statistical learning theory. One of our longer term interests is to connect this field more closely to concepts from statistical mechanics. We have many other interests connecting physics with AI in general, and deep learning in particular. I can currently take on several DPhil students on these topics, and may entertain related questions in computational neuroscience.
    4. A talk: "Deep neural networks have an inbuilt Occam's razor"
  • Self-Assembling DNA

    The ability to design nanostructures which accurately self-assemble from simple units is central to the goal of engineering objects and machines on the nanoscale. Without self-assembly, structures must be laboriously constructed in a step by step fashion. Double-stranded DNA (dsDNA) has the ideal properties for a nanoscale building block, and new DNA nanostructures are being published at an ever increasing rate. Here in the Clarendon the world-leading experimental group of Andrew Turberfield has created a number of intriguing nanostructures using physical self-assembly mechanisms. We have recently developed a new simplified theoretical model of DNA that appears to capture the dominant physics involved. In this project you would apply the model to study some simple nanostructures. You will mainly be using Monte Carlo simulations and statistical mechanical calculations to study these processes. A potential new direction for this project could also be to extend our new methods to study RNA nanostructures.


  • The physics of biological evolution

    "Nothing in Biology Makes Sense Except in the Light of Evolution." wrote the great naturalist Theodosius Dobzhansky , but to really understand evolution, a stochastic optimization process in a very high dimensional space, will require techniques from statistical physics. In this project you will use theoretical tools and computer simulations to study a number of simplified models we have been developing in our group to understand the physics of evolution. We are studying the evolution of protein quaternary structure, RNA secondary structures, gene regulatory networks and more, with a focus on how concepts from algorithmic information theory help explain how evolutionary search is so efficient at finding solutions.

  • Applying algorithmic information theory (AIT)

    While many results from AIT are beautiful and profound, they are often thought to be hard to apply in practice because 1) AIT's central concept, Kolmogorov-Chaitin complexity, is formally incomputable, 2) AIT depends crucially on universal Turing machines (UTMs) wile many practical systems are not universal, and 3) because many of its results are only valid in the asymptotic limit of long strings, while applications are often not in this limit. We are currently trying to circumvent these problems, see e.g. our recent paper in Nature Communications Input–output maps are strongly biased towards simple outputs .where we show applictions ranging from RNA folding to systems of differential equations to models of plant growth to stochastic models for finanancial trading. We are currently working on applications ranging from machine learning to evolution to string theory.
    Examples of simplicity bias in RNA sequences, circadian rhythms, and financial models. The higher the complexity of an output, the lower the probability that the output will be generated.

    Read more at: Oxford blog post on simplicity bias | Phys.org blog post on simplicity bias
  • Design Rules for Self-Assembly

    The remarkable ability of biological matter to robustly self-assemble into well defined composite objects excites the imagination. Viruses, for example, can be reversibly dissolved and re-assembled from their component parts simply by changing the solution pH. How does nature achieve this feat? Can we uncover the "positive design rules" for inter-particle interactions that allow the self-assembly of a particular desired 3-dimensional structure [1]? Can we use evolutionary algorithms to design these particles? Such understanding could have important implications for nanoscience, where objects are too small to directly manipulate, and instead must come together by self-assembly mechanisms.
    This project is in close collaboration with the group of Prof. Jonathan Doye.

    Here is a movie that Iain made about virus self-assembly:


    [1] Reversible self-assembly of patchy particles into monodisperse clusters
    Alex W. Wilber, Jonathan P. K. Doye, Ard A. Louis, Mark A. Miller, Eva G. Noya, Pauline Wong
    J. Chem. Phys. 127, 085106 (2007)
    | arxiv abstract | pdf reprint| Modelling the Self-Assembly of Virus Capsids


    Iain G. Johnston, Ard A. Louis and Jonathan P.K. Doye
    J. Phys.: Condensed Matter, 22 , 104101 (2010)
    | arxiv abstract | pdf reprint | (this paper was selected for journal cover and as one of the journal's Highlights of 2010)

  • The interplay of Brownian and hydrodynamic interactions in suspensions

    When suspended particles move in a background fluid, they experience random kicks (Brownian motion), but also generate long-ranged hydrodynamic flows. This project would use a new computer simulation method, stochastic rotation dynamics (SRD) that includes both these effects, to study flow properties of complex fluids. There is also scope for more mathematical approaches combining non-equilibrium statistical mechanics and hydrodynamics to explain some of the dramatic effects we are seeing. Examples of applications include dynamic lane formation, fluctuations during sedimentation, colloidal nano-pumps, and colloidal "explosions".

      To see the effect of hydrodynamic interactions, compare these two movies:
    • .

    • Or check out what happens when you have aggregation and sedimentation:

    This project would also work closely with the experimental groups of Dr Roel Dullens and Dr Dirk Aarts , and the theory group of Prof Julia Yeomans

    The effects of inter-particle attractions on colloidal sedimentation
    A. Moncho Jorda', A. A. Louis and J. T. Padding
    Phys. Rev. Lett. 104, 068301 (2010)
    | arxiv abstract | pdf reprint | (this paper was selected as an Editor's Suggestion" in PRL)

    The interplay between hydrodynamic and Brownian fluctuations in sedimenting colloidal suspensions
    J.T. Padding and A.A. Louis
    Phys. Rev. E 77, 011402 (2008) || pdf reprint |

    Hydrodynamic interactions and Brownian forces in colloidal suspensions: Coarse-graining over time and length-scales
    J.T. Padding and A.A. Louis
    Phys. Rev. E 74, 031402 (2006)
    | arxiv abstract | pdf reprint|

    Hydrodynamic and Brownian Fluctuations in Sedimenting Suspensions
    J.T. Padding and A. A. Louis, Phys. Rev. Lett. 93, 220601 (2004)
    | arxiv abstract | pdf reprint|

  • Fundamental questions in coarse-graining

    An important source of progress in statistical mechanics comes from better coarse-grained models, that is descriptions that are simpler and more tractable, but nevertheless retain the fundamental underlying physics that one is interested in investigating. It is intuitively obvious that these simplified descriptions throw some information away and that compromises are made. After all, there is no such thing as a free lunch. But how much are we paying, and what can we get away with? We have argued that good coarse-graining procedures are best interpreted in terms of the emergent properties that one is trying to model.

  • Here are two introductory papers:
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