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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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Computational Mathematics

  • Research Teams

    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: Software & Datasets

From the quantum to the cosmic, our research teams develop novel software packages and data products to advance our understanding of fundamental processes.

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  1. BridgeStan

    Software
    BridgeStan gives in-memory access to Stan models via multiple languages, exposing log densities, gradients, Hessians, transforms, and predictions.
  2. chunkIE

    Software
    MATLAB package for solving partial differential equations in two dimensional domains.
  3. Clawpack

    Software
    A collection of finite volume methods for linear and nonlinear hyperbolic systems of conservation laws.
  4. CryoLike

    Software
    The CryoLike Python library is a fast and accurate algorithm for computing the likelihood of cryo-EM images given a cryo-EM map and atomic model.
  5. cryoSBI

    Software
    cryoSBI is a Python module for simulation-based inference in cryo-electron microscopy.
  6. ESP

    Software
    Accelerating molecular dynamics via Ewald summation with prolates.
  7. FFT-accelerated Interpolation-based t-SNE

    Software
    FIt-SNE is a fast t-SNE implementation for dimensionality reduction, scaling to ~1M points in minutes for high-dimensional data visualization.
  8. Figurl

    Software
    Generates shareable interactive visualizations from Python using cloud-stored data and ReactJS plugins via figurl.org.
  9. FINUFFT

    Software
    Efficiently computes 1D–3D nonuniform FFTs with CPU and GPU support, plus interfaces for C, Python, MATLAB, Julia, and more.
  10. FMM2D

    Software
    Fast multipole methods in two dimensions.
  11. FMM3D

    Software
    Computes fast 3D N-body interactions (Laplace/Helmholtz) using the fast multipole method with SIMD acceleration and multithreading.
  12. FMM3DBIE

    Software
    FMM-accelerated boundary integral equation solver.
  13. GeoClaw

    Software
    A variant of Clawpack for geophysical flows.
  14. ISO-SPLIT

    Software
    Clustering algorithm for unknown unimodal clusters using projection-based tests, handling non-Gaussian data, with efficient C++/MATLAB implementation.
  15. Kachery-cloud

    Software
    A network for sharing scientific data, results, and live feeds via content-addressed URIs for reproducible, cross-machine and browser-based workflows.
  16. mip

    Software
    The missing package manager for MATLAB.
  17. MountainSort/MountainLab

    Software
    A spike sorting and scientific data analysis platform built around MountainSort, enabling processing, sharing, and visualization of neural data.
  18. Neurosift

    Software
    A tool for spike sorting and visualization of neural electrophysiology recordings.
  19. nifty-ls

    Software
    Fast, accurate Lomb–Scargle periodogram for time-series analysis using FINUFFT; faster than Astropy, with GPU support and integration.
  20. PolarExpress

    Software
    Fast Polar matrix decomposition to accelerate optimization in machine learning.
  21. QUASR

    Software
    A database of over 370,000 curl-free stellarators and the coil sets that generate them, optimized for volume quasi-symmetry.
  22. Riccati

    Software
    Python solver for rapidly oscillating ODEs with frequency-independent runtime, using adaptive methods to meet accuracy targets efficiently.
  23. SCTL

    Software
    Header-only C++ library providing data structures, solvers, algorithms, and tools for parallel scientific computing applications.
  24. SIMSOPT

    Software
    A framework for optimizing stellarators.
  25. SpikeForest

    Software
    Ground-truth validation of automated spike sorting algorithms.
  26. Spikeinterface

    Software
    A unified framework for spike sorting.
  27. Stan

    Software
    Open-source probabilistic programming platform for Bayesian modeling, offering MCMC, variational inference, optimization, and multi-language support.
  28. Stan Playground

    Software
    Browser-based environment for editing, compiling, and running Stan models with built-in or custom Python/R analysis and no installation needed.
  29. Sumac

    Software
    Subzero Matrix Completion (sumac), a rectified linear factorization of a sparse matrix.
  30. Surfacefun

    Software
    MATLAB package for numerically computing with functions on surfaces with high-order accuracy.
  31. The Well

    Software
    15 TB of numerical simulations of spatiotemporal physical systems, produced with Polymathic AI.

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