My research program centers around the development of novel computational approaches to tackle fundamental questions arising in the study of nonequilibrium systems, with applications to soft matter, systems and computational biology, and machine learning.
One central theme is the development of novel Monte Carlo sampling algorithms to characterize the state-space of complex dynamical systems. Inspired by free-energy calculation techniques developed within the field of molecular simulation my collaborators and I were able to devise efficient algorithms for the characterization of high-dimensional basins of attraction (the set of all initial conditions that lead to a particular solution). These techniques address an open problem in dynamical systems theory and enabled us to answer a number of long-standing questions. A particularly significant result was the first direct test of the Edwards conjecture, a decades-old packing hypothesis forming the basis of the statistical theory of granular matter.
The increased availability of data on the structure and dynamics of biological networks, together with advances in our ability to regulate individual components of these networks, have created the enticing prospect of achieving control of cellular and neural systems. This possibility is broadly significant in the design of novel therapeutic interventions and for understanding the naturally evolved control mechanisms that underlie the functioning of living systems. Yet, the control of biological systems poses considerable challenges due to the high dimensionality of their state spaces, and the non-linearity and multistability of the dynamics. The numerical techniques we develop provide an new way of elucidating certain issues of control, stability and information processing in biological dynamical systems.
Emergent behavior, such as self-organization and ultimately life, are fundamentally connected to a system’s ability to process information. Intuition tells us that information about the environment flows into the system, though it is far from obvious what the internal representation of this information is. There is a fascinating duality between information and the more conventional notion of order that we typically use to characterize phases of matter. An ordered entity should require a shorter description (less information) than a disordered one. This is the premise of lossless data compression: the more ordered the data is the shorter the length of its encoding. Using lossless compression my collaborators and I were able to quantify the phase behavior of a number of nonequilibrium many-body systems, without referring to an order parameter. Currently we are exploring a number of exciting applications of these ideas that span from the identification of diverging correlation lengths to the discovery of new phenomena in models of traffic and animal flocking.
Our work is tightly linked to fundamental questions in optimization and training of machine learning systems. As such we are interested both in addressing fundamental questions concerning the dynamics of learning in neural networks, as well as developing machine learning algorithms for the purpose of control and characterization of complex systems.
- Outstanding Thesis Prize, Department of Chemistry, University of Cambridge (2017)
- Gates Cambridge Scholarship (2013-2017)
- St. John's College Benefactors Scholarship (2013-2017)
- Prize for Best Physical Chemistry Research Project, Department of Chemistry, Imperial College London (2012)
- S. Martiniani, P. M. Chaikin, D. Levine, “Quantifying hidden order out of equilibrium”, Phys. Rev. X, 9, 011031 (2019)
- S. Martiniani, K. J. Schrenk, K. Ramola, B. Chakraborty, D. Frenkel, “Numerical test of the Edwards conjecture shows that all packings become equally probable at jamming”, Nature Physics, 13, 848–851 (2017)
- D. Frenkel, K. J. Schrenk, S. Martiniani “Monte Carlo sampling for stochastic weight functions”, Proc. Natl. Acad. Sci., 114, 27 (2017)
- A. J. Ballard, R. Das, S. Martiniani, D. Mehta, L. Sagun, J. D. Stevenson, D. J. Wales, “Energy Landscapes for Machine Learning”, Phys. Chem. Chem. Phys., 19, 12585-12603 (2017)
- S. Martiniani, K. J. Schrenk, J. D. Stevenson, D. J. Wales, D. Frenkel, “Structural analysis of high dimensional basins of attraction”, Phys. Rev. E 94, 031301 (2016)
- S. Martiniani, K. J. Schrenk, J. D. Stevenson, D. J. Wales, D. Frenkel, “Turning intractable counting into sampling: computing the configurational entropy of three-dimensional jammed packings”, Phys. Rev. E 93, 012906 (2016)
- S. Martiniani, J. D. Stevenson, D. J. Wales, D. Frenkel, “Superposition Enhanced Nested Sampling”, Phys. Rev. X 4, 031034 (2014)