OpenPRC: A Unified Open-Source Framework for Physics-to-Task Evaluation in Physical Reservoir Computing
Authors: Yogesh Phalak, Wen Sin Lor, Apoorva Khairnar, Benjamin Jantzen, Noel Naughton, Suyi Li
Organizations: Department of Mechanical Engineering, Virginia Tech, Blacksburg, VA, USA · Department of Philosophy, Virginia Tech, Blacksburg, VA, USA · Department of Computer Science, Virginia Tech, Blacksburg, VA, USA
Physical Reservoir Computing (PRC) leverages the intrinsic nonlinear dynamics of physical substrates, mechanical, optical, spintronic, and beyond, as fixed computational reservoirs, offering a compelling paradigm for energy-efficient and embodied machine learning. However, the practical workflow for developing and evaluating PRC systems remains fragmented: existing tools typically address only isolated parts of the pipeline, such as substrate-specific simulation, digital reservoir benchmarking, or readout training. What is missing is a unified framework that can represent both high-fidelity simulated trajectories and real experimental measurements through the same data interface, enabling reproducible evaluation, analysis, and physics-aware optimization across substrates and data sources. We present OpenPRC, an open-source Python framework that fills this gap through a schema-driven physics-to-task pipeline built around five modules: a GPU-accelerated hybrid RK4-PBD physics engine (demlat), a video-based experimental ingestion layer (openprc.vision), a modular learning layer (reservoir), information-theoretic analysis and benchmarking tools (analysis), and physics-aware optimization (optimize). A universal HDF5 schema enforces reproducibility and interoperability, allowing GPU-simulated and experimentally acquired trajectories to enter the same downstream workflow without modification. Demonstrated capabilities include simulations of Origami tessellations, video-based trajectory extraction from a physical reservoir, and a common interface for standardized PRC benchmarking, correlation diagnostics, and capacity analysis. The longer-term vision is to serve as a standardizing layer for the PRC community, compatible with external physics engines including PyBullet, PyElastica, and MERLIN.
Figures & tables
Tool
Primary scope
Physics sim.
Experimental data
RC analysis
Optimization
MERLIN/MERLIN2
Non-rigid origami mechanics
✓
×
×
limited
PyElastica
Cosserat rod simulation
✓
×
×
limited
ReservoirPy
Digital RC benchmarking
×
×
✓
limited
ORC
Digital RC in JAX
×
×
✓
limited
PRCpy
PRC-oriented data workflow
×
✓
✓
×
OpenPRC
Unified physical PRC workflow
✓
✓
✓
✓
Table 1: Representative software tools related to PRC and their scope.
Figure 1: The OpenPRC pipeline. Both demlat and openprc.vision produce simulation.h5 , making simulated and experimental trajectories interchangeable to all downstream modules. The optimize module closes the loop back to demlat for iterative design optimization.
File
Producer
Consumers
Key content
geometry.h5
User / optimize
demlat
Node coordinates [N×3] , masses [N] , bar connectivity [M×2] , hinge connectivity [K×4] , stiffness, rest lengths, damping
signals.h5
User / optimize
demlat
Named time series [Tu] or [Tu×d] ; signal timestep
Figure 2: Bar-hinge element showing the four-node hinge configuration. Node Pi interacts with its neighbours through axial bar forces and dihedral hinge torques, with angle gradients computed from the normals of the two adjacent faces.
Figure 3: Versatile applications of the bar-hinge model in demlat : soft reservoir network (mass-spring lattice under dynamic actuation), Miura-ori tessellation, kirigami structure with geometric cuts, k-cone origami, bistable slab, and tapered spring. Strain is visualized using a cool–warm colormap.
Figure 4: DEMLAT Player visualizing a Miura-ori simulation. Faces are colored by axial bar strain (cool–warm colormap), nodes and bars are overlaid, and node trajectory trails show the dynamic response under base excitation. The player is built on PiViz [ 28 ] , a high-performance GPU-accelerated visualization library developed alongside OpenPRC.
Figure 5: Output of the openprc.vision pipeline applied to a physical Miura-ori reservoir [ 11 ] . Left: SIFT keypoints detected on the reference frame, with feature indices and response circles overlaid. Right: KLT tracking in progress, showing per-feature trajectory trails and forward-backward status indicators. The status bar at the bottom encodes per-feature tracking health across the frame window.
Figure 6: Representative NARMA2 benchmark result for the Miura-ori reservoir. The target is generated from the normalized base-excitation signal and the prediction is obtained from the trained readout over the evaluation window.
Figure 7: Memory-benchmark result for the Miura-ori reservoir under the truncated Dambre-style IPC analysis. Linear and nonlinear capacity contributions are resolved across delayed input components.
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.
Nicola Visentin, Maximilian Stölzle, Mariano Ramírez Montero +3
Department of Cognitive Robotics, Delft University of Technology, Delft, The Netherlands · Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, MA, USA · Department of Mechanical Engineering, Politecnico di Milano, Milan, Italy
OpenReservoirComputing (ORC) is a Python library for reservoir computing (RC) written in JAX (Bradbury et al. 2018) and Equinox (Kidger and Garcia 2021). JAX is a Python library for high-performance numerical computing that enables automatic differentiation, just-in-time (JIT) compilation, and GPU/TPU acceleration, while Equinox is a neural network framework for JAX. RC is a form of machine learning that functions by lifting a low-dimensional sequence or signal into a high-dimensional dynamical system and training a simple, linear readout layer from the high-dimensional dynamics back to a lower-dimensional quantity of interest. The most common application of RC is time-series forecasting, where the goal is to predict a signal's future evolution. RC has achieved state-of-the-art performance on this task, particularly when applied to chaotic dynamical systems. In addition, RC approaches can be adapted to perform classification and control tasks. ORC provides both modular components for building custom RC models and built-in models for forecasting, classification, and control. By building on JAX and Equinox, ORC offers GPU acceleration, JIT compilation, and automatic vectorization. These capabilities make prototyping new models faster and enable larger and more powerful reservoir architectures. End-to-end differentiability also enables seamless integration with other deep learning models built with Equinox.
Jan Williams, Dima Tretiak, Steven L. Brunton +2
Department of Mechanical Engineering, University of Washington, USA · Department of Applied Mathematics, University of Washington, USA · Department of Electrical and Computer Engineering, University of Washington, USA +1
Reservoir computing (RC) is a computational framework known for its training efficiency, making it ideal for physical hardware implementations. However, realizing the complex interconnectivity of traditional reservoirs in physical systems remains a significant challenge. This paper proposes a physical RC scheme inspired by the biological vestibular system. To overcome hardware complexity, we introduce a designed uncoupled topology and demonstrate that it achieves performance comparable to fully coupled networks. We theoretically analyze the difference between these topologies by deriving a memory capacity formula for linear reservoirs, identifying specific conditions where both configurations yield equivalent memory. These analytical results are demonstrated to approximately hold for nonlinear reservoir systems. Furthermore, we systematically examine the impact of reservoir size on predictive statistics and memory capacity. Our findings suggest that uncoupled reservoir architectures offer a mathematically sound and practically feasible pathway for efficient physical reservoir computing.
Smita Deb, Shirin Panahi, Mulugeta Haile +1
School of Electrical, Computer, and Energy Engineering, Arizona State University, Tempe, AZ 85287, USA · Department of Electrical and Computer Engineering, Colorado State University, Fort Collins, CO 80523, USA · DEVCOM Army Research Office, 6340 Rodman Road, Aberdeen Proving Ground, MD 21005-5069, USA +1