Reservoir computing has become immensely popular for exploiting physical systems for computation. A multitude of physical reservoirs have been demonstrated, ranging from assembles of nanomagnets to living cultures of neurons. Unlike abstract software reservoirs, physical reservoirs are subject to spatial constraints which restricts the possible reservoir topologies. Here, we investigate lattice reservoirs, where nodes are placed on a regular lattice which defines the reservoir topology and its weights. Despite their simple regular structure, lattice reservoirs perform surprisingly well, in some cases outcompeting classical Echo State Networks. A key finding is the need for directed edges to facilitate information flow within the reservoir, highlighting the importance of symmetry breaking in physical reservoirs. We take advantage of the spatial nature of lattice reservoirs to discover key computational structures within, revealing what these reservoirs are actually doing. Lattice reservoirs bridge the gap between physics and computation, providing invaluable insight for the design and understanding of physical reservoirs.

Artificial spin ice (ASI) are systems of coupled nanomagnets arranged on a 2D lattice. ASIs are promising computing substrates due to the rich variety of emergent behavior, accompanied by considerable control and flexibility. Computational models may exploit the small-scale dynamics of the individual elements, or large-scale emergent behavior of the resulting metamaterial. We investigate the computational capabilities of “pinwheel” ASI, whose emergent ferromagnetic patterns can be observed at different scales. Within a reservoir computing framework, we examine how key system parameters affect performance using well-established reservoir quality metrics. As reservoir output, we consider system state at different granularities, ranging from individual magnets to the collective state of multiple magnets. Our results show that pinwheel ASI exhibits excellent computing capacity, including evidence of fading memory. Interestingly, a wide range of output granularities result in good performance, offering new insights into the scalability and robustness of reservoirs based on self-organized collective behavior. The apparent flexibility in output granularity show that ASIs have computational properties at different abstraction levels, from the small-scale dynamics of simple elements, to the large-scale spatial patterns of the metamaterial.

We explore artificial spin ice (ASI) as a substrate for material computation . ASI consists of large numbers of nanomagnets arranged in a 2D lattice. Local interactions between the magnets gives rise to a range of complex collective behavior. The ferromagnets form large networks of nonlinear nodes, which in many ways resemble artificial neural networks. In this work, we investigate key computational properties of ASI through micromagnetic simulations. Our nanomagnetic system exhibits a large number of reachable stable states and a wide range of available dynamics when perturbed by an external magnetic field. Furthermore, we find that the system is able to store and process temporal input patterns. The emergent behavior is highly tunable by varying the parameters of the external field. Our findings highlight ASI as a very promising substrate for in-materio computation at the nanoscale.

Reservoir Computing has been highlighted as a promising methodology to perform computation in dynamical systems. This makes Reservoir Computing particularly interesting for exploiting physical systems directly as computing substrates, where the computation happens “for free” in the rich physical domain. In this work we consider a simple chaotic circuit as a reservoir: the Driven Chua’s circuit. Its rich variety of available dynamics makes it versatile as a reservoir. At the same time, its simplicity offers insight into what physical properties can be useful for computation. We demonstrate both through simulation and in-circuit experiments, that such a simple circuit can be readily exploited for computation. Our results show excellent performance on two non-temporal tasks. The fact that such a simple nonlinear circuit can be used, suggests that a wide variety of physical systems can be viewed as potential reservoirs.