ffsas 1.0.3

Free-form inversion for small-angle scattering

v1.0

Free-Form inversion for Small-Angle Scattering (SAS)

ffsas is a Python library to invert for free-form distributions of model parameters from polydisperse SAS experiment data. It yields the maximum likelihood estimation of parameter distributions and the normalized sensitivity of each parameter at the maximum likelihood estimator. ffsas comes with the following features:

• Generality: ffsas formulates the SAS inverse problem as a Green's-tensor-based system, which covers any complex SAS models with multiple parameters. An arbitrary model can be easily implemented by supplying the Green's function for forward modelling, i.e., a function that computes the monodisperse intensity on a structured grid of model parameters (i.e., the Green's tensor). In short, users only need to care about the physics for forward modelling, leaving the inverse problem all to ffsas. Besides, it does not require an initial guess of the parameter distributions, the scaling factor or the source background.

• Efficiency: through theoretical analysis, the inverse problem is simplified as a highly solvable nonlinear programming (NLP) problem with a few equality constraints. It is solved by a trust-region method, implemented in SciPy as scipy.optimize.minimize(method='trust-constr'), officially mentioned as "the most versatile constrained minimization algorithm implemented in SciPy and the most appropriate for large-scale problems". The computations of the Jacobian and Hessian are the most expensive steps during solution, for which ffsas uses GPU acceleration and file-based mini-batch computation to significantly reduce runtime and memory requirement. Such ideas are borrowed from deep learning and implemented with PyTorch.

• Accuracy: the model parameters and the resulting intensity in a SAS problem can span many orders of magnitude, and a good choice of unit system is essential to avoid an ill-conditioned inverse problem. ffsas automatically analyzes the scales of data and parameters and determines a proper internal unit system to avoid accuracy loss from input to output. Such an internal unit system is hidden from users, who can use any external unit system for input and output.

• Usability: ffsas can be installed with pip in one line. Its usage only includes four API functions, respectively for

  • computing the Green's tensor G given a model and a parameter space
  • define a G-system with this Green's tensor
  • using this G-system to compute intensity given parameter distributions (forward modelling)
  • using this G-system to invert for parameter distributions given intensity data (inversion)

  A built-in logging system produces detailed and readable logs during these processes.

Quick Start

To install ffsas:

pip install ffsas

Follow the User Guide to learn the usage.

Credits

Kuangdai Leng¹, Steve King², Tim Snow³, Sarah Rogers², Jeyan Thiyagalingam¹

¹ Scientific Computing Department, STFC, UK

² ISIS Neutron and Muon Source, STFC, UK

³ Diamond Light Source, STFC, UK

Funding and Support

This work was supported by the ISIS Neutron and Muon Source (ISIS) of the Science and Technology Facilities Council through the ISIS-ML funding, and by Wave I of the UKRI Strategic Priorities Fund under the EPSRC grant (EP/T001569/1), particularly the AI for Science theme in that grant and the Alan Turing Institute. We gratefully acknowledge their support.