  Reservoir computing is a brain-inspired machine learning framework for
processing temporal data by mapping inputs into high-dimensional spaces.
Physical reservoir computers (PRCs) leverage native fading memory and
nonlinearity in physical substrates, including atomic switches, photonics,
volatile memristors, and, recently, memcapacitors, to achieve efficient
high-dimensional mapping. Traditional PRCs often consist of homogeneous device
arrays, which rely on input encoding methods and large stochastic
device-to-device variations for increased nonlinearity and high-dimensional
mapping. These approaches incur high pre-processing costs and restrict
real-time deployment. Here, we introduce a novel heterogeneous
memcapacitor-based PRC that exploits internal voltage offsets to enable both
monotonic and non-monotonic input-state correlations crucial for efficient
high-dimensional transformations. We demonstrate our approach's efficacy by
predicting a second-order nonlinear dynamical system with an extremely low
prediction error (0.00018). Additionally, we predict a chaotic H\'enon map,
achieving a low normalized root mean square error (0.080). Unlike previous
PRCs, such errors are achieved without input encoding methods, underscoring the
power of distinct input-state correlations. Most importantly, we generalize our
approach to other neuromorphic devices that lack inherent voltage offsets using
externally applied offsets to realize various input-state correlations. Our
approach and unprecedented performance are a major milestone towards
high-performance full in-materia PRCs.
