CCM’s mission is to create new mathematical approaches, algorithms and software to advance scientific research in multiple disciplines, often in collaboration with other Flatiron Centers.
Featured News
Center for Computational Mathematics
Learning Better: Improving the Efficiency of Deep Learning Models
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Flatiron Research Fellow Brett Larsen is developing better ways to train deep learning models.
Applied and computational mathematics play a critical role in many aspects of modern science and engineering, with new opportunities for discovery in virtually every discipline. CCM will focus on developing new tools and software libraries that bring large-scale modeling, simulation and data analysis within practical reach.
Research
Collaborative Work
Machine Learning at the Flatiron Institute
Machine learning has become an indispensable tool for computational science, and it is an active and growing area of research throughout the Flatiron Institute.
- CCM
- CCN
- CCA
- CCB
- CCQ
Structural and Molecular Biophysics
Underlying all biological processes are molecules and their interactions with each other. However, our ability to understand how these molecules function over biologically relevant scales remains very limited.
- CCB
- CCM
Research Highlights
Transition Rates and Efficiency of Collective Variables from Time-Dependent Biased Simulations
Karen Palacio-Rodriguez, Hadrien Vroylandt, Lukas S. Stelzl, Fabio Pietrucci, Gerhard Hummer, P. Cossio
Simulations with adaptive time-dependent bias enable an efficient exploration of the conformational space of a system. However, the dynamic information…
The Journal of Physical Chemistry LettersA high-order fast direct solver for surface PDEs
We introduce a fast direct solver for variable-coefficient elliptic partial differential equations on surfaces based on the hierarchical Poincaré-Steklov method.…
arxiv:2210.00022An FMM Accelerated Poisson Solver for Complicated Geometries in the Plane using Function Extension
Fredrik Fryklund, L. Greengard
We describe a new, adaptive solver for the two-dimensional Poisson equation in complicated geometries. Using classical potential theory, we represent…
arxiv:2211.14537Director
Software
SpikeForest
SpikeForest is a continuously-updating web-facing performance comparison of popular neural spike sorting codes, using a massive (1.3 TB) database of ground-truth recordings collected from over a dozen participating laboratories.
Figurl
Figurl lets you use Python to generate shareable figURLs (permalinks) to interactive visualizations. With minimal configuration, these can be generated from any computer with access to the internet.
FMM3D
FMM3D is a set of libraries to compute N-body interactions governed by the Laplace and Helmholtz equations, to a specified precision, in three dimensions, on a multi-core shared-memory machine.
IronClust
IronClust is a fast and drift-resistant spike sorting pipeline. The accuracy of spike sorting is validated by multiple ground-truth datasets from a number of contributing labs.
MountainSort/MountainLab
MountainSort is a plugin package to MountainLab, a general framework for scientific data analysis, sharing, and visualization.
FINUFFT
FINUFFT is a set of libraries to compute efficiently three types of nonuniform fast Fourier transform (NUFFT) to a specified precision, in one, two, or three dimensions, on a multi-core shared-memory machine.
cuFINUFFT
A GPU implementation of the 2- and 3-dimensional non-uniform FFT of types 1 and 2, in single and double precisions, based on the CPU code FINUFFT
ISO-SPLIT
ISO-SPLIT is an efficient clustering algorithm that handles an unknown number of unimodal clusters in low to moderate dimension, without any user-adjustable parameters.
Fast sinc transform library
Fast sinc transform libraries which compute sums of the sinc and sinc2 kernels between N arbitrary points in 1, 2, or 3 dimensions.
FFT-accelerated Interpolation-based t-SNE
FFT-accelerated interpolation-based t-SNE (FIt-SNE) is an efficient implementation of t-SNE (stochastic neighborhood embedding) for dimensionality reduction and visualization of high dimensional datasets.
CaImAn Python
Computational toolbox for large scale Calcium Imaging Analysis, including movie handling, motion correction, source extraction, spike deconvolution and result visualization.
CaImAn-MATLAB
Complete Matlab pipeline for large scale calcium imaging data analysis.
Kachery-cloud
Kachery-cloud is a network for sharing scientific data files, live feeds, mutable data and calculation results between lab computers and browser-based user interfaces.
Stan
Stan is an open-source platform for statistical modeling and high-performance statistical computation.
Riccati
Riccati is an efficient numerical solver developed for a class of ordinary differential equations whose solution may exhibit extremely quick oscillations.