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Echo-state networks are simple models of discrete dynamical systems driven by a time series. By selecting network parameters such that the dynamics of the network is contractive, characterized by a negative maximal Lyapunov exponent, the…
The distribution of a neural network's latent representations has been successfully used to detect out-of-distribution (OOD) data. This work investigates whether this distribution moreover correlates with a model's epistemic uncertainty,…
Echo State Networks (ESNs) are recurrent neural networks usually employed for modeling nonlinear dynamic systems with relatively ease of training. By incorporating physical laws into the training of ESNs, Physics-Informed ESNs (PI-ESNs)…
Each year a growing number of wind farms are being added to power grids to generate electricity. The power curve of a wind turbine, which exhibits the relationship between generated power and wind speed, plays a major role in assessing the…
Maximum entropy principle (MEP) offers an effective and unbiased approach to inferring unknown probability distributions when faced with incomplete information, while neural networks provide the flexibility to learn complex distributions…
Due to the inherent aleatory uncertainties in renewable generators, the reliability/adequacy assessments of distributed generation (DG) systems have been particularly focused on the probabilistic modeling of random behaviors, given…
Polynomial chaos based methods enable the efficient computation of output variability in the presence of input uncertainty in complex models. Consequently, they have been used extensively for propagating uncertainty through a wide variety…
Recurrent neural network based solutions are increasingly being used in the analysis of longitudinal Electronic Health Record data. However, most works focus on prediction accuracy and neglect prediction uncertainty. We propose Deep Kernel…
The increase in renewable energy sources (RESs), like wind or solar power, results in growing uncertainty also in transmission grids. This affects grid stability through fluctuating energy supply and an increased probability of overloaded…
Chance-constrained motion planning requires uncertainty in dynamics to be propagated into uncertainty in state. When nonlinear models are used, Gaussian assumptions on the state distribution do not necessarily apply since almost all random…
We propose a feed-forward inference method applicable to belief and neural networks. In a belief network, the method estimates an approximate factorized posterior of all hidden units given the input. In neural networks the method propagates…
The Wasserstein distance has emerged as a key metric to quantify distances between probability distributions, with applications in various fields, including machine learning, control theory, decision theory, and biological systems.…
As a neural network's depth increases, it can improve generalization performance. However, training deep networks is challenging due to gradient and signal propagation issues. To address these challenges, extensive theoretical research and…
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…
We report about probabilistic likelihood estimates that are performed on time series using an echo state network with orthogonal recurrent connectivity. The results from tests using synthetic stochastic input time series with temporal…
This paper presents a novel Wasserstein distributionally robust control and state estimation algorithm for partially observable linear stochastic systems, where the probability distributions of disturbances and measurement noises are…
The lack of transparency of Deep Neural Networks continues to be a limitation that severely undermines their reliability and usage in high-stakes applications. Promising approaches to overcome such limitations are Prototype-Based…
This paper presents a tensor-recovery method to solve probabilistic power flow problems. Our approach generates a high-dimensional and sparse generalized polynomial-chaos expansion that provides useful statistical information. The result…
Many real-world systems are characterized by stochastic dynamical rules where a complex network of interactions among individual elements probabilistically determines their state. Even with full knowledge of the network structure and of the…
Conventional predictive Artificial Neural Networks (ANNs) commonly employ deterministic weight matrices; therefore, their prediction is a point estimate. Such a deterministic nature in ANNs causes the limitations of using ANNs for medical…