Responsive Disorder in a Metal-Organic Framework Enables Solid-State Reservoir Computing

TL;DR

This work uses the disordered metal-organic framework DUT-8, which undergoes a series of disorder-disorder transitions on exposure to different guest species, to explore the possibility that configurational degeneracy within disordered materials might form the basis for solid-state atomic-scale reservoirs.

Abstract

Complex systems with nonlinear response mechanisms can be applied as reservoir computers for energy-efficient machine learning tasks. Historically explored at the macro- and meso-scale, physical reservoir computing has recently been extended to the atomic scale via chemical mixtures with strong and dynamic heterogeneity. Here we explore the possibility that configurational degeneracy within disordered materials might form the basis for solid-state atomic-scale reservoirs. Our proof-of-concept uses the disordered metal-organic framework DUT-8, which undergoes a series of disorder-disorder transitions on exposure to different guest species. We show that variations in X-ray diffuse scattering associated with these transitions function as suitable readouts for machine learning applications. A combination of nonlinearity and memory effects in the DUT-8 response allows the system to carry out both classification and time-series machine learning tasks with accuracies comparable to those of mesoscale physical reservoir computers. Our results suggest a new avenue for exploiting correlated disorder in solid phases whenever the nature of that disorder can be modulated through external perturbations-a phenomenon we term `responsive disorder'.

Figures (4)

• Figure 1: Examples of physical reservoirs. In the formose chemical reservoir (top), a variety of polymeric species continuously interconvert. Varying the concentration of monomers or other reagents causes a shift in the composition of the mixture, which can be characterised by mass spectrometry.Baltussen_2024 By contrast, the artificial vortex spin ice reservoir (middle) is comprised of a nanoarray of magnets in varying magnetic states. Application of an external magnetic field shifts the system between states, with a corresponding change in the ferromagnetic resonance (FMR) spectrum.Gartside_2022 Here we report the DUT-8 reservoir (bottom), where the positions of columnar pillars shift on adsorption of different guest species within framework pores. The configurational rearrangement leads to differences in the diffuse features of the X-ray diffraction pattern.
• Figure 2: Correlated disorder in DUT-8. (a) The framework structure of DUT-8 is assembled from dabco-linked nickel paddlewheels (shown as columns) connected by ndc linkers (shown as flexed tubes). Columns are arranged on a regular square lattice but at different relative heights: the ndc asymmetry shifts neighbouring columns. On traversing a square channel, one must encounter exactly two 'up' shifts and two 'down' shifts. (b) Jigsaw-tile representation of the six possible two-up-two-down channel arrangements, with $C_{2h}$ and $D_{2d}$ geometries shown in colour and grayscale, respectively. All DUT-8 configurations correspond to sensible jigsaw-tile arrangements. (c) Two-dimensional projection of the DUT-8 configurational landscape with local order parameters $(\phi,\eta)$. The boundary states are ordered; disordered arrangements are contained within the interior of the map. Interchanging the adsorbate in DUT-8 between DCM and DMF causes the system to traverse the configurational landscape, with a concomitant change in the X-ray diffraction pattern (data taken from Ref. Ehrling_2021).
• Figure 3: Classification tasks with a DUT-8 reservoir. (a) Encoding of $(\phi,\eta)$ coordinates is carried out in three steps. First, a representative DUT-8 configuration is generated; second, the corresponding X-ray diffraction pattern is calculated; and third, a region of this diffraction pattern containing diffuse scattering is discretised to form a 27-channel readout. (b) Classification tasks involve using these readouts to train a single-layer linear support vector classifier against a range of target functions. Test results for each function are shown here, where coloured circles denote correct classification of different integral values. Incorrect classifications (white circles) tend to occur at the decision boundaries. Classification accuracy is always better than that for linear regression from input data (bar charts).
• Figure 4: Time-series transformations using a DUT-8 reservoir. To emulate the effect of changing adsorbate, the reservoir is subjected to a sinusoidally-varying effective chemical field. Monte Carlo simulations were carried out at each time step, driven by the Hamiltonian \ref{['hamil']} and carrying forward configurations from step to step. Note that the DUT-8 state is history dependent: we illustrate this point with representative configurations (in both columnar and jigsaw representations) for two timesteps with equivalent applied fields (left and middle). On reversing the sign of the field, the system is driven towards low-$\eta$ configurations as observed experimentally on replacing DMF with DCM. (b) Representative symmetric (left) and asymmetric (right) time-series transformation test results. The target functions are shown as red lines and the machine-learned data as black circles.