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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. Counterfactual Learning of Stochastic Policies with Continuous Actions

    Transactions on Machine Learning Research, arxiv:2004.11722, 2025

    Houssam Zenati, A. Bietti, Matthieu Martin, Eustache Diemert, and Julien Mairal

  2. Identifying new classes of financial price jumps with wavelets

    Proceedings of the National Academy of Sciences, arxiv:2404.16467, 2025

    Cecilia Aubrun, R. Morel, Michael Benzaquen, and Jean-Philippe Bouchaud

  3. Scale dependencies and self-similar models with wavelet scattering spectra

    Applied and Computational Harmonic Analysis, arxiv:2204.10177, 2025

    R. Morel, Gaspar Rochette, Roberto Leonarduzzi, Jean Philippe Bouchaud, and S. Mallat

  4. The No-Underrun Sampler: A Locally-Adaptive, Gradient-Free MCMC Method

    arxiv:2501.18548, 2025

    N. Bou-Rabee, B. Carpenter, S. Liu, and Stefan Oberdörster

  5. A fully adaptive, high-order, fast Poisson solver for complex two-dimensional geometries

    arxiv:2501.17967, 2025

    D. Fortunato, D. Stein, and A. Barnett

  6. Understanding Optimization in Deep Learning with Central Flows

    International Conference on Learning Representations, arxiv:2410.24206, 2025

    J. Cohen, Alex Damian, Ameet Talwalkar, J Zico Kolter, and Jason D. Lee

  7. CryoLike: A python package for cryo-electron microscopy image-to-structure likelihood calculations

    Acta Crystallographica Section D, Structural Biology, bioRxiv, 2025

    W. Wai Shing, J. Soules, A. Rangan, and P. Cossio

  8. Randomized Nyström Approximation of Non-negative Self-Adjoint Operators

    SIAM Journal on Mathematics of Data Science, 2025

    D. Persson, Nicolas Boullé, and Daniel Kressner

  9. How does Mamba Perform Associative Recall? A Mechanistic Study

    Mechanistic Interpretability Workshop at Conference on Neural Information Processing Systems, 2025

    Grégoire LE CORRE, T. Huang, and A. Bietti

  10. An Accurate and Efficient Scheme for Function Extension on Smooth Domains

    SIAM Journal on Numerical Analysis, 2025

    F. Fryklund and S. Jiang

  11. Classical variational phase-field models cannot predict fracture nucleation

    Computer Methods in Applied Mechanics and Engineering, arxiv:2409.00242, 2025

    Oscar Lopez-Pamies, John E. Dolbow, G. Francfort, and Christopher J. Larsen

  12. Equispaced Fourier representations for efficient Gaussian process regression from a billion data points

    SIAM/ASA Journal on Uncertainty Quantification, arxiv:2210.10210, 2025

    Philip Greengard, M. Rachh, and A. Barnett

  13. A mixing time bound for Gibbs sampling from log-smooth log-concave distributions

    arxiv:2412.17899, 2024

    N. Wadia

  14. Neural network learns low-dimensional polynomials with SGD near the information-theoretic limit

    arxiv:2406.01581, 2024

    Jason D. Lee, Kazusato Oko, Taiji Suzuki, and D. Wu

  15. Liquid Filled Elastomers: From Linearization to Elastic Enhancement

    Archive for Rational Mechanics and Analysis, arXiv:2309.03630, 2024

    Juan Casado Dìaz and G. Francfort

  16. xVal: A Continuous Numerical Tokenization for Scientific Language Models

    arxiv:2310.02989, 2024

    Siavash Golkar, Ph.D., et al.

  17. Trapped acoustic waves and raindrops: high-order accurate integral equation method for localized excitation of a periodic staircase

    Journal of Computational Physics, arXiv:2310.12486, 2024

    F. Agocs and A. Barnett

  18. A Dual-space Multilevel Kernel-splitting Framework for Discrete and Continuous Convolution

    Communications on Pure and Applied Mathematics, arXiv:2308.00292, 2024

    S. Jiang and L. Greengard

  19. Provable Posterior Sampling with Denoising Oracles via Tilted Transport

    Advances in Neural Information Processing Systems, 2024

    Joan Bruna and J. Han

  20. Multiple Physics Pretraining for Physical Surrogate Models

    arxiv:2310.02994, 2024

    Michael McCabe, et al.

  21. Editorial overview: Cryo-electron microscopy

    Current Opinion in Structural Biology, 2024

    P. Cossio and Edward Egelman

  22. Compressing the memory variables in constant-Q viscoelastic wave propagation via an improved sum-of-exponentials approximation

    Journal of Computational Physics, arXiv:2309.05125, 2024

    Xu Guo, S. Jiang, Yunfeng Xiong, and Jiwei Zhang

  23. An adaptive spectral method for oscillatory second-order linear ODEs with frequency-independent cost

    SIAM Journal on Numerical Analysis, arxiv:2212.06924, 2024

    F. Agocs and A. Barnett

  24. Recursive reduction quadrature for the evaluation of Laplace layer potentials in three dimensions

    arXiv:2411.08342, 2024

    S. Jiang and Hai Zhu

  25. A numerical method for scattering problems with unbounded interfaces

    arxiv:2411.11204, 2024

    Tristan Goodwill

  26. On the construction of scattering matrices for irregular or elongated enclosures using Green's representation formula

    Journal of Scientific Computing, arxiv:2408.02881, 2024

    Carlos Borges, L. Greengard, Michael O'Neil, and M. Rachh

  27. Learning Gaussian Multi-Index Models with Gradient Flow: Time Complexity and Directional Convergence

    arxiv:2411.08798, 2024

    B. Şimşek, Amire Bendjeddou, and Daniel Hsu

  28. Dynamic allostery drives autocrine and paracrine TGF-β signaling

    Cell, 2024

    Mingliang Jin, et al.

  29. Simulation-based inference of single-molecule experiments

    arxiv:2410.15896, 2024

    Lars Dingeldein, P. Cossio, and Roberto Covino

  30. AutoBZ.jl: Automatic, adaptive Brillouin zone integration using Wannier interpolation

    Journal of Open Source Software, 2024

    Lorenzo Van Munoz, Sophie Beck, and J. Kaye

  31. Variational Inference in Location-Scale Families: Exact Recovery of the Mean and Correlation Matrix

    arXiv:2410.11067, 2024

    C. Margossian and L. Saul

  32. Active learning of Boltzmann samplers and potential energies with quantum mechanical accuracy

    Journal of Chemical Theory and Computation, 2024

    Ana Molina-Taborda, et al.

  33. Integral formulation of Klein-Gordon singular waveguides

    Communications on Pure and Applied Mathematics, 2024

    Guillaume Bal, Jeremy Hoskins, S. Quinn, and M. Rachh

  34. New Statistical Metric for Robust Target Detection in Cryo-EM Using 2DTM

    bioRxiv, 2024

    Kexin Zhang, P. Cossio, A. Rangan, Bronwyn Lucas, and Nikolaus Grigorieff

  35. nifty-ls: Fast and Accurate Lomb–Scargle Periodograms Using a Non-uniform FFT

    Research Notes of the AAS, 2024

    Lehman H. Garrison, D. Foreman-Mackey, Yu-hsuan Shih, and A. Barnett

  36. Coordinate complexification for the Helmholtz equation with Dirichlet boundary conditions in a perturbed half-space

    arxiv:2409.06988, 2024

    L. Greengard, Jeremy Hoskins, S. Jiang, and M. Rachh

  37. A comprehensive exploration of quasisymmetric stellarators and their coil sets

    arxiv:2409.04826, 2024

    A. Giuliani, Eduardo Rodríguez, and M. Spivak

  38. Decomposing imaginary time Feynman diagrams using separable basis functions: Anderson impurity model strong coupling expansion

    Physical Review X, 2024

    J. Kaye, Zhen Huang, Hugo Strand, and Denis Golez

  39. Cosmological constraints from non-Gaussian and nonlinear galaxy clustering using the SimBIG inference framework

    Nature Astronomy, 2024

    ChangHoon Hahn, Pablo Lemos, Liam Parker, B. Régaldo-Saint Blancard, M. Eickenberg, Shirley Ho, Ph.D., et al.

  40. Incorporating Local Step-Size Adaptivity into the No-U-Turn Sampler using Gibbs Self Tuning

    arxiv:2408.08259, 2024

    N. Bou-Rabee, B. Carpenter, Tore Selland Kleppe, and Milo Marsden

  41. Learning Multi-Index Models with Neural Networks via Mean-Field Langevin Dynamics

    arxiv:2408.07254, 2024

    Alireza Mousavi-Hosseini, D. Wu, and Murat A. Erdogdu

  42. CryoBench: Diverse and challenging datasets for the heterogeneity problem in cryo-EM

    arXiv:2408.05526, 2024

    Minkyu Jeon, et al.

  43. cppdlr: Imaginary time calculations using the discrete Lehmann representation

    Journal of Open Source Software, 2024

    J. Kaye, Hugo U. r. Strand, and Nils Wentzell

  44. Amortized template-matching of molecular conformations from cryo-electron microscopy images using simulation-based inference

    bioRxiv, 2024

    Lars Dingeldein, et al.

  45. Nested R̂ : Assessing the Convergence of Markov Chain Monte Carlo When Running Many Short Chains

    Bayesian Analysis, 2024

    C. Margossian, Matthew D. Hoffman, Pavel Sountsov, Lionel Riou-Durand, Aki Vehtari, and Andrew Gelman

  46. SILVER: Single-loop variance reduction and application to federated learning

    Proceedings of Machine Learning Research, 2024

    Kazusato Oko, Shunta Akiyama, D. Wu, Tomoya Murata, and Taiji Suzuki

  47. Listening to the noise: Blind Denoising with Gibbs Diffusion

    Proceedings of Machine Learning Research, arXiv:2402.19455, 2024

    David Heurtel-Depeiges, C. Margossian, R. Ohana, and B. Régaldo-Saint Blancard

  48. Learning Associative Memories with Gradient Descent

    Proceedings of Machine Learning Research, 2024

    Vivien Cabannes, B. Şimşek, and A. Bietti

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