Related papers: Physics-Informed Echo State Networks
State estimation is highly critical for accurately observing the dynamic behavior of the power grids and minimizing risks from cyber threats. However, existing state estimation methods encounter challenges in accurately capturing power…
Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve…
System identification under unknown external excitation is an inherently ill-posed problem, typically requiring additional knowledge or simplifying assumptions to enable reliable state and parameter estimation. The difficulty of the problem…
Echo State Networks (ESN) are versatile recurrent neural network models in which the hidden layer remains unaltered during training. Interactions among nodes of this static backbone produce diverse representations of the given stimuli that…
In this paper we introduce a new framework to train an Echo State Network to predict real valued time-series. The method consists in projecting the output of the internal layer of the network on a space with lower dimensionality, before…
Echo State Networks (ESNs) are a particular type of untrained Recurrent Neural Networks (RNNs) within the Reservoir Computing (RC) framework, popular for their fast and efficient learning. However, traditional ESNs often struggle with…
Self-induced stochastic resonance (SISR) is the emergence of coherent oscillations in slow-fast excitable systems driven solely by noise, without external periodic forcing or proximity to a bifurcation. This work presents a physics-informed…
A recurrent neural network (RNN) possesses the echo state property (ESP) if, for a given input sequence, it ``forgets'' any internal states of the driven (nonautonomous) system and asymptotically follows a unique, possibly complex…
Deep learning models trained on finite data lack a complete understanding of the physical world. On the other hand, physics-informed neural networks (PINNs) are infused with such knowledge through the incorporation of mathematically…
In this work, we present a deep neural network architecture that can efficiently approximate classical elasto-plastic constitutive relations. The network is enriched with crucial physics aspects of classical elasto-plasticity, including…
Drawing on ergodic theory, we introduce a novel training method for machine learning based forecasting methods for chaotic dynamical systems. The training enforces dynamical invariants--such as the Lyapunov exponent spectrum and fractal…
In recent years, scientific machine learning, particularly physic-informed neural networks (PINNs), has introduced new innovative methods to understanding the differential equations that describe power system dynamics, providing a more…
Power flow analysis plays a critical role in the control and operation of power systems. The high computational burden of traditional solution methods led to a shift towards data-driven approaches, exploiting the availability of digital…
Stock return prediction is a problem that has received much attention in the finance literature. In recent years, sophisticated machine learning methods have been shown to perform significantly better than ''classical'' prediction…
A significant advancement in Neural Network (NN) research is the integration of domain-specific knowledge through custom loss functions. This approach addresses a crucial challenge: how can models utilize physics or mathematical principles…
Echo state networks represent a special type of recurrent neural networks. Recent papers stated that the echo state networks maximize their computational performance on the transition between order and chaos, the so-called edge of chaos.…
The rapid growth of research in exploiting machine learning to predict chaotic systems has revived a recent interest in Hamiltonian Neural Networks (HNNs) with physical constraints defined by the Hamilton's equations of motion, which…
In control design most control strategies are model-based and require accurate models to be applied successfully. Due to simplifications and the model-reality-gap physics-derived models frequently exhibit deviations from real-world-systems.…
General nonlinear continuous-time systems are considered for which its state is estimated via a packet-based communication network. We assume that the system has multiple sensor nodes, affected by measurement noise, which can transmit at…
Understanding real-world dynamical phenomena remains a challenging task. Across various scientific disciplines, machine learning has advanced as the go-to technology to analyze nonlinear dynamical systems, identify patterns in big data, and…