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Computational Mathematics

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    Biomolecular and Biophysical Inference Bridging the gap between molecular simulations and experimental data, enabling quantitative characterization of biomolecules.

    Machine Learning and Computational Statistics Using leading-edge tools and methods to push the boundaries of computational mathematics.

    Numerical Analysis and Scientific Computing Creating fast, accurate and robust high-order solvers for many equations in complicated geometries.

    COMPASS Connecting researchers working on molecular sampling, simulation and design.

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Flatiron Institute Computational Mathematics

Computational Mathematics: Publications

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  1. A fast method for imposing periodic boundary conditions on arbitrarily-shaped lattices in two dimensions

    Journal of Computational Physics, arXiv:2111.01083, February 1, 2023

    L. Greengard, S. Jiang, Ruqi Pei, and Travis Askham

  2. On the robustness of inverse scattering for penetrable, homogeneous objects with complicated boundary

    Inverse Problems, arxiv:2210.11607, 2023

    Carlos Borges, M. Rachh, and L. Greengard

  3. Handbook of Convergence Theorems for (Stochastic) Gradient Methods

    arxiv:2301.11235, 2023

    Guillaume Garrigos and R. Gower

  4. A fast, high-order numerical method for the simulation of single-excitation states in quantum optics

    Journal of Computational Physics, arxiv:2109.06956, 2023

    Jeremy Hoskins, J. Kaye, M. Rachh, and John C. Schotland

  5. Coordinated drift of receptive fields in Hebbian/anti-Hebbian network models during noisy representation learning

    Nature Neuroscience, bioRxiv:2021.08.30.458264v1, 2023

    Shanshan Qin, S. Farashahi, D. Lipshutz, A. Sengupta, D. Chklovskii, and Cengiz Pehlevan

  6. Linear optical random projections without holography

    Optics Express, arXiv:2305.12988, 2023

    R. Ohana, Daniel Hesslow, Daniel Brunner, Sylvain Gigan, and Kilian Müller

  7. Shedding a PAC-Bayesian Light on Adaptive Sliced-Wasserstein Distances

    Proceedings of Machine Learning Research, arXiv:2206.03230, 2023

    R. Ohana, Kimia Nadjahi, Alain Rakotomamonjy, and Liva Ralaivola

  8. Generative Models of Multichannel Data from a Single Example—Application to Dust Emission

    The Astrophysical Journal, arxiv:arXiv:2208.03538, January 1, 2023

    B. Régaldo-Saint Blancard, Erwan Allys, Constant Auclair, François Boulanger, M. Eickenberg, François Levrier, et al.

  9. Eliminating Artificial Boundary Conditions in Time-Dependent Density Functional Theory Using Fourier Contour Deformation

    Journal of Chemical Theory and Computation, arxiv:2209.11027, 2023

    J. Kaye, A. Barnett, L. Greengard, Umberto De Giovannini, and A. Rubio

  10. Adaptive Tuning for Metropolis Adjusted Langevin Trajectories

    International Conference on Artificial Intelligence and Statistics, arXiv:2210.12200, 2023

    Lionel Riou-Durand, Pavel Sountsov, Jure Vogrinc, C. Margossian, and Sam Power

  11. A geometrical connection between sparse and low-rank matrices and its application to manifold learning

    Transactions on Machine Learning Research, December 25, 2022

    L. Saul

  12. PELICAN: Permutation Equivariant and Lorentz Invariant or Covariant Aggregator Network for Particle Physics

    arXiv:2211.00454, 2022

    A. Bogatskii, Timothy Hoffman, David W. Miller, and Jan T. Offermann

  13. Replacement dynamics and the pathogenesis of the Alpha, Delta and Omicron variants of SARS-CoV-2

    Epidemiology and Infection, 2022

    Thomas Ward, Alex Glaser, Christopher E Overton, B. Carpenter, Nick Gent, and Anna C Seale

  14. Approximating the Gaussian as a Sum of Exponentials and Its Applications to the Fast Gauss Transform

    Communications in Computational Physics, 2022

    S. Jiang and L. Greengard

  15. Corner Cases of the Generalized Tau Method

    arxiv:2211.17259, 2022

    Keaton J. Burns, D. Fortunato, Keith Julien, and Geoffrey M. Vasil

  16. Quantum Initial Conditions for Curved Inflating Universes

    arxiv:2211.17248, November 30, 2022

    Mary I Letey, Zakhar Shumaylov, F. Agocs, Will J Handley, Michael P Hobson, and Anthony N Lasenby

  17. An FMM Accelerated Poisson Solver for Complicated Geometries in the Plane using Function Extension

    arxiv:2211.14537, 2022

    Fredrik Fryklund and L. Greengard

  18. pmwd: A Differentiable Cosmological Particle-Mesh N-body Library

    arxiv:2211.09958, 2022

    Y. Li, L. Lu, C. Modi, Drew Jamieson, Yucheng Zhang, Yu Feng, et al.

  19. Differentiable Cosmological Simulation with Adjoint Method

    arxiv:2211.09815, 2022

    Y. Li, C. Modi, Drew Jamieson, Yucheng Zhang, L. Lu, Yu Feng, et al.

  20. Learning Feynman Diagrams with Tensor Trains

    Physical Review X, arXiv:2207.06135, 2022

    Yuriel Nunez-Fernandez, Matthieu Jeannin, Philipp T. Dumitrescu, Thomas Kloss, J. Kaye, Olivier Parcollet, et al.

  21. High-Resolution EEG Source Reconstruction with Boundary Element Fast Multipole Method Using Reciprocity Principle and TES Forward Model Matrix

    bioRxiv, bioRxiv:2022.10.30.514418, November 1, 2022

    William A. Wartman, Tommi Raij, M. Rachh, Fa-Hsuan Lin, Konstantin Weise, Thomas Knoesche, et al.

  22. libdlr: Efficient imaginary time calculations using the discrete Lehmann representation

    Computer Physics Communications, arxiv:2110.06765, 2022

    J. Kaye, Kun Chen, and Hugo U. R. Strand

  23. Catching actin proteins in action

    Nature, 2022

    P. Cossio and Glen M. Hocky

  24. Protocol for iterative optimization of modified peptides bound to protein targets

    Journal of Computer-Aided Molecular Design, October 19, 2022

    Rodrigo Ochoa, P. Cossio, and Thomas Fox

  25. Forced and spontaneous symmetry breaking in cell polarization

    Nature Computational Science, 2022

    Pearson Miller, D. Fortunato, Cyrill Muratov, L. Greengard, and S. Shvartsman

  26. Toward a Geometrical Understanding of Self-supervised Contrastive Learning

    arxiv:2205.06926, 2022

    Romain Cosentino, A. Sengupta, Salman Avestimehr, Mahdi Soltanolkotabi, Antonio Ortega, Ted Willke, et al.

  27. A PDE-free, neural network-based eddy viscosity model coupled with RANS equations

    International Journal of Heat and Fluid Flow, October 6, 2022

    Ruiying Xu, Xu-Hui Zhou, J. Han, Richard P Dwight, and Heng Xiao

  28. Generation and motion of interfaces in a mass-conserving reaction-diffusion system

    arxiv:2210.00585, 2022

    Pearson W. Miller, D. Fortunato, Matteo Novaga, Stanislav Y. Shvartsman, and Cyrill B. Muratov

  29. Compressed Sensing in the Presence of Speckle Noise

    IEEE Transactions on Information Theory, arxiv:arXiv:2108.00329, 2022

    W. Zhou, Shirin Jalali, and Arian Maleki

  30. Deep Learning the Functional Renormalization Group

    Physical Review Letters, arXiv:2202.13268, 2022

    Domenico Di Sante, Matija Medvidović, Alessandro Toschi, Giorgio Sangiovanni, Cesare Franchini, A. Sengupta, et al.

  31. Finite inflation in curved space

    Physical Review D, arxiv:2205.07374, September 15, 2022

    Lukas T Hergt, F. Agocs, Will J Handley, Michael P Hobson, and Anthony N Lasenby

  32. Robust ab initio solution of the cryo-EM reconstruction problem at low resolution with small data sets

    arxiv:arXiv:2209.06420, 2022

    Aaditya V. Rangan and L. Greengard

  33. Quadrature by fundamental solutions: kernel-independent layer potential evaluation for large collections of simple objects

    Advances in Computational Mathematics, arxiv:2109.08802, 2022

    D. Stein and A. Barnett

  34. A Weighted State Redistribution Algorithm for Embedded Boundary Grids

    Journal of Computational Physics, arxiv:2112.12360, 2022

    A. Giuliani, Ann S. Almgren, John B. Bell, M. Berger, Marc T. Henry Frahan, and Deepak Rangarajan

  35. Transition Rates and Efficiency of Collective Variables from Time-Dependent Biased Simulations

    The Journal of Physical Chemistry Letters, arxiv:2109.11360, August 8, 2022

    Karen Palacio-Rodriguez, Hadrien Vroylandt, Lukas S. Stelzl, Fabio Pietrucci, Gerhard Hummer, and P. Cossio

  36. Frame invariance and scalability of neural operators for partial differential equations

    Communications in Computational Physics, arxiv:2112.14769, August 1, 2022

    Muhammad I. Zafar, J. Han, Xu-Hui Zhou, and Heng Xiao

  37. A high-order integral equation-based solver for the time-dependent Schrödinger equation

    Comm. Pure Appl. Math., arXiv:2001.06113, 2022

    J. Kaye, A. Barnett, and L. Greengard

  38. Towards Adaptive Simulations of Dispersive Tsunami Propagation from an Asteroid Impact

    International Congress of Mathematicians, arxiv:2110.01420, 2022

    M. Berger and Randall J. LeVeque

  39. High Performance Equilibrium Solvers for Integrated Magnetic Fusion Simulations

    OSTI, 2022

    Antoine J. Cerfon, Geoffrey McFadden, Jon Wilkening, Jungpyo Lee, Tonatiuh Sanchez-Vizuet, Lise-Marie Imbert-Gérard, et al.

  40. A stable, efficient scheme for \({C}^n\) function extensions on smooth domains in \({R}^d\)

    arxiv:2206.11318, 2022

    C. Epstein and S. Jiang

  41. A Statistical Linear Precoding Scheme Based on Random Iterative Method for Massive MIMO Systems

    IEEE Transactions on Wireless Communications, 2022

    Zheng Wang, R. Gower, Cheng Zhang, Shanxiang Lyu, Yili Xia, and Yongming Huang

  42. HoloML in Stan: Low-photon Image Reconstruction

    STAN, 2022

    B. Ward, B. Carpenter, and D. Barmherzig

  43. Discrete Lehmann representation of imaginary time Green's functions

    Physical Review B, arxiv:2107.13094, 2022

    J. Kaye, K. Chen, and O. Parcollet

  44. Randomized Iterative Methods for Low-Complexity Large-Scale MIMO Detection

    IEEE Transactions on Signal Processing, 2022

    Zheng Wang, R. Gower, Yili Xia, Lanxin He, and Yongming Huang

  45. Cosmological Information in the Marked Power Spectrum of the Galaxy Field

    arXiv:2206.01709, 2022

    B. Régaldo-Saint Blancard, M. Eickenberg, Elena Massara, Francisco Villaescusa-Navarro, ChangHoon Hahn, Muntazir M. Abidi, et al.

  46. Neural-Network Quantum States for Periodic Systems in Continuous Space

    Physical Review Research, arxiv:2112.11957, May 20, 2022

    Gabriel Pescia, J. Han, Alessandro Lovato, Jianfeng Lu, and G. Carleo

  47. Exploring the Adjugate Matrix Approach to Quaternion Pose Extraction

    arXiv:2205.09116, 2022

    S. Hanson and Andrew J. Hanson

  48. Pathfinder: Parallel quasi-Newton variational inference

    Journal of Machine Learning Research, arxiv:2108.03782, 2022

    Lu Zhang, B. Carpenter, Aki Vehtari, and Andrew Gelman

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