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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

Read the latest papers published by our researchers.

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  1. Towards Seamless Interoperability of MPI-OpenMP Applications

    ACM Transactions on Mathematical Software, 2025

    B. Smith, M. Berger, Junchao Zhang, and Hui Zhou

  2. Quasi-optimal hierarchically semi-separable matrix approximation

    SIAM Journal on Matrix Analysis and Applications, arxiv:2505.16937, 2025

    Noah Amsel, Tyler Chen, Feyza Duman Keles, Diana Halikias, Cameron Musco, Christopher Musco, et al.

  3. A fast spectral sum-of-Gaussians method for electrostatic summation in quasi-2D systems

    Numerische Mathematik, 2025

    X. Gao, S. Jiang, J. Liang, Zhenli Xu, and Qi Zhou

  4. seekrflow: Towards end-to-end automated simulation pipeline with machine-learned force fields for accelerated drug-target kinetic and thermodynamic predictions

    bioRxiv, 2025

    A. Ojha, et al.

  5. Study of Protein-Protein Interactions in Septin Assembly: Multiple amphipathic helix domains cooperate in binding to the lipid membrane

    bioRxiv, 2025

    M. Mofidi, et al.

  6. Study of Protein-Protein Interactions in Septin Assembly: Multiple amphipathic helix domains cooperate in binding to the lipid membrane

    bioRxiv, August 12, 2025

    M. Mofidi, et al.

  7. Progressive Optimal Path Sampling for Closed-Loop Optimal Control Design with Deep Neural Networks

    Journal of Machine Learning, 2025

    Xuanxi Zhang, Jihao Long, Wei Hu, Weinan E, and J. Han

  8. Velocity optimization of self-equilibrated obstacles in a two-dimensional viscous flow

    arXiv:2508.05481, 2025

    G. Francfort, Alessandro Giacomini, and S. Weady

  9. Quantitative and Predictive Folding Models from Limited Single-Molecule Data Using Simulation-Based Inference

    arXiv, August 4, 2025

    Lars Dingeldein, Aaron Lyons, and P. Cossio

  10. Query Efficient Structured Matrix Learning

    arxiv:2507.19290, 2025

    Noah Amsel, Pratyush Avi, Tyler Chen, Feyza Duman Keles, Chinmay Hegde, Cameron Musco, et al.

  11. On learning Gaussian multi-index models with gradient flow part I: General properties and two-timescale learning

    Communications on Pure and Applied Mathematics, 2025

    A. Bietti, Joan Bruna, and L. Pillaud-Vivien

  12. DISCO: learning to DISCover an evolution Operator for multi-physics-agnostic prediction

    International Conference on Machine Learning, arxiv:2504.19496, 2025

    R. Morel, J. Han, and E. Oyallon

  13. Learning Compositional Functions with Transformers from Easy-to-Hard Data

    Proceedings of Machine Learning Research, arxiv:2505.23683, 2025

    Zixuan Wang, Eshaan Nichani, A. Bietti, Alex Damian, Daniel Hsu, Jason D. Lee, et al.

  14. Microtubules in Martini: Parameterizing a heterogeneous elastic-network towards a mechanically accurate microtubule

    PNAS Nexus, 2025

    A. Sahoo and S. Hanson

  15. RocketSHP: Ultra-fast Proteome-scale Prediction of Protein Dynamics

    bioRxiv, 2025

    S. Sledzieski and S. Hanson

  16. Random batch sum-of-Gaussians algorithm for molecular dynamics simulations of Yukawa systems in three dimensions

    Journal of Computational Physics, 2025

    Chen Chen, J. Liang, and Zhenli Xu

  17. Complex scaling for open waveguides

    arxiv:2506.10263, 2025

    Tristan Goodwill, Jeremy Hoskins, S. Quinn, and M. Rachh

  18. Learning Free Terminal Time Optimal Closed-loop Control of Manipulators

    American Control Conference, 2025

    Wei Hu, Yue Zhao, Weinan E, J. Han, and Jihao Long

  19. ExEnDiff: An Experiment-Guided Diffusion Model for Protein Conformational Ensemble Generation

    PRX Life, 2025

    Yikai Liu, et al.

  20. Amortized template matching of molecular conformations from cryoelectron microscopy images using simulation-based inference

    Proceedings of the National Academy of Sciences, 2025

    Lars Dingeldein, et al.

  21. Self-reorganization and Information Transfer in Massive Schools of Fish

    arxiv:2505.05822, 2025

    Haotian Hang, Chenchen Huang, A. Barnett, and Eva Kanso

  22. Accurate Error Estimates and Optimal Parameter Selection in Ewald Summation for Dielectrically Confined Coulomb SystemsClick to copy article link

    Journal of Chemical Theory and Computation, 2025

    X. Gao, Qi Zhou, Zecheng Gan, and J. Liang

  23. Error estimate of the u-series method for molecular dynamics simulations

    Applied and Computational Harmonic Analysis, 2025

    J. Liang, Zhenli Xu, and Qi Zhou

  24. Designing objects that are invisible to electromagnetic waves

    American Journal of Physics, 2025

    Johan Helsing, S. Jiang, and Anders Karlsson

  25. Neural operator-based super-fidelity: A warm-start approach for accelerating steady-state simulations

    Journal of Computational Physics, 2025

    Xu-Hui Zhou, et al.

  26. Accelerating Fast Ewald Summation with Prolates for Molecular Dynamics Simulations

    arxiv:2505.09727, 2025

    J. Liang, L. Lu, A. Barnett, L. Greengard, and S. Jiang

  27. Understanding Input Selectivity in Mamba: Impact on Approximation Power, Memorization, and Associative Recall Capacity

    arxiv:2506.11891, 2025

    T. Huang, et al.

  28. In-Context Denoising with One-Layer Transformers: Connections between Attention and Associative Memory Retrieval

    International Conference on Machine Learning, arxiv:2502.05164, 2025

    M. Smart, A. Bietti, and A. Sengupta

  29. BAnG Bidirectional Anchored Generation for Conditional RNA Design

    International Conference on Machine Learning, arxiv:2502.21274, 2025

    Roman Klypa, A. Bietti, and Sergei Grudinin

  30. Distributional Associations vs In-Context Reasoning: A Study of Feed-forward and Attention Layers

    The Thirteenth International Conference on Learning Representations, arXiv:2406.03068, 2025

    Lei Chen, J. Bruna, and A. Bietti

  31. Superfast Direct Inversion of the Nonuniform Discrete Fourier Transform via Hierarchically Semiseparable Least Squares

    SIAM Journal on Scientific Computing, arxiv:2404.13223, 2025

    Heather Wilber, Ethan N. Epperly, and A. Barnett

  32. Charge distribution and helicity tune the binding of septin's amphipathic helix domain to membranes

    Biophysical Journal, 2025

    C. Edelmaier, et al.

  33. Solving optimal control problems of rigid-body dynamics with collisions using the hybrid minimum principle

    Communications in Nonlinear Science and Numerical Simulation, 2025

    Wei Hu, Jihao Long, Yaohua Zang, Weinan E, and J. Han

  34. Simulation-based inference of single-molecule experiments

    Current Opinion in Structural Biology, arxiv:2410.15896, 2025

    Lars Dingeldein, P. Cossio, and Roberto Covino

  35. InstaMap: instant-NGP for cryo-EM density maps

    Acta Crystallographica D, April 1, 2025

    Geoffrey Woollard, et al.

  36. Counting particles could give wrong probabilities in Cryo-Electron Microscopy

    bioRxiv, March 28, 2025

    L. Evans, et al.

  37. Random Batch Ewald Method for Dielectrically Confined Coulomb Systems

    SIAM Journal on Scientific Computing, 2025

    Zecheng Gan, X. Gao, J. Liang, and Zhenli Xu

  38. Recent Advances in Membrane Protein Simulations

    The Journal of Physical Chemistry B, March 13, 2025

    James C. Gumbart and S. Hanson

  39. Sampling From Multiscale Densities With Delayed Rejection Generalized Hamiltonian Monte Carlo

    Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, arxiv:2406.02741, 2025

    G. Turok, C. Modi, and B. Carpenter

  40. PLUMED Tutorials: a collaborative, community-driven learning ecosystem

    The Journal of Chemical Physics, arXiv, March 7, 2025

    Gareth A. Tribello, et al.

  41. Level Set Teleportation: An Optimization Perspective

    The 28th International Conference on Artificial Intelligence and Statistic, arxiv:2403.03362, 2025

    Aaron Mishkin, A. Bietti, and R. Gower

  42. Fast algorithm for quasi-2D Coulomb systems

    Journal of Computational Physics, 2025

    Zecheng Gan, X. Gao, J. Liang, and Zhenli Xu

  43. Understanding Factual Recall in Transformers via Associative Memories

    International Conference on Learning Representations, arxiv:2412.06538, 2025

    Eshaan Nichani, Jason D. Lee, and A. Bietti

  44. Type-I Superconductors in the Limit as the London Penetration Depth Goes to 0

    arxiv:2502.18809, 2025

    M. Rachh and Yuguan Wang

  45. Comment on ‘Pressure of Coulomb systems with volume-dependent long-range potentials’

    Journal of Physics A: Mathematical and Theoretical, 2025

    Lei Li, J. Liang, and Zhenli Xu

  46. The ManifoldEM method for cryo-EM: a step-by-step breakdown accompanied by a modern Python implementation

    Acta Crystallographica D, 2025

    A. Ojha, et al.

  47. The ManifoldEM method for cryo-EM: a step-by-step breakdown accompanied by a modern Python implementation

    Acta Crystallographica D, February 17, 2025

    A. Ojha, et al.

  48. Accurate close interactions of Stokes spheres using lubrication-adapted image systems

    Journal of Computational Physics, arxiv:2407.03343, 2025

    Anna Broms, A. Barnett, and Anna-Karin Tornberg

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