Mirko Goldmann (IFISC)
In the three years within the Post-Digital project, Mirko’s work culminated so far in two published and one accepted peer-reviewed articles and several further publications in preparation. In addition, Mirko co-authored three conference proceedings, one of which won the “Best student paper award”at the prestigious NOLTA 2023 Conference, and he gave several oral presentations at international Conferences His first peer-reviewd publication, ‘Learn one size to infer all: Exploiting translational symmetries in delay-dynamical and spatiotemporal systems using scalable neural networks,’ appeared in Physical Review E in 2021. This paper demonstrates how symmetries in a physical system can be exploited to infer from one dataset a whole bifurcation scenario of unseen dynamical properties of that system. The approach bridges unconventional computing, machine learning, and physics, and demonstrates the development of reservoir computing systems that can generalize effectively to new unseen data, even for changing the delay time of the dynamical system, which is a key control parameter. They were able to demonstrate these abilities using delay echo state networks trained on a single time series of the Mackey-Glass system. As shown in the Fig.6, the once trained delay echo state network can infer unseen bifurcation diagrams verifying its strong generalization abilities.
Figure 6: Two-dimensional projection (x-axis y(t), y-axis y(t-τ)) of attractors of the chaotic Mackey-Glass system for different delay lengths in a), b), c), & d). e) Bifurcation diagram generated using the Mackey-Glass delay system. Inferred attractors by the delayed echo state network trained on a single example of the Mackey-Glass system with τ=100 shown in f), g), h) & i). j) Bifurcation diagram inferred by the dESN trained on data of a Mackey-Glass system with a delay of τ=100.
The second peer-reviewed published paper, co-authored by Mirko Goldmann explores whether the dynamical regimes of operation of a system can be extended beyond the fixed point regime (without input) and still be suitable for efficient computations using the delay-based reservoir computing paradigm. So far, reservoir computing has been based on fixed-point dynamics for the undriven reservoir. The study, however, reveals that under certain conditions, other dynamical regimes like bistable and periodic oscillating regimes can also facilitate reservoir computing. Notably, the oscillation regime showed superior prediction accuracy in various time series prediction tasks. Published as a featured article in the journal Chaos, this work suggests that computing within a dynamical system can occur under diverse dynamics, influencing the conditions for the physical implementation of computations.
Figure 7: Motion modeling based on the MoCap dataset. The RNN was trained on the temporal patterns of running and walking. In the autoregressive mode it can retrieve both motions as shown in a) and c). Due to enforcing the conceptor based bottleneck during training the RNN and by plugging in a linearly interpolated conceptor it is able to generate an intermediate pattern such as shown in b). Each row depicts a single period of each motion pattern at the same sampling rate and with equal horizontal spacing. |
Additionally, Mirko’s secondments in Groningen and Besancon were enriching experiences in these three years with Post-Digital. During his time in Groningen, he further delved into the versatile field of unconventional computing and the intricate theory of digital computing. Engaging in numerous discussions about the challenges of unconventional computing with members of the MINDS group enhanced his perception and approach to research in this area. This secondment resulted in fruitful collaborations with two ESRs, Guillaume Pourcel and Steve Abreu,. Together, they recently developed the Conceptor-aided Recurrent Autoencoder (CARAE), a novel algorithm for dynamical systems. CARAE efficiently and controllably learns from two distinct motion patterns—walking and running—to generate intermediate motions like jogging. Such interpolation of complex temporal patterns was previously only achieved using extensive usage of data and training time. Accordingly, their method reduced the required amount of training examples and compute time/power.
Mirko’s secondment in Besancon in collaboration with Anas Skalli was dedicated to the hardware implementation of a fully trainable photonic neural network, a concept originally co-developed by partners Besançon and CSIC. In the mornings, they focused on developing learning algorithms, which they tested and evaluated through simulations. Their findings indicate that training all parameters of a network significantly enhances its computational capabilities, more so than merely increasing the network’s size while relying on the reservoir computing regime that only trains output weights. This discovery inspired the ESRs to focus on the optimization of unconventional photonic substrates for machine learning tasks. In the afternoons, the ESRs’ work shifted to hands-on hardware implementation in the laboratory. This blend of simulation and experimental work underscored the challenges inherent in moving from numerical models to real-world applications. Furthermore, this experience greatly increased Mirko’s interest in model-free optimization, a key component for developing new autonomous, high-performance photonic networks.
In summary, time in Groningen steered Mirko’s focus toward the theoretical dimensions of physical computing, allowing him to explore its diverse aspects. Conversely, experience in Besancon illuminated the challenges and potential of hardware implementations. Building on both of these experiences, Mirko moved to working on the design of a new learning algorithm with promising capabilities in model-free optimization. Finally, these experiences, together with his substantial and fruitful work at IFISC collectively expanded his horizon, led to new ideas, and significantly influenced his research. Notably, the discussions and relationships Mirko formed with colleagues in the research groups of the Post-Digital are expected to persist well beyond the Post-Digital project itself.