Standard samplers generally perform well if the function or surface they are sampling is simple. In practice, many functional surfaces that need sampling by industry have multiple hills and valleys, others exhibit long thin ridges. These function can also be of high dimension, i.e. depending on 10s to 100s of parameters. For such surfaces, standard samplers will generally only find a few of the regions of interest, i.e. the peaks, and will miss important information relating to the problem at hand.
On the left we show PolyChord sampling LiDAR data giving the height of North Cambridge above sea level. The darker the blue, the lower the altitude and the darker the red, the higher. At the start the PolyChord sampler places active samples (live points) randomly across the space. As it advances the sampling process, it identifies the lowest altitude sample and replaces it with a new sample with higher altitude than all other active samples. A key innovation of the PolyChord sampler is the cutting-edge techniques it applies to efficiently find this replacement point.
Iterating through this process, it exponentially closes in on the regions of highest altitude, guaranteeing that it finds all the peaks (darkest red) with a larger footprint than the sampling resolution chosen (the only major 'tuning' parameter of the algorithm). This provides a simple and robust means to optimise functions, returning a full sampling of the given function with the greatest density of sampling concentrated around the regions of most interest; i.e. the peaks when maximising or the troughs when minimising.
The PolyChord sampler is uniquely capable of providing a full-coverage sampling of a complicated function, even in the presence of complex constraints on the permitted sampling space, and for functions of up to 100s of input variables. This guarantees that all regions of importance are found, as well as providing full knowledge of the functional surface.
The video below illustrates the key differences between the PolyChord sampler and other industry-standard approaches in the context of generating optimal training sets for AI surrogates of Electric-Vehicle battery simulations. For more technical details, please also refer to the PolyChord-Lite publication [1]. This describes the original version of the sampler - note that even this older version is free for academic use only.
[1] Handley, W. J.; Hobson, M. P.; Lasenby, A. N. (2015) - PolyChord: Nested Sampling for Cosmology, Monthly Notices of the Royal Astronomical Society, Vol. 450, p. L61-L65
Although designed to extract parameter constraints when the correct model describing a problem is uncertain, and informing as to which is the most accurate model, the PolyChord sampler has also been applied with great success to many optimisation problems. These include sensor-placement optimisation, generating optimal training sets for accurate AI surrogates, optimisation of fission nuclear plant designs, small-molecule energy-function mapping and Gaussian Process hyperparameter optimisation. See below for more information on these example applications.
If you have an application for which you think the PolyChord sampler could help you gain deeper and more complete insights, please contact us.
Customer Case Studies
Small Molecules
PolyChord is transforming the landscape of small-molecule analysis with Molytics, our cutting-edge technology that reveals the lowest energy state of molecules and small-molecule complexes. Unique to our full-coverage sampling of the energy function, is the provision of information about the dynamical movement of the molecules and complexes, and the ability to probe the molecular structure and dynamics at any temperature. By unlocking this level of molecular detail, we’re pioneering solutions that drive sustainable innovation in various industries.
Sensor Optimisation
Through several projects with the Ministry-of-Defence's Defence Science and Technology Laboratory, we have spun-out an application of PolyChord that optimises the position of sensors in a network. Importantly, and again because of its full-coverage sampling, the PolyChord sampler returns a large library of good solutions that allow for flexibility when the sensor network is installed, whilst guaranteeing the network can optimally perform its intended task.
This framework has also been extended to optimise whilst simultaneously guaranteeing that the network will not fail if a sensor drops out - a vital feature for safety critical networks. Our framework also utilises Bayesian inference techniques to guarantee robust interpretation of the sensor-network data. We’ve validated this approach for designing communications networks for connected and driverless vehicles.
SimXelerate AI-Surrogate Technology
The output of many complex industrial simulations is extremely complex and depends on a large number of input parameters. Whilst these simulations have had huge impact since they are substantially faster than real-life experimentation, they can still take hours or even days to produce output for a single configuration of their input parameters. This makes them orders-of-magnitude too slow to be used for many applications, for example, Electric-Vehicle (EV) battery simulations are currently too slow for use in battery management systems.
This problem has led to the development of AI surrogates, which are much faster to run than the original simulation. However, these surrogates are only as good as the simulation data they are trained with - the PolyChord sampler delivers training data that are vastly superior to other methods currently applied by industry. By delivering surrogate predictions that encorporate uncertainty quantification, the answers our AI surrogate delivers are also guaranteed to be reliable. This is a key feature for safety-critical applications, such as EV battery management systems.