Understanding the behavior and evolution of a dynamical many-body system by analyzing patterns in their experimentally captured images is a promising method relevant for a variety of living and non-living self-assembled systems. The arrays of moving liquid crystal skyrmions studied here are a representative example of hierarchically organized materials that exhibit complex spatiotemporal dynamics driven by multiscale processes. Joint geometric and topological data analysis (TDA) offers a powerful framework for investigating such systems by capturing the underlying structure of the data at multiple scales. In the TDA approach, we introduce the $Ψ$-function, a robust numerical topological descriptor related to both the spatiotemporal changes in the size and shape of individual topological solitons and the emergence of regions with their different spatial organization. The geometric method based on the analysis of vector fields generated from images of skyrmion ensembles offers insights into the nonlinear physical mechanisms of the system's response to external stimuli and provides a basis for comparison with theoretical predictions. The methodology presented here is very general and can provide a characterization of system behavior both at the level of individual pattern-forming agents and as a whole, allowing one to relate the results of image data analysis to processes occurring in a physical, chemical, or biological system in the real world.

We present a metaheuristic conditional neural-network-based method aimed at identifying physically interesting metastable states in a potential energy surface of high rugosity. To demonstrate how this method works, we identify and analyze spin textures with topological charge $Q$ ranging from 1 to $-13$ (where antiskyrmions have $Q<0$) in the Pd/Fe/Ir(111) system, which we model using a classical atomistic spin Hamiltonian based on parameters computed from density functional theory. To facilitate the harvest of relevant spin textures, we make use of the newly developed Segment Anything Model (SAM). Spin textures with $Q$ ranging from $-3$ to $-6$ are further analyzed using finite-temperature spin-dynamics simulations. We observe that for temperatures up to around 20\,K, lifetimes longer than 200\,ps are predicted, and that when these textures decay, new topological spin textures are formed. We also find that the relative stability of the spin textures depend linearly on the topological charge, but only when comparing the most stable antiskyrmions for each topological charge. In general, the number of holes (i.e., non-self-intersecting curves that define closed domain walls in the structure) in the spin texture is an important predictor of stability -- the more holes, the less stable is the texture. Methods for systematic identification and characterization of complex metastable skyrmionic textures -- such as the one demonstrated here -- are highly relevant for advancements in the field of topological spintronics.

ABSTRACT: In this study, we have shown autonomous long-term prediction with a spintronic physical reservoir. Due to the short-term memory property of the magnetization dynamics, non-linearity arises in the reservoir states which could be used for long-term prediction tasks using simple linear regression for online training. During the prediction stage, the output is directly fed to the input of the reservoir for autonomous prediction. We employ our proposed reservoir for the modeling of the chaotic time series such as Mackey-Glass and dynamic time-series data, such as household building energy loads. Since only the last layer of a RC needs to be trained with linear regression, it is well suited for learning in real time on edge devices. Here we show that a skyrmion based magnetic tunnel junction can potentially be used as a prototypical RC but any nanomagnetic magnetic tunnel junction with nonlinear magnetization behavior can implement such a RC. By comparing our spintronic physical RC approach with state-of-the-art energy load forecasting algorithms, such as LSTMs and RNNs, we conclude that the proposed framework presents good performance in achieving high predictions accuracy, while also requiring low memory and energy both of which are at a premium in hardware resource and power constrained edge applications. Further, the proposed approach is shown to require very small training datasets and at the same time being at least 16X energy efficient compared to the state-of-the-art sequence to sequence LSTM for accurate household load predictions. I. INTRODUCTION Recurrent neural networks (RNNs) [1,2] are shown to be more suitable in temporal data processing tasks than the traditional feedforward neural networks (FNNs) because of the recurrent connections among constituent neurons. However, RNNs often suffers from vanishing and exploding gradients problem due to the long-term dependencies that could arise in the recurrent layers. To circumvent these issues variations of RNN is proposed, i.e., long short-term memory (LSTM) [3] and reservoir computing (RC) [4,5].

ABSTRACT One of the most important magnetic spin structure is the topologically stabilised skyrmion quasi-particle. Its interesting physical properties make them candidates for memory and efficient neuromorphic computation schemes. For the device operation, detection of the position, shape, and size of skyrmions is required and magnetic imaging is typically employed. A frequently used technique is magneto-optical Kerr microscopy where depending on the sample's material composition, temperature, material growing procedures, etc., the measurements suffer from noise, low-contrast, intensity gradients, or other optical artifacts. Conventional image analysis packages require manual treatment, and a more automatic solution is required. We report a convolutional neural network specifically designed for segmentation problems to detect the position and shape of skyrmions in our measurements. The network is tuned using selected techniques to optimize predictions and in particular the number of detected classes is found to govern the performance. The results of this study shows that a well-trained network is a viable method of automating data pre-processing in magnetic microscopy. The approach is easily extendable to other spin structures and other magnetic imaging methods. INTRODUCTION In the last decade, magnetic quasiparticles [1], [2] have raised the interest of researchers due to their interesting properties and their potential applicability in next-generation memory and neuromorphic devices [2] In particular, skyrmions in magnetic thin-films are under investigation due to their topological stabilization, their small size, and their ability to be easily manipulated by spin currents [4], [5].

Physical reservoir computing is a computational framework that implements spatiotemporal information processing directly within physical systems. By exciting nonlinear dynamical systems and creating linear models from their state, we can create highly energy-efficient devices capable of solving machine learning tasks without building a modular system consisting of millions of neurons interconnected by synapses. To act as an effective reservoir, the chosen dynamical system must have two desirable properties: nonlinearity and memory. We present task agnostic spatial measures to locally measure both of these properties and exemplify them for a specific physical reservoir based upon magnetic skyrmion textures. In contrast to typical reservoir computing metrics, these metrics can be resolved spatially and in parallel from a single input signal, allowing for efficient parameter search to design efficient and high-performance reservoirs. Additionally, we show the natural trade-off between memory capacity and nonlinearity in our reservoir's behaviour, both locally and globally. Finally, by balancing the memory and nonlinearity in a reservoir, we can improve its performance for specific tasks.

Abstract: Brain-computer interfaces (BCIs), invasive or non-invasive, have projected unparalleled vision and promise for assisting patients in need to better their interaction with the surroundings. Inspired by the BCI-based rehabilitation technologies for nerve-system impairments and amputation, we propose an electromagnetic brain-computer-metasurface (EBCM) paradigm, regulated by human's cognition by brain signals directly and non-invasively. We experimentally show that our EBCM platform can translate human's mind from evoked potentials of P300-based electroencephalography to digital coding information in the electromagnetic domain non-invasively, which can be further processed and transported by an information metasurface in automated and wireless fashions. Directly wireless communications of the human minds are performed between two EBCM operators with accurate text transmissions. Abstract: How to identify and characterize functional brain networks (BN) is fundamental to gain system-level insights into the mechanisms of brain organizational architecture. Current functional magnetic resonance (fMRI) analysis highly relies on prior knowledge of specific patterns in either spatial (e.g., resting-state network) or temporal (e.g., task stimulus) domain.