Simon Etter

Mathematician & Software Engineer

eMail GitHub

Employment

2022
  • Software Engineer at Ackham Capital (Singapore)
  • Main developer of a crypto-currency arbitrage trading bot. Bot was written mainly in Rust, with connectors to EVM nodes and the Binance API implemented as TypeScript gRPC servers.
2021
  • Algorithms Engineer at Synchronous Technologies (Singapore)
  • Developed fast algorithms for factory scheduling. Wrote code in Julia, Python and C++. Created and contributed to various open-source Julia packages.
2019 - 2021

Education

2015 - 2019
2013 - 2015
2010 - 2013

Bibliography

Papers

  • Modeling and Computation of Kubo Conductivity for Two-Dimensional Incommensurate Bilayers
    S. Etter, D. Massatt, M. Luskin, C. Ortner
    Multiscale Modeling & Simulation (2020), 18:4, 1525–1564
    This paper presents a unified approach to the modeling and computation of the Kubo conductivity of incommensurate bilayer heterostructures at finite temperature. Firstly, we derive an expression for the large-body limit of Kubo-Greenwood conductivity in terms of an integral of the conductivity function with respect to a current-current correlation measure. We then observe that the incommensurate structure can be exploited to decompose the current-current correlation measure into local contribution and deduce an approximation scheme which is exponentially convergent in terms of domain size. Secondly, we analyze the cost of computing local conductivities via Chebyshev approximation. Our main finding is that if the inverse temperature \(\beta\) is sufficiently small compared to the inverse relaxation time \(\eta\), namely \(\beta \lesssim \eta^{-1/2}\), then the dominant computational cost is \(\mathcal{O}(\eta^{−3/2})\) inner products for a suitably truncated Chebyshev series, which significantly improves on the \(\mathcal{O}(\eta^{−2})\) inner products required by a naive Chebyshev approximation. Thirdly, we propose a rational approximation scheme for the low temperature regime \(\eta^{-1/2} \lesssim \beta\), where the cost of the polynomial method increases up to \(\mathcal{O}(\beta^2)\), but the rational scheme scales much more mildly with respect to \(\beta\).
  • Incomplete selected inversion for linear-scaling electronic structure calculations
    S. Etter
    ArXiv (2020)
    Pole Expansion and Selected Inversion (PEXSI) is an efficient scheme for evaluating selected entries of functions of large sparse matrices as required e.g. in electronic structure algorithms. We show that the triangular factorizations computed by the PEXSI scheme exhibit a localization property similar to that of matrix functions, and we present a modified PEXSI algorithm which exploits this observation to achieve linear scaling. To the best of our knowledge, the resulting incomplete PEXSI (iPEXSI) algorithm is the first linear-scaling algorithm which scales provably better than cubically even in the absence of localization, and we hope that this will help to further lower the critical system size where linear-scaling algorithms begin to outperform the diagonalization algorithm.
  • Parallel ALS algorithm for solving linear systems in the hierarchical Tucker representation
    S. Etter
    SIAM Journal on Scientific Computing (2016), 38:4, A2585–A2609
    Tensor network formats are an efficient tool for numerical computations in many dimensions, yet even this tool often becomes too time- and memory-consuming for a single compute node when applied to problems of scientific interest. Intending to overcome such limitations, we present and analyze a parallelization scheme for algorithms based on the hierarchical Tucker representation which distributes the network vertices and their associated computations over a set of distributed-memory processors. We then propose a modified version of the alternating least squares algorithm for solving linear systems amenable to parallelization according to the aforementioned scheme, and highlight technical considerations important for obtaining an efficient and stable implementation. Our numerical experiments support the theoretical assertion that the parallel scaling of this algorithm is constrained only by the dimensionality and the rank uniformity of the targeted problem.
  • Erratum: Two-level QTT-Tucker format for optimized tensor calculus
    S. Etter, S. Dolgov, B.N. Khoromskij
    SIAM Journal on Matrix Analysis and Applications (2016), 37:2, 818–822
    We prove by counterexample that the bound on the rounding error given in Theorem 5.2 of [Dolgov and Khoromskij, SIAM J. Matrix Anal. Appl., 34(2013), pp. 593-623] does not hold in general. A correct version of the error bound as well as a modified rounding algorithm for which the original bound holds are presented.
  • FFRT: A fast finite ridgelet transform for radiative transport
    S. Etter, P. Grohs, A. Obermeier
    SIAM Journal on Multiscale Modeling & Simulation (2015), 13:1, 1–42
    This paper introduces an FFT-based implementation of a fast finite ridgelet transform which we call FFRT. Inspired by recent work where it was shown that ridgelet discretizations of linear transport equations can be easily preconditioned by diagonal preconditioning, we use the FFRT for the numerical solution of such equations. Combining this FFRT-based method with a sparse collocation scheme, we construct a novel solver for the radiative transport equation which results in uniformly well-conditioned linear systems.

Talks and Posters

  • Exponentially Localised Matrices
    British Applied Mathematics Colloquium (2017)
  • Labelled Modes - A New Notation for Tensor Networks
    GAMM Annual Meeting, Weimar, Germany (2017)
  • Parallel Tensor-Formatted Numerics for the Chemical Master Equation
    University of Warwick, United Kingdom (2015)
Last updated on 15 November 2022.