From Digital to Physical Reservoir Computing: Co-Optimizing Soft Robotic Reservoirs via Dynamics Matching

Soft robotic substrates are promising for Physical Reservoir Computing (PRC) because their compliant nonlinear dynamics can provide temporal memory, high-dimensional state transformations, and efficient inference. However, physical reservoirs are often adopted as-is rather than pretrained or co-optimized, potentially limiting soft robotic PRC performance relative to digital reservoirs. We investigate whether a physical reservoir can instead be pretrained against high-performing digital reference dynamics. Our formulation jointly optimizes physical parameters, a diffeomorphic physical-reference state map, and feedforward-feedback control using a differentiable physical model and an acceleration-level equation-error objective that avoids temporal integration. As a proof of concept, we instantiate the formulation with simulated soft robots, a Random Oscillators Network (RON) reference, and parallel multi-start gradient descent. We evaluate the optimized reservoirs on classification (sMNIST and ADIAC) and forecasting (Mackey-Glass and Lorenz96) tasks across four reservoir dimensions. Compared with unoptimized soft robot reservoirs, the optimized reservoirs achieve a mean relative improvement of 33.7% across all tasks and datasets, while remaining close to the digital reference. These results demonstrate the feasibility of dynamics-level co-optimization for the simulated soft robotic reservoirs considered here.

Effective Training Principles of Physical Reservoirs

Reservoir computers benefit from the inherent complexity of optical phenomena, which provide rich, often nonlinear dynamics. However, training directly on the reservoir's output renders the system prone to overfitting and computationally inefficient during the training phase. In this work, we investigate strategies to mitigate overfitting and reduce computational overhead through output pruning and regularization. We compare loss-minimizing search methods (Equal Search and Branch and Bound) against an output-oriented statistical filtering approach (Variance Filter) and random pruning, highlighting advantages and disadvantages of each approach and the overall importance of informed reservoir output sampling, particularly for a shrinking latent space. We further demonstrate that enforcing readout selection across the full output spectrum improves performance, especially for non-iterative methods. Additionally, we examine L1 and L2 regularization techniques (LASSO and ridge regression), both of which significantly enhance performance on highly nonlinear tasks such as the Spiral Benchmark. While our methods are of general use, results are obtained from and discussed exemplarily for a nonlinear fiber-optical extreme learning machine. Overall, this study provides a deep analysis of the reservoirs' hidden-layer filtering mechanisms and the output-layer training, enabling optimized performance in physical reservoir computing systems.