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

arXiv: https://arxiv.org/abs/2608.00484 · HTML: https://mlsanity.com/paper/2608.00484/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 51 references that are in the map.
- First posted on arXiv 1 Aug 2026.

## Builds on (most cited first, 10 of 10)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [The UCR Time Series Archive](https://mlsanity.com/paper/1810.07758/) (2018)
- [On Neural Differential Equations](https://mlsanity.com/paper/2202.02435/) (2022)
- [A Simple Way to Initialize Recurrent Networks of Rectified Linear Units](https://mlsanity.com/paper/1504.00941/) (2015)
- [Physical reservoir computing -- An introductory perspective](https://mlsanity.com/paper/2005.00992/) (2020)
- [full-FORCE: A Target-Based Method for Training Recurrent Networks](https://mlsanity.com/paper/1710.03070/) (2017)
- [Harnessing disordered quantum dynamics for machine learning](https://mlsanity.com/paper/1602.08159/) (2016)
- [Discrete Cosserat Approach for Multi-Section Soft Robots Dynamics](https://mlsanity.com/paper/1702.03660/) (2017)
- [Soft yet Effective Robots via Holistic Co-Design](https://mlsanity.com/paper/2505.03761/) (2025)

## Abstract (arXiv)

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.